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Long coherence times with dense trapped atomics
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00:00
this collisional narrowing and dynamical the coupling very much and I want to thank the organizers with vitamin for inviting me that I come for missile which is far far away so if you want to know how far if you imagine has the the blocks the and is and will be imposed on the polarization this would be the polarization so almost Twitter followers difference and the slope was done they basically my students you also did most of the work is not post OK in G that was the Jean the Donald is a state unequal but in the book is also graduated this is done in collaboration with 2 Tilley Globes muqarnas models of the people from Princeton and the core with corporate also for white man and so what you see here is that trapped cloud of atoms the temperature is stand out you michael kelvins this'll will be due models of of Indianapolis still notice just the somebody of art on and sitting in an optical lattice in the density is quite high is they on the order of 10 to the 13th and 14 onto the center with a Q is about 4 or 5 orders of magnitude then sell then there is a atomic fountain so if you go to experts in atomic physics which modeled about long coherence time they would tell you 2 things 1st never looked at the utterance give them fully so they have the fountain which this thought and then it goes down to be able to encode dated and 2nd became the density at all so not the even in these low densities of optical fountains the interaction between the atoms is the main enemy that limits the performance of a comic books OK and I'm going to concentrate on the opposite the gym and and to show you very dense outcomes they get almost a million times denser than use optical fountains atomic fountains and to get these density I need to do it and indeed you will see that to get long coherence and in this Aegean is a challenge so 1st what they want to do is to tell you why we bother why
02:02
we do the opposite by we use trapped and why we work at the high densities so it for this audience I will use these example of a quantum Emily so people have showed that you can that a quantum state of a photon onto an atomic and salmon we will use the collective interactions so the fault another inductive each protocol Apple but provide some a collective excitation is sometimes called it became state in the public system and for that you need the optical density of the cloud behind so this is the optical density behind means that it's really dense and and this is a fidelity of upcoming memo so you see that you have to go to get nowhere else you need high optical densities soon at high densities to couple effectively a fault on to this atomic and somebody so we have to go to high density we have to go to to move 2 trips there are some others that their motivation which reaches the full these audience you can achieve stole money out people fought on many onephoton this a pi phase shift in and out of thought on in these kind of systems which combine high densities and long coherence time will know you can make you can they collectively coupled such somebody to a superconducting qubit people have done similar things and you can make clocks which portable it and I I was I was 1st this aspect of the problem is this is a unique model system so what we can show you the high density means the government got with each other they collide they that they they induced the sheets on dada is so it's an interesting manybody system at the same time they're all very very well isolated from environment so people you be following even after me with that you know how to isolate your to a system formed environment the environment is typically dirty it's composed of magnetic noise at compose of the electronics we have similar examples in this system the environment of 1 of the outcomes is all about problems in the system so environment we should think of a to have a system is 1 apple but we understand it very well so we're going to start a system that we understand very well but I hope you'll see that it's walls why because we can really established in the tools that will use just to give you 2 0 into what is our experimental system so lot of standout recording interacting skim off will be due this result because leopards these 2 course younger begins so it's they followed tune you don't stop of photons we do all the standard cooling scheme and some left bundled calling once and typically what people doing such set ups the achievable Aijun corners it so you probably seen this that the velocity distribution pixels many many times this is the peak of the bull fashion Connes that but in this talk I am going to concentrate on a firmer ground so it cloud quite close to BEC the phasespace density if you know that this a few percent we realizable is it 2 wee out code we have advanced but is a classical I we use mostly classical language to describe the motion of atoms you're not far from the quantum the Genesis what lot whatever system is the ground state money full of will be doing this is the hyperfine splitting 6 agent there's often called the clock transition why's it called the company's not because it is useful clocks for example the GPS clocks is this this why do they this physician because it's very well Cocke dies and very accurate images well going through the modification so this is they out 1 of the elements in this is the other 1 is called 1 minus 1 and it's is to code to 1 side you see that we need to focus to connect them so we have to divide the this would go control at a microphone and out of thought on not technical advantages of using these 2 levels rather than them all a commonly known as the alters the your transitions and 1 of them is that this particular magnetic field which is called Magic magnetic field this transition is the money in incest OK so the insensitive to magnetic noises in the Ottoman you totally insensitive to electric noise is so well related in all the talk I will not discuss about the interaction with environment when I environment and in the other models in that they're which interact and collide with my and and and this is the kind of Fe obvious elation weakening impose and we have a few days ago about as much better than 99 point at the centers will mention so it's my was we know how to control the way so it's hard to high density and they're going to be interested in the effect of collisions I think in the collision will affect us in several ways as it said he'll it's good it's bad and it's beautiful so 1st I show that collisions of would be good in the sense that they can bore the coherence time and this week or collision mailing similar to motion knowing in emotive blissfully view I show that called collision when called out of school life is a very unique type of collusion anybody could single collision event completely randomized the motion of the out of this is called S with Scott that if you so it's a different kind of fluctuations and the skating nature event completely randomized you'll spectra among the distribution thank popcorn noise collisions also bad good now but if you want to do echo suppose have some Gennady as people showed before you can easily go at it with an adequate inspection I but because of cohesion the environment of our twolevel system changes as a function of time so a common will fail and we have to do many anklebiters in this community is called and the coupling and I show you how to understand and optimize them and and that the company in the presence of collisions and finally collisions of soul of bath boxes was also mentioned before can be characterized by a spectral function so it's a very clean spectral function at the winter and it comes from the for it out of the correlation function which is focused on posters for collision is exponentially decaying so we can measure it and we can optimize the dynamic and the for this particular bus that we so starting with the good collisions squeeze that
07:56
helps notion of fluctuations which help is very very old and always as for newspaper when he's used friends if and what they realized is winning you don't animal in the liquid you get that much snow alliance then when you do it on a solid many orders of magnitude nowhere oil and a year later this is the result of the fluctuations the fact that that in this environment of the molecule is changing in the molecules moving OK of alleged without extending the it it's like a selfmade echo all undermines anemic and the coupling the system is performing on its and this was labeled demonstrated that had been any other type of system quantum adults michael public is set up and well going to show on Belgian and that is only about going to this 1st it's useful it would help us in 2nd year they said we have the controlled system so we are not fighting a very complicated environment but we are fighting the collision about spectral which we understand very well and we can control so what I what is the system
08:53
so this is again the this is Lundegaard 11 and what I'm showing you here the trapping potential ax differently on 2 internal states so you see the fact that level separation depends on the position because of the clock and exaggerated here I made a 50 percent differences in the optical that that we use the difference is dying is on all of 10 to the minus 5 but still being an atomic clock will always limited by those small effects so we have to fight so the fact that an alchemy sitting at a high energy level means that it has a high and 11 separation and keeping a low energy level because a and separation this is the result of that nobody knows how to make a perfect in the sense that it does not stored energy that we do our best but is not of so what happens if there are no collisions at low density every up on has a different frequency in reality the of oscillating in the letter you could think that the frequency as a function of time but it is of little think of a quantum picture of an atom is such OK so each L here this is the phase of the function of and we have aligned with this law is the frequency of each of any difference so these are the has been slow befuddlement that so when you see that as a function of time we get a spreading the phase distribution and when this this division becomes why say pilot the UN we have to face on the contrary if you look here the collisions between outcome that means that have started from slope then after sometimes it collides with another outcome so that it was hot and I would collide with other atoms would become there so the slope changes so you can see that now we have instead of female slopes we have this sort of diffusion in phase space you up down up down which means that the width of the distribution laws not linearly with time but only square this so it's still which is good so this is what we measure in order to measure the
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width of the distribution as a function of time we do what is called lance spectroscopy as many people here said we prepare the coherence of the pieces on the socalled by over 2 past would put us state the equator off the blocks fail then we wait a variable amount of time and then we met the coherence on population and we measure the population is the 2nd part of a 2 twopart which is shown here so you see we have with this coherent superposition acquires the phase and when this phase becomes distributed widely distributed we that on the fringes so here the flanges and this is low so the collisions you all know this is the collisions per 2nd and this is 10 times higher densities all the other parameters of this state and what we you did because we see this in the than ever was on the fringes which corresponds to the coherence in this example after a 100 ms source also you see that when you include the density initial you get off the fame because the announcement about here this is about the time of the 1st collision that the decoherence the Council so even with your naked eye to see that high density the coherence time is longer than the low density of so we get a long and so no spectral induced by collisions if you look carefully you can see also that the shape of the decoherence the shape of the Quillen function changes so we start off with a golf see and this is not the general on this depends on this system did because the they the coherence is the forward transform of the spectral without collisions so here we have of the gulls inspect along we of the gods and the coherence and it goes all the way to the noise level but he'll at some point the Golestan goes into a linear flow which is an expert so this is not intervals of this depends on the shape of the distribution this is the expression relating coherence which is the other of this set of diagonal phase and and this is the late so the width of the distribution in this way to see when the linearly go that Gulston when it's quilt it goes like an exponent in this exponential decays universe it does not depend as and full gets their Wegener's spectrum and it only fails to the correlation time of which in our case a reminded effectuation so collision without a lot of this is for some courses we know exactly what the correlation function is an exponent so we get an exponential decay in this is universe so now we
13:09
repeat this measurement we measure this decay
13:11
time and exponential a gym so this is what we measure the decay time and who would change many parameters for example we change the density so this is the collision late and we change the temperature we we change the temperature we change the images decay time so this corresponds to the decay time at low densities when there's no provision and what I hope that I convince you is that corners and this is the light of collision includes the coherence time as you see here the thing and and also the collision time depends because it's diffusion process so it depends on the square of the Inwood in this decay time without OK and and this is what you expect may and this is what our measurements so we see no slopes here as you includes density import coherence time and we see the expected behavior as a function of the way in which it is because what is sort of nice feel is that you can see the the molecule bestowing the all if you want long coherence time you want to think so 1st you want small in gender thing for our system it is low temperatures because the temperature changes the the in which how much how much in which energy of the clickers sample and also we want highdensity so what is the combination of low temperature and high density in offered it's called
14:29
phase space density and you can see that we have got a quarter so this is indeed the universal the system all that you have to know is what is the phase space density and some atomic constants and as you change the face presenters you see all these different densities and temperatures callups on the scene of slope so that's all you have to lowtemperature highdensity if you long coherence time because densities would stored collisions has the I I want to mention very
14:58
very briefly that when you go to the highdensity energy and many many physical effects at the Cu I only told you want that the quiz wind up on this is this scuttling quizzes changes the trajectory changes the energy but this is another example because all the problems in part also by this effect being wise interaction and this has led to this fascinating physical effects which closely in favor phrasing which is another mechanism for recall I'm not going to discuss it but at this now it's a very active field so many people are becoming interested in what happens to outcomes at high densities and what kind of effect can actually help us at high densities which we used to be the forbidden energy from a single tried as it is not always and also mentioned the other experiment which it we did to get those that will perform on block suppose you don't care about collisions but you still want high densities is how do you do that how you take many outcomes FIL volume but keep them from colliding so this is the ingenious solution it's called the multiuser laid off it's a very very including quantum states but for our purposes it just means that you make an optical lattice and you make sure that in each side of the luckiest an exact exactly 1 outcomes which hasn't hope and this is of course this type of the local then you can use this system and you can do the coherence and measure the coherence time and stole information and this is the opposite of it you have absolutely no collisions so this also exists OK so people have thought about this problem before 1 below 2 names of before because the vote carefully about so they're smart people so and and what what the model for describing this fluctuating a frequency is usually a very simple effective undergoing corresponding to a twolevel system this is all excited state is about atomic frequency and then you have some still hostage so this is the facing modern people discussed me and this is a lovely how it looks as a function of time if you take a certain up along the fleet optimal the tuning formalism of fluctuate something like this and you take this this values from some kind of a distribution which I call the folding modernist bonding and you have to know what is for example the correlation function of this a store courses and many people assume Gulshan forces that such as these people because then you can make a nice predictions know Our pulses of conduct occlusion doesn't look like it looks small thing what happens for a particle out on it is moving in the a pretty good experience at a constant frequency and then it collides with another Ottoman Iowa's again I you that cold collisions in this Scotland gene other very dramatic even after a single collision event and Apple changes almost completely its energy OK it's got those 2 or the election with the same probability we call them how the collision or 1 demise including so you you should think after a single collision event you have this this can to jump in the frequency and most completely chosen New London value form the distribution because still a thermal molecular OK so let's compare that after it what what is seen different between these 2 forces so I can take the same distribution for both of them which is governed by all of this is that in which I think I can even think the same correlation function so this and this can
18:15
have the same as for example exponentially decaying time correlation function but still there should be some kind of a difference because you see this leave a like a continuous on bosses and if you skip that on so there should be a difference and we should be sensitive to this difference because doing very precise spectroscopy so this is reality this is what we see in our system or what we expect to see and I'm giving you some odd example will people of seeing this kid fluctuations sometimes it's called telegraph noise when you only have 2 levels we have not levels but you see small systems often jumping frequency other than a move a continuous this is another example with a single molecule so we like this model very much because it's very simple and it also corresponds to our experiment for example if I want to know what is the effect of collusion I can do a very simple calculation which I do together with you so I'm again looking for the coherence which is then some beloved of this acquired phase I just have to integrate although these some of discrete constant bosses you see how simple it is so if there were no collisions I just have to integrate the phase so you see the face is just a constant tuning multiplied by time and then when I put it into the distribution I've ever told you I just never the coherence is the for advanced form of the spectrum can't quite spectrum the spatial coherence time so when I do this I just have to sum over the London'' said and they get this very beautiful result we actually discovered it but then we found the tape and all of its long time ago so this paper the and look how simple it is so all you have to know is what is a forward pass form of the spectral this is the the the coherence without collisions and then this is the last ones fall and you have to know a single parameter was which is the collision with a focus on collision and at the end of is analytic the so this is a very simple model and it also to how case another nice thing about this model easier did you not assume anything about the spectrum we don't assume that it's calcium looking it can be anything you don't even have to assume that if his final moments and I discuss what happens when you it we have affected distributions a bit later so doesn't
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walk so we we take our experiment we have a gall simpler we can conclude the and the galley and then we can again use analytically and get what we expect to see the decay functions and show you again this is the coherence now I took the envelope of the flanges as a function of time this is what we measure at low densities of those who a fast decay and a pile density we get this in this in coherence and now you is this analytic for analytic functions without any free so measure everything we measure every all the particles here we have no food and we can get almost perfect agreement about so we can get quantitative it few percent level without any fit parameter understand the effect of collisions oldest or plastic bosses in our system it's a good model system we and and and OK so as
21:18
I said we have a simple analytic model that describes as what fluctuations to prospective so I'm showing you suspect long but don't be afraid before I showed you go here last therefore you really so is this so if I showed includes of coherence I'm going to show you know InGolf perspective is the same so what I did I talk in a different distribution dishes assimilation and this is called a student the distribution and it has a powerlaw decay so it's belongs to this live a family affect distribution and then taking that those would be federal and certain in fact which means that no 1 knows they village so this is a a a the tail with 1 and a half and and this means that the system and has no 2nd moment but fruitful smaller and when we come up with respect the continuous without collision without punctuation as and it is with fluctuations we still see this knowing so it behaves normally even though it has no 2nd mom so it's still knowing on the other hand when they take the tail of the distribution to the case law well this is now a division solutions effect OK if the sliver distinguish and what we think this is the distribution result collision and be the best thing is we is collisions instead of becoming a node becomes wider so on the 1st moment I villages fluctuations would opposite effect itself knowing the distribution that make it wider and false you could say this is not physical and and in some sense you I but I want you to remember that for example the Gaussian distribution below and so on already has a big building voting 1st moment so it is up to some file cup of this is physics this is shown here out so you've seen these this is the label fluctuations and this is the favored the width of the spectral so we say that when they when the 2nd moment villages with the collisions board and the spectral as opposed to the normal behavior which is knowing of the spectrum and this is the Gaussian distribution which is fast and of course the for task from often Antony is an exponential we start with an exponent and collision give us an exponent so this this constant of interviews and I think skipped them at the medical report although it's extremely simple remind you have this very simple discrete model on we have to do is to to solve a random variables and when you do that you can mathematical people in this we had some help at least for what is called a stable liver distributions the Platalea which I showed you his mathematical equally so I say it again if you have a fine at 1st moment you get knowing of the spectrometers and if the 1st moment I villages were Gaussian distribution is there is there is need of Europe's cultures of 1 then you get the opposite effect so this is sort of manifestation of the central limit dealing if you add virus no matter what the hour they always supported thousand and this is called diffusion in this will be in so the diffusion and I I want to give you another manifestation how these things work so what I'm showing you here so this is a if I as a function of time and this is the coherence and let's look you in the beginning so this is a normal distribution it has a fills moment in this division that had the 1st moment inspect on to get the the coherence of the former task form and you always get his old that Ivins and then you have a collision event so a collision event in the language of the you know is sort of resetting time to see all you forget the past because it might allow collision completely said the dynamics the completely randomized and the energy of the atom and therefore for the frequency so you have seen so again you start with the overall deliver the the derivative and what you get is that the query the case slower on the other hand if we have this vector is and we have been building fell small met so the mathematical property what is the price that you pay for having such a wide frequency distribution you can be seen from the derivative in the forward OK so you became very fast initially but then you slow down and then you have a collision event which elicits time and again you get the infinite that even if you that here know all of Quillen is the opposite and it it creates fossil decay of coherence old boarding of this so now let's go to the 3rd topic which is we have these collisions with situations we want wouldn't follow people on in which the the blue a call and people have discussed here equal along a let me show you can look at these 2 pictures so in our language and call is instead of doing that the by buying them it at what is a pipe by do we prepare to live a system each 1 of the state's a Q metaphase and then the by byproducts what makes this opposite and if conditions of static we get this phrase online and then we went out of my so this is what you see here and and this is done at low densities so here we don't have coalitions and we see that on the decay time and then we see the echoing city go up from 5 milliseconds to about 80 ms so we get the fuck off when the enforcement echo walks because it compensates for the was ideal for that that which is static no no collisions and remind you there's no environment if we do the same at high highdensity so fast of this is about 10 times the density for to see that the they is better this is what we call before this is the collision knowing OK but then when we tried to do their call when we try to invoke the dynamics we go from maybe in MS we almost only know face because of collisions and then you can think about it if you have a single bypassed even a single collision event is enough to almost completely undermines the dynamic which means that whatever phase you accumulated between these 2 byte as you will not get the opposite phase in other ways in a single collision event is violent enough to be stored in a cone so if you want to do things to what would have to do is to many many bypasses and in particular the number of BI pulses has to be much larger than the number of star us the number of collision events in again the way to think about it is now I have these many bells of the events which was them we can call a call for example the installed and only when there is a cohesion summoning them and we are going to fail and all the other bells are going to be successful OK so that the started to just by pulses and and most of the but most of the tales divided by bypass will not have a collision will compensate only the bells will will collision event cos will contribute but the contribution is going to go down because the is short and because if you also random what forces were going to get public and this is what we see here so we'll Winkleigh's the late of the pie positive this is for example a squad of an article that coupling ladies is faulty parts bills of filming that and this is the coherence standard we measure so we start with on all of a hundred millisecond coherence time this is what should you fall and then we get up to about 3 and a half seconds Quillen time is this about 200 400dpi persons and you see this nice public and again what will the the public on form it Council defended as you increase the number of bypasses you decrease by the same amount of the contribution of a collision event but then you have to take them as a square root of defend because is random walk to get the square of which is nice because as many people they told you to be more and more by parsers is difficult at some point you're going to cause damage because your bike as a sum of perfect no matter how hard you try and so this is not the goal of a quantum state and of course we have to show that his general on so this is done for the 2 positions on the bill of sale issue the state and is why state and we see that there we see this on the nice on the coherence after I think 3 seconds and is the same for that and if you want to leave and mostly we have to do it for the entire
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blocks film and this is as people said Paul system although in out this is the bosses them over the off identity so we want to keep the blocks filling factor it does not stand part because of this the phrasing so that undercutting hands and what I'm showing you the experimental picture of the blogosphere somebody mentioned we knew who was measurements book optimizer blokes feel when the process is being young during a moment some processes in Arkansas remotely up and then we need more but for you know bosses says and we we concocted as a and for them to say after for effect that this this bosses system all of it that's what happened so you see for example that it shrinks in the equator this is because of the phase and it's gonna be able to fix and use the 1 processes which it because the population and and this is a more quantitative description of the density matrix transformation as I said all atoms interact with each other this means that if we think of our method to whatever system then the frequency of a twolevel system depends in a very complicated way on the induction is the Thompson in particular it depends on the difference between this coupling this is this is the scattering of people up state 1 blot on to state though and this is another means that 1 in state to this is a small effect actually does all that in in our common will be the another cell almost the same and this difference is only points % of the tee because frequency shift people know OK so we're looking on a small effect what are these effect do it means that as a function of the population if I change the the height well I'm along the blocks here I get a different frequency and this is manifested still taking a different plate Susumu what the velocity is doing is he's twisting so it's not a house Villani as before it is not only about dating and intially that it is twisting and it's very interesting to measure this twist because this is this is artist squeezing operator it is important now so we can measure it using dynamic and the copying it's a very small effect fortunately for us what we are doing with can be company with taking a stake here and then with the pie possibly go boom boom boom to a changing the sign of what we're doing well now link on the other perturbation except this 1 because it's the probation depends on the proper on on the side of the population if if you and if if you because the opposite side so it's like making making a looking on we have modulating the population of the outcome was that bypasses and by that we are on the sensitive to something that changes with the population this is the nominal affects all of their efforts go away and we have in the initial results which seems to be in agreement with the T. it and but the It's still clinging on so I was very naive language to describe you the collisions but as I said we have a an exact mathematical model for them which we understand very well that MIT remind you again you've seen this picture only 2 or 3 lectures a this is called the overlapping because what is the overlapping and not under some assumptions which are not always correct you can look on the coherence of the phasing as a function of an overlap between 2 spectra this s which you see here is a speck function of the bath this is the for transform of the time correlation functions of the fluctuations and as I told you so but I we know what it is for our collision modern and this is your system this is that the system and and and the system it what you were depends on open port so this is manifested here so what we want to do now and and editor so the with us on a single measurement is done we want to Cocke I've s and for that want what we want to do is to to the very simple filter and the same we know is that the function and how do achieve it that the function you take your system in your excited with a continuous lobby parts was not bypasses it's just long bypassed which statuses them up and down and up and down and this gives you a bit the function was this this well centered around the frequency that use so what happens if you convolve a delta function with an unknown function just get the decay depends on the spectral function on the OK so this is what we do modeling system at a given our differences he only got and we measure the decay and this gives us 1 point and which it would do it again and this gives us another point
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and you say and this gives this following graph so this is that the frequency that we use this is the decay rate measure so each point here is that is a whole measurement of the decay you've in the fall and let me assure you begin green points are about to those interesting stops as nonmonotonic and now we have a tool that that naturally skip the red ones and only concentrate on the situation this is Stewart is said we have a good to we far system so what you should do you should compel their fueling again was no parliament those to the to the adults and and you see that there is an interesting about a here the lens and I promise you I'll remind you again why do we have inspect all because a for a transform of a correlation function of a Gaussian process as simple but you see the bit a surprising feature this comes from there oscillation frequency that the psychologist evidence forget about the motion of the outcome which was to this little which because of its all thought but to say that if you model ecosystem very far you get in those with another resonance frequency of the system so this is probably the oscillation frequency without also so moving and if you die the system was obvious stationed that frequency you see that actually instead of fully reducing the the Quillen say that says so we can if you want real sensitive to the motion of the in this menu in the so now what we measure in and let me also mention here we will consider there's a difference between a day that's this what end discussing the pair and their so even eventually doesn't agree with itself had had an experiment shows the want your interview is and and even his told you is a monopoly because in this Aegean will we don't modulator system strongly is not with the cup and there's a mathematical definition of a weak coupling say is the amount of the defacing of the system at the coalition time of the bus this is weak or strong coupling so this is this is not happening is that we pick up the overlapping begun poachers along and you need something else and this is the solution that we understand that as well as if he we have it is 1 QE which survives this is a big assumption so what do we do next now that we know an enemy now that we can optimize the boss we can try to do then I becoming which is optimal and we know that in the previous lecture a foot for missed a and again I see the difference here that you we have a bath which is in inherent and we can get rid of it because we need many outcomes and they collide there's nothing we can do about it but is simple we know and we understand it well so what I'm showing you a bit complicated this is now we do they not occur the coupling and this is the number of parts that we give and this is the coherence answers so we passes and we get better and better coherence so its 1st lookin' that this is what we get with the PNG this is been banned of periodic identi by the company and a lot of sequences discussed extensively this is you in in this concatenated only see that it slowly
36:22
you can see that in our system the PNG performs best now these are the lines here at locally kindly because they're not your reader another experiment so what we did here we do with the measured aspect on that's way to be noisy and put it into the overlapping the got and this is the this is their performance we expect for each 1 of the dynamical coupling because you know what is the future for each 1 of them they know it but on experiment to see that saying that the agreement between this experiment in that experiment look sort of reasonable it is to get the same the same plant and and both of them I agree in the sense which which bus sequences that though the mass actually we can pull this analytic and we can show that for a lowend Sambath Bechtold Scipione G is the best solution send them a you you may you may be able to
37:10
see here so this is again the overlapping the so this is the food the function of the G is of the few the function of you wait for the expert to see that you would have no sirens you it's very very flat so had I had a sharp cop in the spectrum as many people said you would of course would win but because the and soft it doesn't like you would any prophetic 1st attention so let me summarize
37:36
this pictures so I showed you that for call that Comecon sambas they have to be dense in order to be useful for example from always so collisions are in hell there must be collisions between the outcomes collisions can be would make increases the coherence time no the spectrum this is another just to this motion going in and out but do we can that we can have all that a monatomic viable so we can really understand it quantitatively I showed it the specific of fluctuations that we do is this cold atomic collisions our very unique in the sense that a finger could you collision event completely under my eyes respect and this is very different and the uses a Gaussian process and if it's 2 different predictions so in some sense may made by measuring this but the effect of collisions on the specter of this system we can tell you if they are how although soft but if we have a good enough excuse so it's it's said that the the the copy we can't they did that the coupling between dynamics and spectral and use it in the opposite way because we know how to measure spectral very accurately I showed you that collisions also bad but we can still so that if you want to do echo call we we have to me many pulses so this is called anemic and becoming and we can get coherence time of space 3 or 4 seconds instead of 100 ms if feels that some 100 busses I showed you that this this kid collision being such a simple system I can give a I we can we can ask questions which we could not ask fall for example we can ask what will be the effect of collisions for distributions without moments when we saw that the 1st moment of the distribution by villagers medical sheep and wider then we get the opposite effect of fluctuations the widen the spectrum they shorten the clearance time we saw that we concocted the Bassas's is this in the simplest way is just to give a continuous lobby oscillation to your system so that that the function that you have to convolved with the unknown spectrum and that gives the simplest interpretation so you know how to measure the spectrum and the degrees is 1 queuing up with the other but for would and goes in this demand you is long and I'll skip that because again talk about that so I think you
39:50
here for a very clear talk we have time for some questions so the question was about the modern so
40:07
states and I'll always so in a modern selected stay the warnings or not so interesting become they also from the fact that the atoms are trapped in a nonuniform envelope threat so unpleasant but if you can make in optical lattices which has it is that the constant intensity that he was not a boarding but nobody was able to do it so far what is the definition of the coherence time that using the instrument the what is the definition of the I will how are you define it like detector known exponential decay and find some rate know it's it's if you wanted to contrast of that obviously there's it's their expected in some allow the edge of the offdiagonal element of effective way to make the juice crews among you as much as as long as you answers this is to have the coherence you ask what is the core also at I what is the coherence was what is the coherence time yes it's a 1 of indicator no it's a start to the problem as a shot and then interview more bypasses at some point you start to do more damage then than you do good and this was discussed and we also have a paper we are writing on that so if you want to add that no more than then you have to include the noise in the control of the federal pie parses benefits for example we give 200 bypasses now imagine that each bypass has a 1 % l all that a limited never to handle and we don't know where we are so in our case I showed you of course the best results you said that to see game G works best in Europe case but they assume you only measure the component along the rotation axis of the CPM people's right no we bosses tomography so we measure the entire looks that that's the question all right so I I think I always using a pure dephasing model of no menu menu measures a decay times for C. P. and G. you use a measure both components but it did you get the same decay time for both components yes I showed that that will be very astonishing when there it's not for the following reasons that but you up to
42:42
the light what 1 of the component is as you well known is the easy component it's it's the block state will you put your by so basically you know you'll just what they can out the insensitive to well the other 1 does this so it's it's a gift worlds so to get this quantity with that will turn out there to fix a little difficult and you also like between because the number of classes then there was a public 1 of them would stay sensitive to the noise in the control and 1 would be become I mean it just said that's the yes yeah yes but but in in all these not in all these that that the other central control is good enough so that the sales from the control not cause any difference between books that makes sense not completely but maybe we can discuss that after of course for example instead of giving by positive you can see here we give some his quote by minus by by mass but there are many to that you know well actually all come from animal community and that you have to do in order to hundreds of bypasses and not know then your system OK I think we have to move on thank you very much again I
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Titel  Long coherence times with dense trapped atomics 
Untertitel  Collisional narrowing and dynamical decoupling 
Alternativer Titel  Suppressing decoherence with dense optically trapped atomic ensembles 
Serientitel  Second International Conference on Quantum Error Correction (QEC11) 
Autor 
Davidson, Nir

Mitwirkende 
Sagi, Yoav

Lizenz 
CCNamensnennung  keine kommerzielle Nutzung  keine Bearbeitung 3.0 Deutschland: Sie dürfen das Werk bzw. den Inhalt in unveränderter Form zu jedem legalen und nichtkommerziellen Zweck nutzen, vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen. 
DOI  10.5446/35328 
Herausgeber  University of Southern California (USC) 
Erscheinungsjahr  2011 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Informatik, Mathematik, Physik 
Abstract  Atomic ensembles have many potential applications in quantum information science. Owing to collective enhancement, working with ensembles at high densities increases the overall efficiency of quantum operations, but at the same time also increases the collision rate and markedly changes the time dynamics of a stored coherence. We study theoretically and experimentally the coherent dynamics of cold atoms under these conditions. A closed form expression for the spectral line shape is derived for discrete fluctuations in terms of the bare spectrum and the Poisson rate constant of collisions, which deviates from the canonical stochastic theory of Kubo. We measure a prolongation of the coherence times of optically trapped rubidium atoms as their density increases, a phenomenon we call collisional narrowing in analog to the well known motional narrowing effect in NMR. We explain under what circumstances collisional narrowing can be transformed into collisional broadening. On account of collisions, conventional echo techniques fail to suppress this dephasing, and multipulse dynamical decoupling sequences are required. We present experiments demonstrating a 20fold increase of the coherence time when a sequence with more than 200 pi pulses is applied. We perform quantum process tomography and demonstrate that using the decoupling scheme a dense ensemble with an optical depth of >200 can be used as an atomic memory with coherence times exceeding 3 sec. Further optimization requires utilizing specific features of the collisional bath, which we measure directly. 