Master class with Alain Aspect

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Master class with Alain Aspect
Hanbury Brown and Twiss and other atom-atom correlations from photon to atom quantum optics
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Fifty years ago, R. Hanbury Brown and R.Q. Twiss, invented a new method to measure the angular diameter of stars, based on the observation of correlations in light. The analysis of their experiment in term of photons prompted hot discussions, and eventually led to the development of modern quantum optics, based on photon-photon correlation experiments. Similar quantum correlations can be observed with bosonic and fermionic atoms. I will present such experiments, after recalling the significance of the HBT landmark experiment.
Keywords quantum optics
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maybe you that that in order to be sure you go you know this Gold Oak candidate in 45 minutes to 1 hour and a half to 1 stores and after I'm not joking I mean we could go on details soldiers give the general ideas of Morrison on and details and so what did the idea of this masterclass what do you expect well 1st how many of you are doing a quantum optics OK How many of you are working with scores the items the same physically fit so well the other people what are you doing what is your subject OK and what OK at the same time None of photonics for the next round of Fulton Inc OK for makes means novel Tom OK we agree and the Photonics Mintz collected by these real Photonics will receive OK maybe we should be in the light grows to the screen can you try to touch the knobs until something happens the idea would be to use 1 it's for
you OK for me is no problem at the it's for you maybe we can put Italy the higher another walk like that I an experiment is too and how it's probably better write the Tokyo so did they chose this
objected when they asked me you must crossing the section of the act of the so it's all physicist would come here to this conference of so the reason why I chose in this subject it's because the 2 it's about 2 subjects which have been very important in my era scientific life I 1st started working on quantum optics and then I moved to complain about the arms and more recently using the rhetorical about but I revisit some fundamental phenomenon of quantum optics revisited with atoms so I tried to follow the analogy between photons and penitents and the as you will see uh various analogy but a resourceful differences and I think about it is what makes things really interested so I have to admit about somebody Rahman
please and although correlations and we are going to review it would be tougher so quantum optics and I have to ask those enabled the have a nice often seemed to correct it's a piece of plastic a right to cook the age you or something like that because I I I would do an experiment and 1 of many to prepare my experiment very good tennis was nice as maybe this is just number at the United States thank you remember to do to claim it back otherwise I would put it in my book at the next time I go to an airport they we put me in jail it would work would probably work so it
did you the about the history of quantum optics in order to understand why he should be somebody very East experiment was so important was held of the Emerine run tweezers experiment will not always what is around into his experience looking good so I'm not going to to waste my time because I think it's very very important to understand that it's OK to me that I'm just arriving from Paris I had my students is morning there was giving lectures morning in Paris all rather than biodiesel OK and by the way that people are really interested in quantum optics I just that diocese will come 1 of the authors of this book and I am very pleased with the book I mean
I'm very pleased we how coverage University Press has made a very nice book we use 1 of these you know Didier so that they can find them at the Virgin affordable cultivate it's not expensive these we negotiated with them you you you get these big book of 800 pages 450 EUR or something like that so if you're really interested in quantum optics you may be interested in that it has a lot of things I will be using today is going to be in this book and a lot of things so we'll be seeing tomorrow nite will be in his book OK it's not working yes it is work so what I'm willing to bet
you tonight 1st explain what was the yammering run and we experiments and why it was really remarking quantum seats and them we think most of the people think that it was really is the starting point of quantum optics was long we will but you have to realize what it was a stopped .period then I was switch to Adams and show some extra the results about Hungary trying to ease but not with but without and it was done with the best of all helium and it was doing collaboration we see the university announced that and then I will talk about more recent experiments about their of quantum greatly that films produced in some phenomenon I was described so we are going to break we felt once an optimist so start wheezy run in 2 ways correlation experiment this is ever run into its experimental as it was published more than 50 years you 953 there was no reason located so it was the Aldermary love the mystery Oct then Alliance for accusing relied on a pinhole and was a filter to isolate a single line in the spectrum of mercury so you of small source .period like salsa but anyway it's not it's appeal and that it's irradiated by concurrent then you ever been spit up here and 1 for committed prior here and 1 for them with a pair of their and the 2 fell 2 1 to Blythedale scan the exact image of each other all Yukon slight database 1 so that it will not be exactly the image see these very involved and what's the experiments was about to was about taking the focal current but you won't hear the full talk around that you up there
and looking at the correlation for the 4 so what you are looking at is the average of the product of the photo parents now where Parramatta
R 1 and R 2 and T and depressed wonders are 1 and all to other positions of the local community pride or more exactly 1 is a position about 1 and a half to ease the position of the major about what it means that I am allowed them to look for the correlation function for onto the course our 1 adjustment that is 1 is exactly the image of the other 1 now dying Shia I can change the daily between
what arrives here and what right there just by changing the length of the cable OK 1 meter of cable Reserve 5 nanoseconds pocket so I can add some different lengths of cable and so I can study the correlation function as a function of the daily and finally I'm interested not in the correlation function itself but in the normalized the correlation function that is to say average of the product
divided by the product of the average seoul correlation will be revealed by the fact that she too is bigger than 1 OK if there is no correlation the average of the product this accord to the product of the emirate OK so to acquire 1 because 1 minced no correlation G 2 bigger than 1 means courage OK I feel what are the murdering exactly he we are going to you 1st assistant Jessica although all nite and all football addiction I suppose most of you know what is assuming classical model it's more than ever the using for instance in an awful clinics or in any photonics life is this described as a classical way or being Maxwell which OK
and the only thing which was quantized that is not there so you quantized detector and the light is not quantized anyone summer classical modern so when you build a series of the photoelectric effect you find that the for the
current base professional tool the what we call the light intensity which is nothing else that the square moderate use of the complex amplitude of the electric OK everybody agrees on that don't dictate to interrupt me OK I understand that we have plenty of time so you can interrupt me and there was no progress will be more than happy to give more explanations if you of anything which is not here so the government and density is proportional to the height and density which is proportional to the square the motorists of the complex electric field here OK so this is a
result of the experiment so you here come and now I represent 1 foot applies and the major the 2nd 1 so the 1st experiment they did was an experiment in which they make are 1 off to solve and price are exactly on top of each other but they changed their lives here and what will they observe when the delay is long enough there is no correlation G was 1 but when they shot then there is a clear correlation and it goes up to the value of 2 and the weak but you won't hear this the correlation back so what does that mean it means that in the photo current your refrigeration OK and the fact that you have this correlation means that the free duration the photo current I'm not free duration due to knowledge in the photodetectors because clearly the noise in 1 Fidelity by it's not too
related to the noise in the office of the price it means at this knowledge is recognizing noise in their life so what you will be then-CIA the knowledge in the light set free duration in July and now what so you some durations there's a
correlation died when you beyond this correlation but it becomes independent so this is the idea of this and spinal cord Gration back he turns out they merrily that the correlation of the bad clearance time here is nothing else than the reciprocal of the language of the people so you over the line the spectral Orion and they find that these reciprocal and which means on the altar of nanosecond you know it's a it's a discharger on boats about 1 year at the the the width of the line so it's about depicted nanosecond now 2nd experiment now they make "quotation mark 0 so they 0 but they the team to increase the distance between the 2 detectors of course when P 1 is on top of it to when the dispenser 0 it's to factor of 2 we have seen it already had the same reason that
previously and now In this case and when the separation is bigger than a certain distance called the corner strengths what is but the understands that there are no free tuition so it means that if you take 2 points
there is a saucier you take to balance close to each other you duration correlated but if you will far away then the situation here infiltration their armored this what it and what is interesting is that the court saying that you of him it's a quarter to toward number a wavelength of the light divided by the Angola on which you see the saucy under which 4 these related to something which would be familiar to Dutch physicist it's related to those in need you wanted see already but it's another story so these very important ways it's important because it is the humble man into its well not optics people there were not doing that for firm for discovering a beautiful thing synoptics there where astronomers and they wanted to measure the anger of a matter of star and the idea of them I thought this was to say that by using these methods you might have something which is related to area of a matter stock so it was they were also a submissive to moderate the anger Europe the amount staff and this was a key point talking but for the time being we
not yet going to look at that well yes we're going to have have to look at that so the idea is that by monitoring the week Of these what is called the G
2 operations factions and we comment about that later you measure the colorants although correlation length the Korans lengths and then you can then use those of my my mother and my protein discovery you can that the use the euro they and at this point if you want aware
indicated in optics you probably have at least once in you Korea half student in optics of the mightiest instead and
therefore which is also devised for murdering under a diameter of stock it's not the same the mike some stare and a format consist of having a mirror the mayor of looking at the stock which is far away and recombining the been coming here and that being committed there and then if you look carefully here you see a difference fringes it comes because it comes from Star which is far away is a source of 1st approximation at point like source OK and so you want interference fringes so what you are murdering here when you look at and difference fringes what you are looking at is at and end difference between the field arriving here and the field arriving there so what you are looking at is the so-called G 1 correlation function which is a correlation functions between the electricity and amplitude which is clearly different from that 1 because
remember that I is proportional to the square so the so-called G 2 correlation function Is this fall although correlation function in the complex electrical amplitude when he's won his 2nd still don't really need by and David about little station I did not invent them probably missed among them is responsible for this invitation G wireless 1st of the intensity G. Dewey 2nd although in intensity but I think it would be more clear if it was cordial toward then it would be sick of all the fueled and this 1 is fall followed so clearly it's not at all the same of experiment so what did they bother to invent the midfield after my cancel what the reason is the following well 1st what is the idea of Michael
so the idea is that because of the examining events at the Red Sea
yeah you of a Grand Slam which is good what is related to the Fourier transform all the distribution of intensity on the star which means that it is exactly this formula that is to say that the coherence length is given by land divided by the hour on which you see is a stock so basically you measure is the same thing but by a method which is still totally before she was that you are fringes and so when you increase the separation at 1 point the visibility of the fringes the case and this but there is a major problem you all of her of atmospheric troubadour for duration and atmosphere and here you are a difference between this and that which means that in the past differences free by only 1 wavelength the French move by 1 fringe Stacey OK and actually what happens is that he even in the quietest and most you fringes moving like crazy my concern was an outstanding experiment would
observe the fringes and taking this is a very good contrast that to book 80 per cent that it would increase its operations at all 70 per cent and indeed and it worked beautifully but that badminton ace 1st it's very hard to make automatic 2 2 to recall the real signal you need to have somebody as smart might as some and 2nd many people trying to improve 1 might assume that felt by having more stable stuff was something I got and they could never make better by Midas so there was a clear desire following something in us and this is something else this is something which is not sensitive to atmospheric duration and
I need explain that in a moment and of course I for
size that we don't have the same correlation function and that hybrid to and his insensitive to atmospheric situation
OK no let us try to understand but don't mean what we do when we do the
Embry right with experience and to understand that I am going to look at the electrocuted but they receive in a given point soya sauce which is an important source remembers that the stars and cornstalks and the but that events interference about important sources so in current sauce is made of many independent it should the image the waves and that the virus waves totally random phase is related to each other pocket which means that the electrocution but you receive he is the son of Minarik refused so I use complex notation here and my complex electric field here is the sum of many terms on that fact and there is something fundamentally wrong minute that the phase of each of these terms is a runner Maria so this is also a random variable and you are the son of many independent random variable and you don't know the reason whether you get when you the son of many independent random variables Central
interim you get a guy ocean process so what you get here the surrender of electric field which got ocean process and got Goshen persist you are a very nice and about to cure you have affair which tells you that all higher although correlation functional call moments can be expressed as a function of the 2nd moments and for instance is an example I remind you that this a 4th although moments you can express it as a function of the sick of all the moments is a well-established foreign rights holders this year up from government does not is just an example of this moment theorem about the process In Europe if you look at 0 0 G N R 1 acquire up 1 "quotation mark 0 eulogy to a course and these when all that I don't know how much you know about the ocean process but these related to a from among about provoked there would like that you appreciate if you have the light intensity I of which is projecting quantity you never know but
average of the square His year that all the equal to the square of the average OK His pushing Schwartz inequality would appreciate it's OK if I score stand the sequential but as soon as you regulations this is bigger than that and even a process is gunship then he has he was a factor of 2 is characteristic of adoption process focus so the just about your cases
of what is written here and so now you see him obviously that you don't have the same thing but the 2 sing several natural because mister on is murdering G 1 and hammering run into his somber during G 2 and this function as a sudden which obviously that 1 of the same week maybe there is a factor of 2 to somewhere but just a matter of definition you of a certain size and yourself and with the new of the same weight he and their souls are really muttering the same thing but of course it's not opposing factions here read him totally the expression EDI outfall electric here I wanted to win it you so false although 2nd so it should be clear for everybody but he's only mathematics let us try to understand well before Queen father 1st but the
Government of the story of
Science named built beautiful stare and the from in Australia in reserve you see the size twin there's sold there over here the big nearer have reflected OK and they focus on a detective here a reflector and the focus on the detector here and get cable or send a look at the correlation signals and here you want an example was bit out of Cruises which is a bright star of solemn and mostly in here and you see that the Korans length is about 60 minutes so he drops a 16 at from that they did the diameter of the
start of play although example of filed Liberia at Susi 16 at the 20 matter etc. so it works and here you see the medium and compared to Simitis of a different in the bike is on a different matter you are talking of it indifference demands very precise alignment of very well polished nearer she is you don't have anything like that you just can't quite make it unaffordable detective you will care about interference fringes Kia correct I put it on a detector and then you of the photo currents and then electric signals that you take along with cables and it works now the model must remain in various reminiscent of his makers from it's a just infuriates but he too the case indicates now you know they have come demure here they're separated by you should maybe 10 terrorist OK and everything has to be extremely stable because indeed they do some kind of a difference between the light amplitude but demands modem technology it's at the right their right to one-century so there was no equation of doing that in the fifties in 1950 is but the 6 worry about work it really work but the reason why am explaining to you all that of course is not just a view of nature and history of the 1st I'm not an a strong tomorrow and the 2nd is not really the topic I want to discuss so under a grant which correlation was predicted and observed and used to a .period diamonds have more than
50 years civil when both it's because equation of the interpretation of the Embry run into his coronation and comparing the classical reversals of quantum and depredations provoked a debate that prompted the emergence of more than 1 double takes and is what I want to explain still it does
go back to the classical wave explanation for the Embraer renters correlation which is really simple game because I have many random amplitudes I am somebody makes regulations because it kind of run indifference to create a difference was a random phase matriculation that the idea focus so it's quite easy to understand and these writing again what I wrote here etc. so far and in Coram source and that's a different durations are related to 1st although core inspection and is what is written and now we're going to bring the and I would return
alive but I don't usually you this what problems when I passed a laser beam so scatter and you can see what what is what is called the Salazar speckled the laser speckle is due to the fact that the virus sponsor of my scatter here make a run the phasing on the way from so what I get on the screen on each point of the screen is exactly the sort of many where was random fate but it is constant it's fixed nothing change while a source like that the relation between the various phases change all the time 1 of the main needs then it would be mitigated then we for the various phases change all the time so it's more complicated like that but the
same idea so if I was looking in the brain here and if I could look at the scale of 1 sample 2nd that is exactly what I would see I would see exactly what I've seen here OK I would say he's speckled butter but then when I stand the spot them all the time because the various phases of the barrios where rates which are committed here change all the time because his father changes all the time and I understand the Embry Bryant his experiment if I have told the directors separated by less that's 1 grain size here the situation we will do that but if I have 1 technology and 1 detective there and in the part of changes all the time there is no courage OK and the coronation on which this is fixed the swallowed and the Omega but the toast and so I have a very clear and the presentation of the Umbrian run to its observation good there is no mystery OK but then
something interesting happens you knowing that died when you wanted to develop an
expression and you want to apply for morning believe it or not it was already like that that OK and so as a wrote proposal and their pride from on and they worked about the referee state this absolutely India come that an object that it's worth it cannot work and the east the reasoning that was used by the referees and not only by the referees by many physicists at that time it was just after World War Two glorious triumph of quantum physics soul Everybody wanted to talk about .period of if you think Endara fault what is this correlation function you the probability of detection 1 foot Hampshire you of the forwarded to detect a foot and so the correlation signal is about the joint probability they probably did other joint detection of 2 its so the other in Niger to correlation ventures is a problem the date of joint detection of 1 sort or another point out 1 and 1 for on point out to Dynegy and suppress them correlation between the detection of the foot as the denominator is single probability of detection here and seeing the probability of detection and outcomes is the argument of the referee Richard said a photons obviously in the world stock which is far away the stock is is meeting focusing its inquiry and
it's obviously the and particle if it is independent of the probability of joint detection is exactly equal to the product of the probability of singer detection so you are going to want to acquire what you are not going to object to a quarter if you the 2 accorded to it would mean that the can there there is a bigger probably did too big to fail don't grows to each other that to get that far from each other so they can buy the CDO that
independent photons emitted in the stock the hands of tumors as a way can be like that so nominee OK sold under the brand to its whereabouts stupid people they began to argue with the referee and they began to not only argue with the referee but trying to make a point and 1st they believe that they will talk for a number of described so these experiment was meant to prove but there was indeed a benching these why they need this experiment it was on the table talk Lambert satirical fertility prior car and they they I observed G 2 1 4 2 and then they began to argue but like these balls wave and particle so you should not consider lights only ask independent thought of it's you should remember in the back of your head that is also a wave and they never opted not human by which they could demonstrate this formula OK but I have already used she to acquire 1 press G 1 and the they correctly and that Britain's is formalized the following week and I insist on that the factor 1 which is here what you 1 of the you add the only independent particles so his argument of the referees that is not how you think but this radiation and is made up of many ways each pair makes a big deal and you look at all these did not switch are jury and go around and you know would don't a mathematics then you get the 2nd which is and they say if we take into account the fact that we have waves then we have to succumb and here that point I don't resist to mention certain things that I found the fury of civil war in a paper by inched let us stop for a while about them I hope you have some ideas about the story of quantum mechanics 19 100 what's blank drunk say is the only way to understand the black with radiation as to what to me that exchanges of analogies between radiation and matter of quantized did not see the light is quantized 6 exchange of energy of course 1905 Einstein stays alive squandered by the light is made all of the Qantas was scornful of in 1920 of something about but it's made of released squandered and yes many arguments for about among them the famous argument about the photoelectric effect we can do that tomorrow tomorrow nite I would speak about that tomorrow nite but so where many of the arguments by the way if you have never read the paper by please read papers by each side that crystal clear its papers you can give to students I would say in the 4th year of university really
arguments are so clear so if you read newspapers you would read many things and that so 1905 is laser light is made of particles but Einstein obviously was not stupid in your waves and he knew that in order to understand and DeFrantz diffraction and many phenomena of that kind you need to represent light by waves so we do what you want obsessed by his progress on the 1 hand he was deeply convinced that light is made of particle but on the other hand EU that lights also behaves like a wave and the 19 on 9 unification as conference in sizable you of the proceedings of this conference and you can find this paper on the wet bar and in the view of the reference the during media argument coming to the conclusion that life is both a wave and a particle among these arguments he derived this is sorted out he did not it for this phenomenon he directed 4 the city because each time resigning he thought of a situation which is the following you are the vessel here With a moving water so the world can move and that on 1 side are you of Black will be radiation and on the other side you of a particle bouncing so you were gone and he looks but the trip duration in the position of this war so it makes 1 of his reasoning that the and shinily can make puts a thermodynamic constraints on a dust will be something more than me constraint and at the end of is able to calculate the fruit duration the about
radiation and the following gets bogged down for something which is equivalent to that OK why but please a formula he of 1st there is a free duration I would have the radiation was made of particles on it and the 2nd is a term I would get a flight was made of waves on and because they had little terms I know all that radiation is persuaded by sees gorgeous piece of the 19 . 9 OK Hui the Wall came only in in 1923 wave particle during would Sony 1924 in 1909 after lunchtime was already arguing about wafer you for mocked for part but anyway OK so it is going back to very and we saw on the ground with their own any way they could not commensurate so you know what happened that rated Australia the reason why they need the the operators in Australia I the Peabody must
rise other more open minded only because it did not know yet both Fulton and stuff like that would also there anyway there were allowed to view there is a different matter in Australia and work of these
events I'm going to prevent the commander of away of understanding the Amery Ryan to his correlation because the argument that like is blows away the about the accord in all it's a little far-fetched Gates is just the hand waving ending it was not fully satisfactory and so In the 18 is a beginning of the 60's people are beginning to think carefully about these equations and the mosque final you available final but the most famous Royal Albert what Bloomberg prize a few years civil and we can say is that the growing global gods and lower prices for explaining the amber Browne and tweets experiment in and the reasons White gets another prize is not only because he explained every Bryant with effect because after all just armory Bryant with effect can also be understood by classical optics the point is that for all the world for understanding number arrived 2 weeks similarly went he then worked a variety of quantum optics formalism which will there waiting for the next agreements about really quantum state of rides and down the violation of benzene according to its etc. it's wholly Glover with liberal that clearance formalism for quantum optics but he did not think about the I'm reminded and I'm going to give you a of the reasoning so the stone there was invented by final so there is debate about 5 North American drone of Phoenix which is very involved the art of calculations but when you know the reason you recognize that it is about that and were made it's really a very key so the total that is the following you have to look at the which are an excited state waiting to begin at 17 under with the king and what'll detector here and that data are waiting there waiting to detect afloat and you are going to other joint detection so at the end the dollar are interim state that the Falklands and little detective got excited and there really is an electron which is amplified and that the pride and then you get the OK so initial state final state by what perpetuates the probably did to will from the initial state for the finals an average of carefully might cost in quantum mechanics and they don't need Moscow today the amplitude and a square moderates of the amplitude so although I get to individual to go from here to there have to be careful because Apple possibilities to move from here to there was a possibility that the vote on it in here is detected there and the foot on admitted he had detected there I represented by diagram but it could also be that the foot on here is detected that the fertility is detected there set in initial state Sinn Fein mistake when I have to bust To will from an initial stake to a final state I must speculated barricades what want and subject 2 objectives OK if I do that if I said that 1 begins here I have an indifferent start and it is it's a different story which is responsible for for all of the increase in the probability of detection compared to what you would have use the photos the is isn't clear so this is the basis of the interpretation of the primary broke and which affects about 2 million more specific when you are many amid the generation of his many amplitudes makes for durations and then you get to the ocean process and you get the factor afterward but the basic phenomena is that if you consider only 20 dental detector is the difference between this diagram and that diagram which makes but the intensity as an
interference turning it all the probability of detection as an indifferent start many social probability of joint detection is not just the product of the probability of single addiction but the basic from so why wasn't really a landmark when global role these because it was the 1st time that anybody the was mentioning tuneful infotainment different effect what do indeed bye to Forkland France affect what I am what I adding in the speculation I'm adding to amplitudes but each of these amplitude is related to all something happening to 2 foot so it's not at all and the difference in ordinary space it's not a few propagating in all states it's something which happens in an abstract space which is that products of the space describing the 1st floated by the space describing the 2nd vote so it's called full-blown Don amplitude and now I have a difference between 2 foot on amplitudes and it is by no means you can't put it in all of the new respects it's it's a mathematical future and now that we know for that man single about single photon states it said there are all these and downloaded states all this feature of Malta on quantum optics we know that each value of 1 of these strange phenomena violation of this inequity it's each time you were 1 of these phenomena you want something which at the at the base of the European and difference between 2 fold on all 3 foot on all 4 on amplitude so it was the 1st time that somebody was reasoning during all the indifference of Tinseltown amplitude that is to see a difference which do not happen you know all there is space but difference which open in abstract space at 1 point I would like to emphasize his what is written here this really want to think about it because I think it's very supportive and very wielded the reason why the 2 photons are detected together he's not because there is a kind of attraction of interaction between the 2 of them OK there is no interaction between the 2 of its Peul Wonderland difference effect which makes the the Manitoba border to detect both of them on top of each other rather than suffer from Mitchell actually it's related to the ball statistics and it's just equivalent In a sense To the phenomenon leading to what tension pronunciation phenomenon leading to some pronunciation the fact that we have to move on they prefer to be close to each other and there was a guest of the close to each other in the configurations of its interface space yes there in those the really in both Boston real space and the inability to space so in in the phrase base 1 of my yes so I'm talking I'm talking of the face which is a space where you opposition the OCT so they like to be those of us like to be in the same elementary sales you knew what is the elementary said of the face-to-face sedimentary sale of volume the cube of a brand OK you you draw X and B and the 60 mentioned OK and seed Amanda said his age the bills prefer to be in the same day as it's called the bosomy announcement in view of some allegiance situation assess where there is always the 1 was on a small problem of unconditional so which is initially empty you use the word that
as long as the park yes it is a few balls in this cannot undertake are far away there is no point is that the are following but the detectors are close to each other for all all of yesterday yes but this is perfectly correct so if you have only 2 emitters and 2 detectives not perfectly right the correlation function G to which show oscillations but now we have many cookbooks and every washed out except at 0 distance just like way to write fringes so it's perfectly correct but the effect so that this year the point I want to make his multiple that won the band they want to make is that for instance Isabel's action compensation for an idea is not at all you to kind of attraction between the Bulls and they don't attract each other they just prefer to be on top of each other because of "quotation mark differences it's what Einstein wrote beautifully in a letter to show in 1924 I'm sure most of you have seen this reasoning courses about statistical mechanics but you didn't know that the 1st to ride the reasoning was Einstein shutting it you know in 1924 and started the paper about what we call the both the centralization and so it used actually without mentioning the usable as statistics that is to say is that the stakes in which you consider that the particle cannot be distinguished for each other so that if I have use any change 2 bodyguards is 1 state only and not to eukaryotic out account for and so that I'm John had not mentioned in the debate but just doesn't without mentioning and socializing you send a letter to understand very polite and saying you know when I when you back private or annoyed because there is something wrong with your statistics and so lunchtime writes letter and say your perfectly right I was not clear enough in my paper the statistics which reserves for my way of counting the particles is not at all an ordinary statistics and I'm going to show you the difference and I'm sure you all of you you have to boxes and you know what you want to put 2 balls In the 2 boxes OK so Jessica they are faultless meeting you got put the 2 the CIA all you can pull the all you can put the ball number 1 this year and the number to hear all you can put their number at Wilshire and ball member y Cia all the city's most statistical independence OK but then study said I consider that these and this is a same because I cannot distinguish between the 2 particle structurally this only 1 case
which is this 1 which means that now was my way of counting these we happened once said of the tide this will happen once out of the time and easily happen 1 3rd of the time so do so out of the diamonds the 2 particles will be together lies in the classical away it would be only 50 per cent of the fact that up to it and so and Chancey my way of counting means that the particle all statistical independence they'd prefer to be in the same box but they don't prefer because there was an attraction is very clear they briefer because he a way of counting knew the result of the statistics and so here I insist on the fact that the currency from and that it doesn't come from a rehearing direction OK OK enough for insisting on that so that's what I want to say that it is a printer a procurer softened the
man violation of medicine according the home when nominal effect if you know what it is it's a direct the unit that these effects you up and differences between 2 particles yeah between amplitudes associated with the Vatican OK it was not yet finished because 1 the laser was cemented in 1960 there was a paper by Monday and which was wrong Foster involved on you and they say always amazes it would be very easy to observe Ziemba Bryant with effect and then is that lower replied that and saying no laser light should not sure the Emory rhymed with effects there should be no bench and he a lot the quantum theory of course but I think you for explaining all of that and the question was settled by experiment Nymex round artists and very happy to show that always 1st I'm going just to with have died and is going to show you a citation of the debate over global just to show the kind of stolen that these people are using this an excerpt of the of Euratom soccer Yukon market that you can never ordered from Clorox we shall indicate that this prediction is misleading and for when inappropriate molding of the maze of hawkers sold lower say they have not understood anything of so was interested so now we express it 1965 intensity of the duration of the gallium arsenide laser was 1 of the 1st semiconductor lasers and what did 5 Mister Armstrong he found that the usual threshold the mold is always talking of single the threshold the mall the meets random noise like a narrow band that would souls with free tuition above threshold it's knowledge is characteristic of a quiet amplitude stabilized the elicited no more free duration no more robbery Bryant with effect because I remind you that provide to it's about the situation if you don't have regulations I square is equality square of became so operator which means that you have duration was cleared of mines OK and now beautiful experiment by erecting not beautiful undone and by erecting in Italian this the 1st time that anybody sources call this occurred we this year 1 of the probability of joint detection .period more 92 was not exactly tomorrow I'd like for you 1 2 days I will explain that it will sell more alive light OK can you of the French and he too was a value of 2 going to 1 and then he uses a laser which is a single mom laser well above threshold and then everything's substantive free so this was a demonstration that Glover was right when he was laser then you don't have the average rent which affect how easy well again then the predation is quite easy if you think interim the summit classical more than that it was his mother in which is a classical wave I hope most of you know but to describe a single on laser well above threshold you use a formula I like that with constant amplitude both phases which are certainly fusion which is responsible for the line with the famous Charlotte downside but it's just a phase and anomalies in amplitude knowledge which is negligible or if the laser is well above threshold this is negligible so if you consider the intensity of the switches is a square of the it is exactly Const and it's not contradictory with the fact that there is a moderate language and you do the fusion of the face so easily correctable therefore ladies at well above fresh and so we use you are the prediction that there are no free duration was observed by Armstrong and by if you insists on describing it was a quantum formalities and it's quite involved and that the end of the day it amounts to making the world of oil is a moral claim that because you probably know that to describe and laser well above threshold the best way is to use it wisely classic or state of the Alberta which is basically equivalent to the
switch of quantum state which have also provoked the oppressor cordite OK In the final item in the forefront of high hopes that the governments you that the murderer into its effect it is very easy to understand the flight is this quiet lasts and electromagnetic waves but you won't really reception quantum effects the flight is described as may default so I'm run into is is really intriguing for party so why not do it with of I like applicants now and I used to pray with .period now I like to play with don't let us do it without so adamant about correlation 1st
experiments was the removal by a Japanese group nestled and engine is and what they need is
that basically sensing strictly equivalent to the Embry Bryant was expressed they here have the truckload items in the drop not improperly called that it's in a truck it was neon atoms and by some kind of optical bonding process they cannot Adams leaking out of the truck so they items of 14 from the truck and they're not sweet just like every right ease underpinned OK so they have a narrow streets in all the tools to make the sauce small enough there are all the leads and the electrostatic you're lends easier to war where is easily don't technical but what they have here East to lead actors 1 detector on that side and 1 the date on the low side and Indianapolis can be detected 1 by 1 because when they arrive on the south-facing I would expect that the gain in a moment when they arrive in the cell face down testimony on Adams when they arrive face and Eric Thomas and
so it just like that of a political game and here 1 another 1 OK and they look at correlation between these and it's OK and they look at it versus the that could relate for then descendants of our service almost no signal rejection decorating and that is what they found the vessels of data they
indeed there is no 90's people began to to realize that there was something interesting to do in looking at correlation In upcoming density of truckload guesses if a switch from photos to what what is the equivalent of light intensity just like a density of foot so when I speak about on the equivalent of intensity is the density is yet to be density OK and so the question was do we have something like that of rerun and wheeze affect the way you ask for instance the fact that the average of the square of the density is equal to 2 times the square of the average is exactly what you want and for guests if you think of a Bulls you of you were out of the guns OK and you look at the statistics and the probability 2 of 2 bosons close to each other really literally crows in real space provided 2 of them close to each other is larger than statistical independence and the factors affect too it's due to the Maxwell man distribution so this was demonstrated by Kigali but there was sensing beauty 48 was the 1st experiment of that can result was done by Eddie Gomez and white man GRU knows it well the first one was option ,comma states and what they did was a following there had been talking about the and we get out of there was a probability of through good accordion and when there was really collision the atoms would this year because would be expected Freud was dropped there would be expelled out of the truck OK so there measuring that by looking at losses OK looking at losses state could evaluate the rate of 3 collisions and what they found is that this rate of 3 political region was the to 6 died what you would expect if it was in it but not if it was if the probability that 2 of the 3 political edition was Joseph cube of the
density he was 6 times larger but they need more than that then they went to Boston Jiang Station souls a lower the temperature and went wasn't station and then they observes that the rate of losses decreased by a factor of cities where they found the factor of safety but it was closing book wife because it was emotional state is jersey equivalent of a laser what is the ladies these could be on laser beam Sabine in which if it is a single mother ladies it's been in which all the fault of are in the same mold of the electromagnetic fields you can these models the electromagnetic field as a kind of wave function of the photo all the thought of himself described by the same way function but doesn't think non-state is exactly that a bill shambles state an ideal was out and I must say it is an ensemble of items which are all in the same way the function
and you don't expect any food duration because it all this right assembly functions there is no room for free duration the situation could from and that France between various ways function with various phases when they all in the same way functions there is no possibility of refrigeration you convinced that the states so they come back and then I realized that really studying this kind in manner so we need something in 2003 was more and more interesting and they're out there is at least here you just put in the in case you're interested in putting a color of you had that there are more and more smart measurements consisting of observing correlation in the fruit duration of density in your truck or laptops but all experiment Our about after the density of the is just like monitoring affable current and so we pass equation what about individual atoms correlation function
measurements of the kind that Shimizu done in 96 but the and only 1 so we consider ways advanced technology the proceeded to represent this kind experiments with improvement in the experience and so we're
locked into studying the umbra remind was effect we make testable here but established here it absolutely wonderful for these kind of experiment for the following reasons you know of course that you must electrons OK and you know that because if you must electrons there are really 2 completely separated set of revelers you other states in which the 2 would trauma positive spin and you of all the states where the toward trunk of Ontiveros this is a set of singlet states and this is a set of triplets states why treatment because this makes being 1 and spin 1 committee and McCaw 1 and quarter rule and minus 1 while this is a sequel 0 2 at a single pocket now it is remarkable you that you cannot go from 1 set of states to set of states by interacting with like wine because interacting with light you cannot free speech very selection rules you cannot free individuals in the office of the troubled by interacting with Jack so if you set of trade that you stay in this type of trade that when you what others all blind or anything so if you start with model which is in the innocent of regret for all practical proposes the lowest traded state which is serious plays role of so you can bring it would result in lieu of a arisen side you use risen on-site 1 . 0 . 0 8 micron you can use it to directly the act of course there disarray that cause then trapped there all the usual trick that people always scholar atoms can for all practical proposal is a bronze state but it is not the real world stage the Rio Grande that is a senior at Rusty its 2008 from Buell which means that this is just like a warm the best 1 dealer stronghold of analogy which is there really to be released them if you just a direct was right no problem it would keep quiet but as soon as 1 only being treated state goods grows to a piece of Martin it between indicate in release 20 electron wore white is indicated for the following reasons are that gets close to a piece of modern another part of the ion amid or anything now the static and direction but that was false whatever you want there is an electrostatic and given direct interaction electrostatic OK and when an electron was near there is a moving magnetic fields look at the view from the from the select few and the magnetic field country theater and if you freed 1 of the bullet from and then that case here released 20 Electoral Board 20 votes is more than enough to itemize anything to begin it was fired a convoy Yukon extracted from from Yukon itemize most of molecules etc. book which means that when I don't write about guns on a piece of metal 1 electron extracted does this ring a bell in your mind photoelectric effect it's
just equivalent to single photon counting here we have seen at County and so we these you can repeat the kind of experiments but the bordered on looking at correlation to .period correlation then we can do to what correlations exit the rights of their own pockets
so this is the way it works busy apparatus we really is enough to say to you about that so here we are reminded the callers to trap but as the more helium the tree states remember triplet state as he for 1 so you of a magnetic moment experimented so we can trap it in a magnetic strip OK so we tried the Adams here and from time to time some of them for all we convinced them to fall by doing some trick OK and here as the detector what is are detected the detector is at a loss about all that the piece of metal or it could be a piece of my daughter wastes and elect a chanted ,comma OK if you you know what it is today ,comma deprived but it's much more subtle like that it's called a Micro Channel relates that is to say here you have millions of smaller tumors and each tube so
you other children like that this is a good time for the children each dubious over Wizard a year of alkali something like that idea OK and then you arrive on stage here so you of press motivated Sheehan and -minus year when you apply 1 thousand votes or something like that when the leaders of our studio arrives here let's say here there is 1 electron which is immediate and it from subtracted here because you have a potent political tensions and between polarized here then 3 electrons will be admitted accelerated this year now I have magnetic strong American etc. This is an enterprise but I don't have only 1 I have 1 million of these jurors here which means that when matters that will he out of arrives here on the other side of the break here
I macroscopic burst forth I can detect was a truck that that can ruin ,comma scope and I can detect it was inactive OK by the way the system was crucial to to the discovery of a bull's-eye action ,comma state government established here we discover that in 2000 and that it was because we had is that dictum that we could see that we indeed was champion settlement us him so you must never neglect instrumentation and technology actually How
detector is even
smarter benefit price because the gain if you understand that each time an optimum arrives here on the other side the urinary that rather than just having a big electrode and saying we have an optimum somewhere we use daily alliance and by looking at the difference the time of arrival on the ends of the alliance we get days where you have to do the right Of course it's not easy because electric signal propagates verified very fast on the line itself the all the all the virus is not exactly the of the although the validity of the light so you have a big problem that it is too fast you're actually just not fast enough but that treats for his instance in order to decrease it is a beautiful tree that we did not invent admitted to the engineers are really smart but if you want to decrease the validity of propagation in the wire just make a point and then you have the ratio to the space between 2 readings toward the diameter of the costs of the upper and middle sitting here is role so well using tricks like that you can indeed there will be at arrived and sold we can tell where the atom arrived with a resolution of 200 Mike from Inter were very disappointed the people who know this technology have told us we would obtain 20 we got to wonder on the 1 hand we were disappointed on the other hand when we consider the situation for people while affability prior here that we have a diameter of final sentimental so or should fall Bloomberg migrant is not so bad it means that we have been detected like that and he's just like the inclusion of the East and apartment filled with prior working in parallel nobody has something like that you know this is beautiful because so we have about resolution of 1 and we have a special resolution of 200 migrant is not so much so where were disappointed but happy anyway and we decided to use this is detected and done out to be
very useful and so now I'm going to ask you
to concentrate to revive the somewhat we have because it goes back to dissuasion of what means a correlation what is exactly coordination and he's away we have done the experience about With a cloud that all the articles of the trapped in 1 of the magnetic dropped 5 should OK so it's a fair more clout is notable said it's clear that it's so I don't know who wrote the novel getting maybe 5 or less than 1 might creates a really cool but anyway it's and suddenly we are going to let the cloud of 4 so now we have a crowd of cola In my client of course that comes with a rival the detect and what they say is that my detector is a three-dimensional detector can you understand why it stood dimension here but in addition I all the time of arrival and after 50 57 director of 4 all the items for weighs about the same barrels a day which is about 1 meter per 2nd and because have a resolution of 1 nanosecond I can Dale the Vatican opposition the clouded with an accuracy of 1 enemy was 1 of only 2 resolutions that adhering to whatever might of Micro the meter horizontally but I can make a recall of position of all the upcoming nightclub so now in my computer I recalled all the positions of all my atoms in my back and now I can look at the statistics what is problem beating a nite allowed to have 2 of them separated by a certain distance distance being understood victory OK separated by a sudden victory and I do that and when I do the study states what I observed these nothing because it probably to win 2 out of such a certain distance is basically 0 From that diaries not 0 but is almost all the times you but then I don't panic I repeat the experiment and then
I get to the correlation so I do correlation on which had seen northeastern but anyway I'm still going on and I do correlation which chasing nothing and at the end of the average of the correlation and then the signal repeaters Hey what I should do His 1st rage and then ruled that the correlation because the correlation is beginning some board so if I have enraged many sidebars and I got the correlation there is no correlation between the 1st of all in the 2nd 1 so there will be no thing so I take 1 somewhere I don't know nations it's an noise but I repeat I have arranged and
this is what I did she had for instance rules Vatican direction I get about I don't guess is that it is a beautiful but because it does not go to 0 but due to and the reason why does not go to school it's because of this program of the 200 migrant resolution and I'm going to explain you that the progress of the detector resolution again because of the sentiments adjust their I'm whatever you want to to use to calculate that the court has volume which was described the correlation function in 3 dimensions is the Fourier Transform although the supervision of the density of sorts and when I say forward transformed I mean three-dimensional Fourier transform so assaults which has a certain shape and the correlation functions we the Fourier transform all that and it turns out it's because of the technology of the kind of magnetic dropped but we use it turns out that the in the source as the shape of a cigar the very inundated the volume like that and do you know what is afforded us all together the returns policy guarantees a no it's a pancake yes because you are the only mention free transform soon now the mansion for a transformer is wider so this gives is a pancake so now what we're going to what is a bad day and we are going to explore pancake with detector which has a separate which certain reservations and unfortunately the resolution base while they're here that the thickness of the bunker which means that we have a convolution here when you we explore and which crosses we convolutions and his convolution reduces
the amplitude of the signal when you of the beach and a and reduce although mentioned no problem because the size of the detector is still less than the size of the but anyway you cannot avoid the rejection due to the self-image OK and that is why we have the expected rejection factor of 15 which is exactly putting out 1 . 0 6 1 . 0 7 rather than yes yes very good very good questions but you know these experiments are so difficult when I am going to tell you where you students on the other students but students anyway these are really cutting-edge experiment we apparatus extremely dedicated cigarette when you a chance to do an experiment we even if it's not a perfect were due yesterday that we have repeated the experiment with this young radical so it's a very good remark but it took us 2 years to go from the initial situation to the other was so we prefer to with the experiment which was not perfect but which was the first one so when you the chance to do an experiment 1st can be quick and that is that the jogger it's better to win the 1st experiment quick and that is not to be the 3rd with a clean experiment the idea is to be the 1st and then to lose 2nd kids and that you know anyway as so it's a very good not bad OK so that is what we do that .period and now what we have done and this was our world is beginning to study the various
parameters so for instance we decided to change the size of the floor you know when you the stars not easy to trim the size of a star but here we could turn the size of the source of which is the size of resources to shore "quotation mark that adults in an Armani dropped when this whole the sizes bigger OK because public farther when I've gone there sizes smaller so this is what we have here when the temperature decreases the size also source decreases souls of Fourier transform becomes wider is what we see here so we have made plenty of money check but we understand that receive this is very saying it I this goes on and on and on and on well 0 0 is a
stain on our look at what I see here is the same whatever the axes these drawbacks is wife even when I sprawl the dimension in which I reservations anyways a reduction the size of the wrong actually I think is radiation 0 0 0 is a single point there is nothing you can do you can scatter like that's got like that of Scott like that the central point is always the same so the amplitude here is the same not not on the
3 carriers but this is the same whatever the Dimension X Y and Z you always have the same there the same value of its 1 . 0 6 0 1 . 0 7 pocket this is disappointing but that the way it's OK anyway so we checked that we understand all that we don't and then what we did
was the freezing temperature of the cloud the transition grew from a fellow cloud which was something I 500 not getting through to the end of locating and now we have a legend and what we had was a state flat no correlation and you see if it was 1 of 4 1 0 6 we could so clearly we have the resolution so we go from these 2 that so these was approved that it was really an analyst was alive and so we
were very happy and we see aware laptops are very busy and we do beautiful expression and send them back to close down all articles of faith of pseudo but then there is some more applicants can get not only as Maryland but they can also promised and you don't have the of fulfilled its OK yes it was really is look at net this part of the publication of the book that is going
I think we can get the highest scissors a beautiful story that theories terrorists but we have been experiment and we cannot have announced that it was a year of not so fast enough that we cannot this because you were intoxicated by the its now I want you to know that the of used Over the
years the world you know not result the cities what is stated that when you when you do what they call the shots only you always suddenly a sample the bank said that before the court grants to establish around the things we tried to observe that we never succeed in observing but anyway here we wait all the time we cross the transition and we wait so there is no discussion with us all the time to establish that fun compensation OK but the equation is it would question it so although we tried to do an experiment it didn't work I mean we could not see any time daily for establishment of and we a situation where it was more likely to what it was in a very elongated ,comma state which is so-called was the condensate in Europe was the said we would expect that it would try to start here and then started here and start there and that progress here it will develop but did not but of course if you have a better time resolution maybe someday you can have it yes you I want to talk to "quotation mark food duration because it's an experiment which is very difficult and it's good quick and that the experiment so yes you of 4 duration not if we don't want
to comment is a major it's what you have to understand is that there are a significant thing in this rafts these these dimensions OK and the Vedic already mentioned if you would approach but the the glacier is nothing else that the resolution of the detector but
this is meaningful these is meaningful OK this is bigger than this which is the biggest you if you if you block so this is what we wanted to show because we were changing the width of the CIA but unfortunately all along that they mention the peak is much narrower than the detector sold with a view of year is the width of the detector and the singer and then there was a favorite of the original interviews in which they were claiming they realize the Bose-Einstein condensate were full of guests in Lebanon as I hear you saying I'm going to recommend using lasers VCR are identical not working yes of course abatement and state it's something which is more or less in Fillmore equilibrium was thermal components it's an object which in dynamic or equilibriums that you take part in costing unit dropped in the you reduce the temperature and at some point To speaker of free when the wave packets of unhappiness at certain point they will condense in the state all the truck but is there is still a fraction which is unconvinced and you offer more acute between and governance fraction and the command structure but it it'll beats like the at 100 C U of a curio between the with Walter the it's something similar OK the laser is definitely not it's a molecule urea with anything what I was mentioning is that the adults in the condensate after all is described by the same way franchise just like all the fault of a laser beam at described by the same way French these was the analogy of so many things but I didn't see that the laser is abolished and compensate only if I say DDI was wrong because I have a last-eight strictly speaking is an object which isn't thermodynamic or equilibrium for the bait but you mentioned above those of the Organization of photons is in a sense the realization of a situation where you are photons exchanged between the court announced fractions and defuse the light switches and commenced so the newspaper rehearing easy another burst of liberalization state for photos the reason is not a position on the fateful photos it's on now goes to local and state in the same sucked all the fault of cried but are in the same says of the phase space the violence of correctly is mainly that families 1 thing that will include yes actually 2 of them in that is why you can't use it for including the actual basically gentle punitive in you you have landing and the you know that this is about CRB but delighted said the beam which is propagated and talking of electromagnet the quantized therefore limited to I forget about the amplified OK which has produced might raise now I have my beam of photons that all described as the same old the entropy is 0 these while you can use it for properly the basic idea of laser according you that the laser beam escorted the looks hot
because he got value but actually from point of view about dropping this is so if you are smart enough you can use a fund entropy 0 OK so the different is a very interesting question in this indifference that would proceed evidence it will
happen with tournaments we we have mentioned you phenoms like to work on top of each other add intervention but be careful the whereby intervention is this problematic so for parents I consider little busses but if I consider it between here
what I must do is unceasingly tries the global order with function which to particle or whatever you like to quality it and the signature rise means that I on this and that was a minus sign so rather than adding I struck and because I substructure is going to be at the zoo it is a poet principle the family don't want to be on top of each other but look before looking at the experiments now the kids really interesting because if I observe what I expect I will have the average of square is less that the square of the average the event was placebo no it would violate Bush's shorts phobia but we are going to observe it why is possible because now we are seriously doing quantum mechanics we are not allowed to speak of events in the United classical number we have to use a single 1 sensation AA and dagger creation and an elation operator and if I brace this category number by up idealization destruction and creation operator then yes I can so this would be if we observe that these will be fully quantum 109 to it was because you have 2 choice I that you describe it was a wonderful bodies and that for what the lake and accept or to Iran's than black but on the other hand if you are molest you just explain it was classical waves here we stand and there was no discussion there is no classical description was fair .period so we need to expedite our yes and the world might I will explain at the benching of a single particle on the benching of a single particle
artistry yours in sense just nobody had seen but it's freedom in the sense that the fact that if I a single public and if I observe at once I can't observing the sick dying because I destroyed it those in the benefit is the on a family on anything OK the idea of I did benching with a single particle is when I send a single photon sprinter I would detected either on 1 side of the story that there on the other side that no 1 will sign this independent the fact that it is above all a phenomenal this is the 1st meeting of intervention these meaning of intervention 9 docking of 2 across the practical don't like to
be on the of these another meaning of the word intervention should be confusing to winning OK so so people have tried this is a really fascinating phenomenon OK observing directly the correlation between 2 friends so people have been trying to observant say trial was a strong EU semiconductors and they can the extremity proud because they say the bottom line is what we will do observe so was not the family each affected probably principle at what we observe and are really very very very very proud and look at this case here it's 500 thousand here 490 thousand 100 which 0 is really very very very rule he so are very happy with that but OK well it's it's a minor effect on the other hand the notables ratio is leading us toward their services but that all the problem with electrons I'm not really surprised at electron don't like to be on top of each other the repetitive
that my friends who are very good mother sent her malls are screened they behave like neutral particles because of screening it's Akira OK so I trust that this is an experiment with neutrons unit of neutral and they came that have key but consider carefully the scurvy and suppose long-term export and the reason why should that is not because I am a critic of that I had not expected neutronic that many people widespread neutrally state that is not possible to observe that the signal signal to offshore issue is not the sole aim is just to say that people are
fascinated by his effects so we thought maybe without the means to be easier to so come with colleagues in Amsterdam the team of investment then developed an experiment in which set the truck on the billion for an alien from the post of beautiful experiment because it wasn't the same dropped you have a mixture of William for an idiom 3 and there are informal contacts at exactly the same temperature and because magnetic moment are about the same he means the same size of glove look at the 2 species of the same temperature since I was a the in the trumpets of Iraq and by choosing correctly a radio frequencies at the very last moment you can decide to extract 1 Osceola species so you are going to compare directly with Dobbins wizard 3 Indian for Everything else being the same the same size in the source said temperature center received focus so you just changes but Of course there is something that you
change you change the last and when you for Of course change something yes there is a change something wonderful Winchendon Mass remember getting no should not change yes this change where this change because indeed they follows a similar city but have different messages so that the word wavelengths are different so the rest wavelength when arrive on the detector are different and there is a racial fault reasonable waving so the only difference is liberal wavelength when they arrived on the detector so we execs Vermont and this what observe when you would we do it wasn't your
fault change with the was In on 3 continents now you see that the width is media here Monday that the boy affects difference and because it's wider here then the reduction in amplitude easily less here that he thought we understand so here you want dire of pure comparison of boson again fair and it's that the arising being exactly the same so it's a beautiful I would say textbook expressed so it's a pure point of statistics effects
and now sure of dialog fueled by that they can't stop but if you style I'm going to do the landscape also more progress in quantum optics hostage was good with photons and costs we have embarked to do it with laptops and allow me to drink little so we are
going to look at it don't beat into
various landmarks in quantum optics soul 1st there was a technical achievement which was to develop off Fulton counting just after World War OK you know that there were walk to Watson about unity to the Europe electronics and that's a victory with a rather everything soulful the counting was amended and is what prompted the development of more than 1 will take you can say that more than quantum optics did developed ways of proceeding to ask the question what these a probability to observe a .period here and now and there that also died looking at the correlation function between the probability of detection of photons in 2 in space by died Wallstreet early them about invention leading to all the phenomenon of modern quantum optics Sierra are we are pursuing the same goal by developing singled out the detection results indictments space because when you were result in time space you can build the correlation function and so we observed utterly can remind but we get the supplementary benefits we could compare fountain and bows white nothing we nothing like variance wistful what was the next step but the next day observing correlation anatomy cascade for so it was and 67 the idea is
that if you work it out With 3 like that if you get excited the act was the opening for and with electron collision OK you will not lose electrons you excited that here then you will observe the 1st looked on in the 2nd Fulton and people able to rueful for correlation between the 2 foot and it was a way to monitor the lifetime of the intermediate level it's at their focus so it was it was a mistake we used to the idea was that this phenomena to produce 1 dollar for dollar and use it to test best inequalities the 1st that was Clouser you the 1st experiment in 72 and then I need much more integrated experiment indicate late OK the queen what is equivalent was at the equivalent the without arms dealers Monica of association you'd take a molecule dissociated it's very similar to producing powerful enough to be cascade like that the aging in border as little correlation she has observed that the 2 weapons optional produced together she has not observed and then and now a real variable that step full of bears in nonlinear crystal I want to describe discredit experiment because this was really something because of the shock for people doing non-numeric thinks the thing and
don't know I would rather no that's that the bond waiting on narrow pleats were thinking only of classical with and so that an experiment called parliamentary version which consisted of sending you movies being on a to nonunion asked Crist also we Cory only Uzi and their way getting donations a tree consuming our 1 and only up to such that Omega 1 person get to it costs only yeah you and you got absolutely render an account of that by multiplied "quotation mark OK if you walk away a wave of sedating up Omega 1 away was later you have to make do with to "quotation mark indicates sermon the difference frequency it's a direct around soul proposal OK and sales of accounting has been clear that Clinton has been here and a continues to in there you couldn't see the world you physics but some people say they hear you want the following schemes you photos these absorbed age about all media you and there is something I can be in Turin in here and you are the 1st photo age about Omega 1 which is and the 2nd focus age about only 2 the changes the equivalent to this describe things like that all described by multiplying "quotation mark where not really because if you take seriously a major issue the 2 photons which are here should be limited by bears so what people the is to take detector CIA and rather than having it back so we just observe the density of ride and see continues being the good photodetector single photon detectors and they look but by correlations and they observed that indeed there is no is that city's schools although the average rate of detection is constant and the average rate of detection Wisconsin there is indeed a strong correlation between detection here and there the photos are emitted by the US this was the what is the
name of fighting there getting be experiment in 1970 it 17 years to show that the pair of photons emitted in this process up and down and nowadays all multiple sources of pairs of entangled photon are based on suspense support but to demand the report of understanding and technical improvements pocket this
was In yes this is a bad feeling well the famous homed in an London experiment was designed to martyr of the directly delay between the 2 foot of the bed and these protection 2 the man on which you cannot exist and amended never being here which is determined by the phase matching condition it's bank of not electors which means that basically the diabetes Liz and then to the minus 30 seconds that some really very very almost simultaneously so
only contemplate that we realize that but there should be an equivalent was optimists Of these process and what I'm going to describe now and then we will stop maybe the
following you don't sound
that In the present and pronounced state as soon as the densities large enough it's no longer an ideal guys there are certain direction and the term of interaction is proportional to the density which means that at the end of the day the equation you write your oven interaction durum which is a product of the the have to write you was absent state with events at the end of ah if you want to write so should equation fall and of which is he taking into account the fact that their interaction with rights as usual are out of the actual square of over 2 we
are no it's not what I want to write what I write the shooting immigration time indifference OK so what I want to write his jersey and in an internment without the usual it's too square about when to meet again on Tuesday the if the potential the traps but when they master but then I have another term which is the potential due to the interaction with the all the optimists and stock is proportional to the density and the density is a square of the wave function so evident which is something like that which means that when I am when I am going to rights especially the equation I'm going to write H and what I will get these square divided by 2 women Blood we are rests sites where all that to the site and these will you give me an equation which is called the show Odinga nonlinear equations now you have people working in Photonix when you are in the media which the care nominee narrative you what exactly but durable but can you think this is a field that that Cuomo of the field here and indeed the .period for producing a 4th so is strictly equivalent to a fall where mixing process so the recent direction during the a chunk of state is strictly equivalent to would normally narrative a 3rd of all the money narrative :colon care money narrative in uninterrupted this has been demonstrated the next group of infuriated send the MIT group of Kigali furious civil and that demonstrated four-way meeting with their it's balancing 2 was a jungle non-state aroma against each other they said the probe and they get a 4th wave it's a relief always makes the idea makes 3 waves and I get the 4th OK you recognize process OK and they call would even amount of reserves or is there a simplification of rights as Aso's is upbeat about its small probe and you get to see
focus now you can as yourself the equation what happened if
I don't have probe then I will have a spontaneous parametric process I will have a creation of this and that Tennessee you a sense it's analogous to what they have here the case
going back to fairway 3 ways these history mixing knowledge freeway mixing 1 you while you owning I used and you only got 1 and then you get only a 1 on side you bet the I'm the only too and then you still have the Bund which has been debated and then you if I don't put this was going to get idea that there only a 1 and if I want to describe this currently have to say that the His induced by vacuum figuration and if you don't like the idea of a configuration is this is due in the formalities and to the fact that I have ,comma data switch on noted the in which Arnold 0 between the AA and AAA back which is equivalent to saying that you vacuum for duration the fact that the
commutator tumbled 0 it's equivalent to saying that the vacuum Patricia senior U.S. and senior you made 3 ways you will sell false while you remove these 1 what do you get you get despondent as process including a pair
OK this is what is predicted we
have make we have relaunched told city against each other without putting brawl like our friends and we have indeed all deserve better that's how do we do that still wonderful Detective Willie Mays a collegian here and we let everything fall as I told you already that there is a cloud of 14 he passes through the detector and I make a three-dimensional image of the clouds and he has had a series of cuts when the cloud the bulls through the American and you seeking With these through the detector is just like a city year going through the detector and this sphere in the fact that they have bear both Adams the board directions and conservation of energy and momentum this year that they should all of the same diversity so after US Open died in this here my students have done a beautiful computer work
so as to show you that I hope it will work I hope it will give work yes so I want to show you that not it doesn't want to work maybe the company's success OK so I don't show it I wanted to show Europe virtually into two-dimensional showing that after the collision that many adults on a two-year honor on the whole OK it corresponds to all the items it did in various directions always the same the city of K so now we we have this is called the best way of collision how so you see again the cloud going through it so you see a cut of the CIA and the top of this year CIA going was it OK yes this has years where visibility did actually it's administered is momentum space because you wait long enough you have a very dinosaur also gave the BCS smaller you go out there and you wait for a long time so you dying of fright and then you will go of style that of fright because everything drops like pick your the collision here and then everything drops and then he goes through the detector but the size is being compared to initial size so its momentum space so now that we know
we have the computers Israel's construction of all the evidence will call correlation between opposing sides and yes indeed we see is a signal of correlation showing that that when I not only in 1 direction and I don't mean the opposite direction strong OK but now we had the it is student was saying what I want to rule committees all the correlation and then you look at correlation he and
direction very close to each other and again find
correlations and what is the Hamburg so the prettiest ignored the
Due to collisions like that no going in physics but these this is really an effect due to the fog that I Minneapolis and eats incoherent and then I have the Embry Grant was effect but could incoherent it's 2 possession custody it was action condensate are not incoherent so what happens here actually what you wear that you revenue source many collisions like that but if you look at correlation between 2 items which are here I must forget about the past which means that they have the density matrix in which many career entities but they trace over the past and by tracing over the past months I transform of course it should deposition into mixture when I called the degrees of freedom unit status the court in accordance some board when I Fall gets some degrees of freedom I get 72 which is in Corea Sudanese a versatile phenomenon in which it even looks can because we forget about the fact that I on the other side these very .period them again curiously is being observed only recently with footnotes to board of the music's Freeland and who farmer abroad to receive an observer but it has been done very recently to express OK so what we have at
this point is that we have observed Babylon dozens of day the words in a spontaneous Indiana at picks process and you are going to get who the other bowlers that so what is point of that but what this quantum you that in the same sample or something we call I have seen Denizli these correlations that Baghdad mothers fathers billboards and the operate brand which correlation which off before Oquendo indifference effects and everything is in the same description so I need to know what the formalism for understanding the woman image of it's really "quotation mark don't because we have observed more recently squeezing in the number of difference do understand what Obninsk squeezing the number of differences that here with happens let's suppose that
I look at the scene of the Mafia and Fulton County I have shot noise but shot Nizam in indentified detectives and 1 for them other statistical for duration of the all the all the rules and 1 OK now he is I detect and which is probably crossed when on but I do think that do and understand that is the decoded for duration which is the root of OK these the situation here and there I'm maturing independent for duration on the difference and 1 minus into should be of no although all the rules of any 1 person let z uncertainty increase very much on something you don't want to murder you know all this to reduce the uncertainty on what you want to measure the duo is considered what used to be considered until recently asked the staff of Wonder meaning it was not a true 1 because you you are not going to be isn't there but it was considered a start quantum only the best example of that in case you are interested in the following when you have a good being overnight for isn't a perfect laser you want to investigate Zepeda teammate except that there is a short knowledge the fact that because things are so stable that you have a class on distribution of photon which means of the false certain died you count and vote on and you are an assault on the route and and so you still get take and 1 medium and that this a small but in there if rather than having a powerful acquired Salazar the you have what is called the and squeezed in which is a beaming reach the 3rd down I begin a very rigorous then you got out and uncertainty on the intensity measurements deal the shop there is a price to pay I bed the price to pay if that there will be an uncertainty on the face on that being which is bigger than uncertainty and on the face of a laser beam but if you don't get there for a measurement of phase if you just want to measure for incentive in absorption you are happy to weather-beaten which is squeezed in intensity and you I'm not unhappy that the phase is not well defined OK so this means
that the CIA with there of Adams and it is likely that there is a whole to work at and from met deals of quantum stand out but
what would amuse me would be to produce not to produce on the big government at their produced but to make an evidence of the fact that we produce and that's about it and that amount in momentum space what do I mean when I might want to switch court I'd like that I can but they can also work that and down the line means that this is not I all but and the insists it is boss these are given that the and the fairy destiny that I producing the good after deposition although to what those flying like that there is a saying do what is not the way to decide what to write that are you surprised yes but intended you know I've been working on environmental 30 years yes it's surprising you the barefoot doctors but produce like that and not just saying is just like a splitting of that which is dead
and alive where shooting that isn't almost surprising that there but the difference is that we have not seen shoving of captain we have seen in public for the circuit so you know the idea that I would have the territory is assigned to what was being seen as detonators late like these and like that "quotation mark we needed that and the in-principle yes the
idea is here if you produce senior Denizli these and not you can recombine haven't been skater recombine speak and then you look at correlation between the detection he detection there and you change some face somewhere is crazy is not crazy about it does being done with footnotes In Paris Street Danville people have done an experiment in which they demonstrate something like that because environment domination you will have a better view of the font arriving here which creates a barefoot and we just need that as they this and that and by recombining regards that demonstrated that indeed you want some correlation with depends on the face difference we had done so we know how to make nearest these the always like birds is called rock bursts Yukon reflect the act of understanding the speaker it's a standing wave applied the pharaoh died which is short enough to didn't do the amplitude scalded by about 2 brought sewing principal research and experiments could be done
without and the where are going to try it I hope it would not stage 17 years to do it because it took I remind you it took 17 years between the demonstration of producing bears in the parliamentary don't formation and the demonstrating that they are in the ongoing and that if it works then this kind of scheme might be used to best known three-year effect of smarter and I we finish with that you may have heard about 1 very exciting development of drug called about those in recent times III what is called quantum simulators the idea is to use a truckload of problems to simulate situations of electrons in Saudi so for instance people who would talk all about domes in lattices beaten with stunning waves and study phenomena like the Mott transition in my lab we have food items in random
potential produced wastes I am obsessed by with we make a speck of it makes it is all the potential as it allows us to study art of synergies all the potential and we observed what is called out unnecessary organization which is 1 of the means of commands much OK and here if we don't develop the scheme like that so we called the old fault crazy states these serious like which have been imagined by waste of governance smarter but nobody has seen them directly maybe we called governments to what ought to be in the BCS like state and study the property of the slightest OK so we have written a proposal with some smart commencement theories to propose this kind of thing so what is a conclusion
on the conclusion it's went 1st conclusion is that in
order to do experiment like that you need to what many smart
people and of course year there are many spot people in in our world and by the way he said people are interested only funeral people were interested in considering foreign and a postdoc with us they can say we are interested and we received we will discuss that good conclusion that Sterling the these random phenomenon we spot it's really amusing and it doesn't seem more confidence it's more complicated than just face the truth experiments are more complicated more difficult
but there are still several ingredients you don't that we thought of it 1st you can ask this in energy terms is interaction terms here very large as you know it's very difficult to to 1 of Fulton's interacting with each other off calls on narratives but is not the narratives always weak and it is 1 of the major problem for good OK she without arms you go we have what is called fish vise allowance and we can really increase very much interaction between atoms when we won the war observed the effect of interaction sick and there was all this idea of mental simulators the announcement of programs Gold announced another programs we just so difficult that we know we cannot solve them with computers the reason why we want what quantum simulators was expressed clearly by fine Line in 1983 the many believe programming condensed matter these and other non-government about the costs it's so complicated that you cannot even dream to other computers to contradicting that but if you can about costs in a situation similar to the situation of electrons in the Saudi then you can best what up so that the idea of quantum simulators and the last point send growing theories crazy but very smart think about maybe 1 Riyadh-based photon by Adams may the recent sitting with the fact that I've domes of the mosque as you the emerging also gravitation and quantum mechanics is not that it's an open question and said theories think that when we're going to pick up and down the state what all that kind you need assurance of the because you want his massive objects and when also what wonderful reputation ,comma maybe simply durations at rights at the show I deserve all the items through like think at 1st although we have a clear difference is the fact that we have found and bows etc. but there may be more and so this is why we are continuing to pursue this kind of stuff so it was a wrong review of certain fundamental phenomenon in Fulton quantum optics overview on some advances with a called Adams I hope he said meet what you were expecting all not expecting but at least I hope you are satisfied with that we can still have questions think Europe the we small questions don't this date we can't go back your yes we do with our will is not there working "quotation mark stories not nothing is nice but there was something going state the air single with a right not all of the 1 which are the condensate OK you can have the following major at they didn't drug ground state any quarter 1 and a quarter to winning at 3 you have many items on this and then CIA boss Maxwell Grossman is additionally except for the ground state when of a microscopic population looking so would fill the 2nd time that non-state this year government with the guests of honor during the if you have something like this there is still a Russian in a letter the the only 1 another feet now it seemed that that is what I have written here this is isn't there are these an infield description each other on the sensitive to defend their actions by all the other ones so that was an infusion description this storm is interaction you to all the other items that it's similar to the laser beam getting in on the nominee no you cannot safe accusing etc it's totally described by what it thinks books of of non-Americans it's called them only notionally shopping I question it decision kind of equation which produces terms which produces several accusing etc. so we have this kind of phenomenon except that we can't June the interaction we can't make it attractive already received we can't make it big smaller accounts etc. and but we can reach our level of normally narrative which is much larger than what can be done enough money in Europe so it's says astutely self-indulgent but in that sense yeah it was 1 the tolerating social it's also yesterday but in a different With these might cost going both generalization is a phase transition which she's in a sense for all the because you have sent molecule reburial focus to phase transition which is driven by the temperature the laser phase transition this is equivalent to those feral magnetic To the fair-minded decode power may make the transition is occurring .period except that in the case of the laser is not driven by the temperature is driven by the but is driven by the the but the barometer of the laser if I remember where you Yukon riots How short writing you can writes the equation for the laser amplitude of the mall the year of the so this is the attitude of the modern game the because laser the costs a 2 Our 1 for us is saturation Parramatta which is a square divided by sensing it's in the city of saturation -minus 1 there is probably something like a gum here and they amplitude OK the the equation for the laser of power is a Parramatta describing the invention of population but it's a reduced Parramatta East are is bigger than 1 then you go out a solution which is different from 0 the something's missing nests you know you cannot because if you like look session solution of the equation then the century solution for all but he's either a accord 0 which is of the laser doesn't work at all Our united by 1 breasts a square divided by ii sat maybe there is a factor of 2 but we don't care equal 1 which means that yes minus 1 accord 0 which means a squared divided I say it's the costs are minus 1 and something missing now that yes because our minus 1 so if our is bigger than 1 woman another solution for the ladies OK these about matter which described how you cross the transition between not that easy to raising the strictly equivalent to the equation because if you the rewrite the the correlation formula monetization of you some insecurity principle are always an equation of that kind of but the big difference is that in the could the transition from the feral magnetism to borrow magnetism the apartment that is not the experimental admitted certain things like Jean divided by to see the correct temperature so 8 the 3rd phase transition in that sense but it is not a phase transition grievance by the temperature it's a phase transition driven by a paramedic which is the amount of the being that you have in your amplified to you understand this equation here the evolution of the after June that it increases because of the population inversion in decreases because of the losses in the cavity and your oversaturation bombing this is in question so and there is a very interesting problem that it in the regarding this analogy there is something mysterious in the in the laser transition that when the laser starts North in the equation that you what is the phase of the race and so you have all these argument about spontaneous symmetry breaking and the fact that my laser which is in front of me there is a mysterious phenomena called sport that has symmetry breaking that makes that move face states a supplement you you have exactly the same problem was monetization when you quarter as some foreign bureaus agreed temperature nothing in the equation that their minds a direction as amended but anyway basis southern direction and again you can invoke the spontaneous symmetry breaking people announced by the allied to speak of spontaneous symmetry breaking you exactly the same problem was abuzz emotional state nothing in the equation that you what is the phases of this condensate but people invoke a spontaneous symmetry breaking but you are not forced to do it in quantum optics we don't like spontaneous symmetry breaking and we think that it is not necessary but the answer writing so yes yes it was the 1st year of the war it you say that the only thing which is event if you destroy the laser beam not resisted Atletico theory but that's a quantum states you can't say that these quantum state does not face but when you are going to murderers of phase what are you going to do if you are going to compare it With a phase of a and that's my government we'll be a measurement of the related phase between the 2 entities a measurement which gives you a given faced in other words it's for quantum mechanics the face of the cannot exist before the measurement it is a measurement which makes effects you see that there is nothing inconsistent and saying my laser beams here has no phase How can the value but when I was a Muslim and I have to find something and so evident immediate image from students be following going to make mechanics formal holdings which is I think a very good preparation it is a classical in which the the complex amplitude of my laser is a random variable was aware final during the modules about calculated with the equation with there but we just phase which she's randomly uh between 0 and 2 5 which is between 0 and 2 and then I said these idiots ensemble so I described my laser as a member of the ensemble so when I'm land lays in front of me a switch it on and then these ladies quite so sudden phase but actually it's a member of the began summary and the honorable thing is the the the world offices well tomorrow nite they used to tell you that the single susceptible to more alike going to talk about difference with a single photo it's went on that the single photon Arsenal phase OK because it's a folk state folks status the face but we could anyway and different speak with a single at and I can tell you before we did express the experiment was seated around here many people told is competition guilty or not going to observe anything the no face the foot on us in the face but I can take my photo speak it into recombinant sorcerer lady he doesn't know phase but I can speak overrated phase difference and so you see my teenage of taking it in and out of an ensemble see these 1 as a phase I don't care what it is but it does 1 and now I had the phase difference Ivan interference on if it works but be careful it does not work always because if it was working always between me and that hidden variable do exist and hit the right level do not exist because with a database of so this is just to annoy you but it's about that but it is true I mean these teenagers are very good except that you must know that sometimes brick but before that breaks out very useful so you have to see the moment when they were asked to quantum optics the basic idea is to cut correlation function I will never observed directly as a phase of a laser I weeded out the laser and deferring all beating Weezer policy later and when you take all that into account you don't have you never have to invoke spontaneous symmetry breaking it convenience but you don't have to say that it is a fact of nature people in condensed matter are quite serious about that the things that it is a fact of nature but at the end that we agree in the future this congressional it is also good Facebook Mario Williams and particularly useful when prepare these this means there is very little of his little of this Tuesday and we life it's around here know we yes yes but it is so is the answer is yes but it is irrelevant for the phenomenon I'm enduring it doesn't mean we're when he does not play a role or in observing the facts of the correlation the reaction was agreed and then it should be In the density matrix describing the various governments but as I told you when I do with the emperor Bryant Reeves experiment I forget about the 2nd partner so I do a partial trace from my identity matrix Insulza all washed up OK you this summer it's because of special traits so I Transformers :colon entered metrics into work the mixture and so the sample just looks like a total Inquirer sample like a summer crowd should provide that only half of the adults these ensemble looks as if the whole crowd booed course of yes "quotation mark the question which the material this that best work breweries trigger from 1 point of view and not from another once a word that the early years of the yes you can say that the world and that also were you billion extra absolutely so why it was to what does to Lewis when the mechanics said that take the same recalled in and now you're looking to correlation needs direction and then Ziemba remind to is correlations and you are not going to have a bright which was built by a so these so you have chosen medium bowler describes on a part of what we observed so the only consistent description of everything we observed is a signal continuation description of it's very relevant those only fits that's too there is no way to understand by classical by classical could direct considerations that what to use the word not to use any of the leaders of the is have relations with the area is a number that's us I explained you I can perfectly well understand the Embry Bryant to its effect if I have the idea that it is only way but that's soon that I think that the partygoers 109 lined with effect must be if you want to take into account the fact that you particles then you need to use a 2nd equitization because anything that civilization is the right way OK what is waste there can be classes of quantum phenomena that mental phenomena folksinger partygoers it's wave particle annuity day the fires that I can send the an electron building and therefore mountain observant difference but it's always single particles all of these can be be described in ordinary space I can have a way French and propagating and all the Uri space so I can make a sense of that by thinking of classical ways and that the end deciding that the square holders of that weight is the probability of the taking the particle here OK these a consistent image but then as soon as I have to talk to us then if I want to have simultaneously the party stated the wave aspect I cannot expect as I cannot avoid signal quantification I only consider that partygoers and they don't look anything it's that Newtonian mechanics works but the I sufficiently detailed looking for is a discovery Ribery's correlation I cannot avoid 2nd quantity to describe the consistent with the whole world you the stimulant nobody so you you use stand for Monday's Wiese creation operators and uh but you know all that using 2nd Quantas Asian dates to account automatically the quantum statistics because you write the data when you write that the candidate of AA and a bag equals 1 he takes automatically into account the statistics of once and I am not familiar with tournaments but you write that the antechamber data costs so what it does to hear or whatever then you take so automatically into a crevice statistics of family the at the 2nd decision it's a mathematical ordered to words To what Indian and about the mechanics when they take you where you have to say that the dominant and that's it there which is forward and in its and Tractebel so sick of quantities Asian it's a technical ordered to work to take into account automatically the statistical at so so you have the addition of the amplitude with the correct statistical weights and the fact that on so You Want Want to simmer tries and then fall Bozo knew of Tucson tries to use wire how it works and I think that there is no way to escape that but I think that it is very important to understand that there are eerie 2 different classes of quantum weirdness optical quantum weirdness ferries and what I told you and I would go tomorrow evening the single particle beam speaker item 1 side or until site there is no classical wave which can do that to classical ladies always speaking to Z's 1 class of quantum weirdness game by seeing what is remarkable for its use of the mechanics for single about cost and that you can always think of classical ways in northern respects as soon as you up to you can think of amplitude not in the ordinary space in an abstract suspects and he's from that that normal Connecticut it's none of that group getting From that when you try to take these abstract space and to say that what happened really space and then non-league none and none of Indianapolis so really condom accountants of minibus courses much of unless there is a very important question that's OK thank you


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