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Quantum dynamics and quantum control of spins in diamond

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I turn good afternoon how we're ready to start the next session but but before we do just a quick announcement about the bank with the banquet will be here on downstairs where we had lunch on the 1st day before they move this outside and everyone is welcome so our 1st speaker's love over sky and he will tell us look upon dynamics and quantum control spins and I I don't think you're month coming for finishing lunch or and I don't know I will be talking about things we care about all vertical collaborators with my for much of the time working with the heel with the group all from a handsome prone technical you're still Bill and for all with the group all the actual 2 hours away from recently the a lot of
interest in a in individual quantum spin solid state and people have studied a lot and some of the systems are probably known to you these quantum dots which which been popular variable last few years of bombs in silicon were they finally achieved the ability to work with a single of those the Center and the the subject of my talk and the center so why do we care about individual spins and solid state will histories goes and their mood for at least small to medium scale quantum information processing but they are rules for the human figure in spintronics and photonics and this is probably very the most fast growing area of the potential implications I precision metrology and magnetic sensitive man scale again huge area they're very impressive potential obligations but of course as
always we are facing a grand challenge how to control single quantum spin solids and for this we need to so quite a few fundamental problems to understand dynamics of individual quantum speed to understand how to control a hope to preserve its coherence and how to generate and preserve independence between 1 and for all these so this is the picture which initials what we want to do I want to be able to pick up a single spin solid-state the whatever we want and Perelman and spins of diamond they constitute an excellent there's that police that along here it's time there individually addressable and controllable both altered so that it could
and at our disposal we can and excellent menu of than any of the GOP and protocols and just to start of the traditional in production usually they are analyzed and classified using mums expansion when we have evidence of 0 order 1st order 2nd order and so on assuming that there the distance between their dynamical to carbon bosses there's more and the simplest 1 spear order dynamical department well when we waited that light pulse the flight of stomach stomachs we consider tries it sold there has been a lot of introduction so we compare this to be due protocol the way that light pulse which twice the plate pulse weight and we can compare to make them put them inside each other or witless Russian bowls and achieve more impressive credible however the foreign you probably for fears starts working with experimentalists there is a moment of truth when you realize that what there were all these fancy and beautiful theories you're going they're totally useless and you have to do something much more mundane something like also errors or the fact that these generated doesn't have not then we call range and build your beautiful suggestions with you there go down the drain all you have to do something else so so what other problems with a standard approach 1st we always hear about the norm such move to an end well and the all these norms grow with the size of the buffer so whenever we're right is beautiful expression norm of age multiplied by Tao don't forget that this is essentially you think and it is not a small parameter that you you think 2nd of unneeded to conditions in reality I'm not satisfied because the yield ultraviolet couple the illusion large but still will know did the work became a at long times is not quite clear because again of these the nature of the cumulant expansion and accumulation of pulsars and perfection is also more on the spilled so this is why we have to usually do some numerical stuff to really help the experimentalists and assess how the code will perform in red and for so so we can do it this way or that way and often we can do much simpler thing than they did not as impressive from point of view but they produce rating would result pages in
so what will be my about 1st of all quantum they control the name of the company in the sense there lately has been spectacular progress there were 3 papers published in different journals probably within the study spent 1 month or so at least I remember Ronald only at some point inside the core the paper an archive and you have or paper an archive and so was but it was fun a 2nd helping to detect decoherence protect the quantum gates and I will demonstrated to protect quantum algorithms in the solid State and correct me if I'm wrong but as far as I know this is the 1st to puberty quantum computation with individual so that's that's the which we finally achieve so what about the characters in the story the simplest impurity in diamond is a substitutional nitrogen we take away problem with nitrogen instead would have 1 access spin so there's been 1 these guys green guys about like Institute doxepin but our environment which 50 your source and and the coupled to each other will language that all but when nitrogen it's Backus see the transformation happens good or bad that becomes a good guy we have these beautiful nitrogen Lecture Center which carries our central spin systems or our you did a vector the red 1 is the electron spin which where after it's actually it's a speed of 2 holes so the total spin is 1 and there is also a nuclear spin of nitrogen 14 it will be interesting 1 all nitrogen-15 among and they're called on site and it will play an important role later and in the center of the skull where the boring direction to a large number of nitrogen so what so good about in the center it can be
initialized manipulated the read out optically so we can look at a single individual spins solid so why is it possible there is a very interesting and not completely understood the school level diagram but to make a long story short we have spin 1 would have 3 sublevels 0 plus 1 minus 0 sublevel if we shine and photon it gets excitable excited-state stays there on the 2nd and pulled back and the needs of water so every time I put on important out for them the photon but if we're in 1 of those states we can be excited then make what is called in this quantum-chemical jargon intersystem crossing and we get stuck in this shelving state for a long long time for 300 nuns almost in the so and even when we come back we come back 1st to equals 0 state so we started here but an engine we came back here and when there is a transition from here to here no visible photons are emitted so if you are in the middle of the year port on the input and output and for the but if we're in this state support on the nothing so and even when this nothing over where polarized in an equal 0 state with typical polarizations of order of 90 per cent or higher which is so initialization and readout simply by shining a green place nothing else now let's look at the
coherence so here we have these nitrogen reckons the center we apply some magnetic field we forget about this level minus 1 it's not of interest for us it's an ideal and here is our cues and we have lost these nitrogen atoms but because of the different parameters a certain frequency is very different from the of this transition so what we're dealing with is a pure dephasing there is just effects of level splitting between these 2 levels and there is some operator which describes time-dependent action of the BoF on on a cube yawning the phasing there now how to deal with its of course we want to make our you want to be completely honest it's a many-body quantum non-equilibrium problem which we have no way to address the analytic in at least and this would have some good parameters which we don't but of in this particular case it appears that due to the fact that Our about fields negligible back action from the central spin we can we replace the field created by the BoF as it just as a random seed number field which is a Gaussian stationary mark was known in that process which is characterized by 2 parameters on the the strength of the noise the which is determined by the spin bought up in between and the and the bottle nitrogens and the correlation time which is determined by the coupling between nitrogens between rings and and we can do direct many speed modeling we can run simulations with beings we can run simulations with than thousand spans and again make a long story short we just can't confirm that it indeed but these very simple model is would not is adequate for our experiments here is the correlation function here is what we get for spin-echo goes just taking numerical simulations and versus analytical model free evolution so the the agreement is very good so what Q. bed unit Gulshan rented in the Gulshan stationary McCaughan now just
being to complete the story we can look at the experimental free decoherence the this is red also experiment gray line theory we can expect it to start time and therefore we can extract the coupling of the qubit to live our theory using modulation induction signal it is because of hyperfine coupling of the nuclear next just to make sure that our mean field models in the correct we can spin I call and we see that in the decays of the predict you for minus 2 Q of decay and the correlation time of the Baucus this 25 microseconds which is long enough for us to do that and go to copy so
so our 1st step quantum control in the name of the company extended coherence time of a single in
this 1st of course since nobody has done it before the only fenders before us of question was always which protocol to choose from the spread of from and we start with analyzing 1 after another 1st was started with P. wake simplest protocol more of you chose and were rendered problem right away it it short times the case 4 times faster then we would like to only at longer times it becomes here instead of thirds would have 1 so if good it's simple but unfortunately the case fast and not what we want so Let's 1st PNG it appears that the PNG as least so the decay at all times beautiful now of course who want to try to concatenate that and we see that plastic at all times if we concatenate used and if a concatenated BMG's sold to cable times and no improvement absolutely no improvement which means that will be just programming the more difficult could sequence without any actual any advantage
so model well 1st of its Kenobi statement but I want to reiterate that of that the hearer spanking can be extended well beyond 25 microsecond well beyond that correlation time of 2nd modernist expansion he used gives us a completely wrong predictions because instead of these decay for BBDO which PMG we care is that of color to the 4th with the help of few symmetrization a concatenation gives no improvement and simply because would have cost more than they can always will have 1 over on the square 2nd moment of these noise is formally infinite and that response to what is probably that that go to north of the law hamiltonian isn't it actually it's not quite independent but it's finding that hurts it's much faster than anything any other time scale in our to restore so if
we know the protocol to be BMG we start running it and we immediately see that x component of protective well and y component is not of the so what's wrong the answer is also obvious control pulses of and it's actually interesting to
see why they're not profit when we're trying to control our the center within the actual experimental situation you she that during the whole path would have only 1 2 3 a selection and we can bring them out so again all this beautiful rotation for a rotation frame approximation the so all this beautiful rotation the frame approximation inapplicable if we have a very hello soul driving then we need to see what we expect to see beautiful rather Salesians of this but when the driving becomes stronger because this is what we need to achieve very short pulses you see that we don't have these beautiful nice oscillations is the the worker and speaking styles in some statement would be John another from up to down stays there for a while jumped halfway immensely and shows the sequence of fast jumps and falls so and this is not an experimental lawyers busy she's reproduces completely by simulation this is just what happens when we tried to drive our speed the past and of course and it introduces a lot of errors in the pulses and we need to characterize them so we did some work how to develop a scheme for the period of the pulsar is then we should study how there's accumulate wealth of that and was sort of interesting stuff hope kind will talk more about this so the bottom line
is that if we apply pulses along acts x component is preserved well why not but if we apply pulses along x and y and use these ex-wife or sequence which was the of the we see that x and y are protected well and this year's time is indeed extended so here you see that the design time is an original about 7 ms although started with we can look at other I
periodic sequences unity unity so what do we see well 1st we do not expect them to work very well because we have a hard in the body and indeed they do not for as well as we expect but there really is a deeper problem with them if we look at the Boston School of also the and here are the simulations where the EPA process where the the parameters of a repulsive taken from experiment so as the steel ex-wife for performs much better than you did and of course encumbered incomparably about better that you unity so robustness to pulses placement or control that again
if we choose well practical correctly if we take into account the errors and if we do things clear very in manner than we see exactly what theory predicts and what does it the 1st or any number of pulses the decay should have these 4 the 2 minus t Q so if we take spin-echo for piles of a pulse of 136 pulses and scale they should fall on the same master curve and this is exactly what its and if we measure the adherence time as a function of the number of pulses should demonstrate and glued to her and again this is exactly what the experiment show so applying 136 bosses adherence use increased by a factor of almost 13 Ritchie 9 microsecond which of great and well actually I wrote here only at the site where limited at the time scale where started being limited by T 1 process so what practical opposed inimical to copy to but this is what happens what what happened last year the
same were doing some other things using dynamical the copying to improve single spin of dormitory or to do the detailed probing of the needs of topics being bot which surrounds a single in the center so we take a single center and started their own dense beans which are it which form an effective by for these particular sense so essentially again in users' ability to study mesoscopic spin dynamics
but this is only half of the story
protecting its spins is would but we want to do something useful with that and for this we need many of these to talk to each other to process information in some way and the world 1 particularly useful ways to make in east of each other is the use hybrid systems Egypt systems are very popular now because because they combine the best features of different qubits which we know about so here in particular of situation to put in these on to the words and use the non-mechanical oscillators as Databoss between them the centers there's been a suggestion to use spin chains but the simplest 1 which you can think of and the moles probably widespread is when we use relative as a processor for quantum information and you speed as a member so and annually with many billions
and lead to get here want to do something useful with so if we think about standard mold of quantum operation of course doesn't work what we can do is unprotected quantum gate but only protected or we can do a protected storage but then we kill the copying not only between their different cubits all which have different time scales but also between our Cubitt and about so we can efficiently preserve the state we can efficiently isolate Our in the center but in order to perform some interesting computation we need to change this thing when it appeared electron spin currents of talking to the this is what we want to
achieve and to build is we need to be able to combine the inimical to govern pulses with the gate operations in a seamless fashion so the couple and compute at the same time and again since we're dealing with hybrid system different units have very different Pekearo some control so our electron we did that will start at the top in our and strong nuclear spins just barely start to so by the time the electron spin get here's a nuclear spin just stop abruptly if we so if we try to control the nuclear spin it takes much longer than that from the picture of so we can essentially the choice of either the couple they electron applied and the company but there no gates possible because with the couple it from the nucleus or we can go gating without dynamical the company but then again we don't have any gate various or I wouldn't look about this you know there was no way out and the way out to use the
resonance Mrs. this and and for this topic all that got gates would present a copy so that our system in more detail in our they can bring this is the Hamiltonian which describes as he is a very fast decay here electron spin I is the very very slow where removing nuclear spin so you can see for instance there here we have to megahertz hyperfine coupling but the driving were applied to the nuclear speed is only 10 kilohertz and this is a very typical figure so let's look at what happens in irritating free if that trunk speed is in a state 1 as equals 1 and weak nuclear rotating around z because the star of fuels if then naturalism the state 0 the star is absent we can only drive the new this flawless loner dates from the accepts
so the only problem here is that the electrodes which in the past between this is the essence of the name of the Cocke and but the nuclear spin should keep track of what was the electrons they long before we started the company at 1st sight then the contradictory but in fact if we look at the motion of the nuclear spin if we start from the state 0 it will be 0 all possibly from spin so that from been will be 0 1 1 0 if we started the electron spin state 1 it will be state 1 0 0 1 and in general the Hamiltonians a different but these rotation axis for the nuclear spin their called they're very close to each other simply because they're both called to x this is just a formal expression so you see that there that their product is almost 1 minus some small parameter and fortunately as announced when these something becomes small and to understand what happens at
this case we can just look at the house being replaced in this case we during the time Tao would have exactly half a rotation around the z-axis so if we start with a strong state if prepared firearms then acts around there the x-axis and then another firearms so the result would have minus of the nuclear spin if Linotron started in the state 0 then with the rotation around x feel rotation around the which does not think and then again rotation around x so all all state is lost X that a that's a resonance and now we can go something went
but 1st we should understand that the resonances that here is just the graph of this function social before dining g there should be less than 1 nanosecond of a hundred microsecond times so this is very of precise requirement should be satisfied if where make an error by 10 nanoseconds the committed to draw two-person born but muted there is also a beautiful thing that the work in this resonance with do nuclear speed additional rotation but if we're exactly you did your number or full workstations away from the as then we can unconditional nuclear spin rotation which is not interrupted by interaction with their so we can do all nuclear gets only by changing the
interpulse and doing and broken concept 1st is protected controlled rotation gate and here you see of the electron starts as a spin 1 the your peers oscillates around the X. but if we are in the state 0 venue stays in place shows only a little bit of T 1 and this is the mean state demography we show loss of the ability of the state of the bill state greater than this way use 97 per cent although where mean about 10 times longer than their decoherence time free induction decay now we can do
something more interesting people stars just the defacing we can show that we can go beyond the t 2 time and which still high-fidelity gets so what's been done here to 15 of microseconds daytime time is longer what you want to do is to create a bill state and again we can do it with for the company bosses on and from and the properties of carbon pulses Linotron but in the on the thing we each we need to care about keeping precise and of the resin and and why would you see 460 impulses we're going in the same way as the Nordic adherence was for so so we
have a working again with a couple of the electron were created decoherence protected game for the nuclear spins where doing it on the time scale which is twice larger than 2 to so and some other this close that but the if it that should select 1 so we can take
2 cubits would have electron spin and the nuclear spin growers algorithm converges in 1 iteration but still if we look at the total time needed to perform the algorithm it is 300 micros and our t to time is only 250 like this so this is the block diagram and this is exactly the scheme of the pulse is applied in their electron channel and the name of the channel I just told we just keep driving very slowly with very slow small driving and will just keep that adjust the distance between the electron to govern pulses you there a half integer number of reflections and if you look at the Grover's
algorithm for instance if we want our target state is 1 up were obtained with a fidelity 95 per cent and here just that experimental snapshots of different stages of the girl robbery 1st will prepare it course proposition freely do of inversion creep again and restored state so the fidelity for the target state 1 up is 95 per cent for our states is 93 90 291 but in all cases where bump of lakes per cent the although again our algorithm time use 60 per cent longer than the spin at all so how would you achieve high-fidelity beyond coherence which is great
so just as a conclusion that diamond based quantum information processing becomes competitive because was not only our work but in general the community working in this area demonstrated already spin photon entitlement protect the gates and dynamical the company so would have all 3 crucial ingredients at least for small-scale quantum information processing coherence time can be extended we show 25 fold and no enhancement of people show comparable figures that article the coupling can be efficiently combined with gates and we can even do of protective algorithms at the Times which exceed teaching times spin-echo time with the fidelity above 90 per cent and just as a side note I think it's nice that this was the 1st to commit computation on individually addressed in state space so thank you for your attention thank his love for finishing voluntarily goes back on schedule but we do have some time for questions so maybe a sound stupid but the what if you want to go beyond the 1 when we need to load a couple for performance IMU-Net in principle it can be done in principle but there are other ways to that that so just right now it's more like It's not they actually made because by lowering temperature you to 22 you have to 1 in minutes Woodruff so this will yeah probably I'm sure I forgot to say the most important thing this is all done at room temperature this as I have sort of this kind that I was wasn't hitting the of those taking the mostly in the betterment audiences in I forgot to mention the crucial thing this of all room temperature so essentially what you have you have just an objective 1 laser and a piece of diamond which you can buy for 40 dollars and that's it you have a quantum computer no I'm serious I'm not joking well yes you need microfabrication led some or how many carrots diamond is this or smoke the speak about a couple millimeters by couple million but don't show to but it's very odd believes it looks like a piece of all plastic has a lot of nitrogen the and and this is very nice so how that you go to that 1 and 2 its what would be the perspective wasn't appear but yeah well again the 1st week down the there is a very successful effort which recently also there was a Nature Physics published last year where people were able to place to and well placed maybe again the work to in the centers which were close enough to appreciate great interact view dipolar interactions but at the same time far enough to be resolved optics so there has been already demonstration of 2 polar coupled individually addressable and these centers actually if I had my computer in half thing a little slide on this because we did the simulations for this it will also show that we can go far far beyond to final also so decoherence protect gates can be done in the skies have case you toss a room temperature that's the limited number 19 no I think it was something like 50 K and much of it but there build be a room temperature as well the fall of the system in the differences in the 1 of thing that maybe let me add 1 more there has been a spin for optimal complement the mastery of last year so just entangling probabilistic entanglement between 2 and V is just a matter of time whoever doesn't for that's so do use these ugly environments with lots of might chairman melt clean mom with very few nitrogens can lower your between what and the 1 with the 250 microsecond procuress time it was a plane 1 but that doesn't really matter we can do well cases the output if you want to get a lung clearance times each year guilt would into this was the 1 with the where the algorithm was done 250 micro so it was a clean 1 but we still need couple carbon carbon carbon-13 spins you cannot go without a it anyway OK so thanks again
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Metadaten

Formale Metadaten

Titel Quantum dynamics and quantum control of spins in diamond
Serientitel Second International Conference on Quantum Error Correction (QEC11)
Autor Dobrovitski, Viatechslav
Lizenz CC-Namensnennung - keine kommerzielle Nutzung - keine Bearbeitung 3.0 Deutschland:
Sie dürfen das Werk bzw. den Inhalt in unveränderter Form zu jedem legalen und nicht-kommerziellen Zweck nutzen, vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen.
DOI 10.5446/35320
Herausgeber University of Southern California (USC)
Erscheinungsjahr 2011
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Informatik, Mathematik, Physik
Abstract One of the most interesting challenges in modern physics is to understand, manipulate, and control materials and processes at the level of a single quantum spin. Beside fundamental interest, this research is important for applications ranging from spintronics and information processing to high-precision metrology. Nitrogen-vacancy (NV) impurity centers in diamond have recently emerged as a unique platform for investigating quantum dynamics, decoherence, and quantum control of single spins in solid-state environments. NV centers demonstrate an unusual combination of spin-dependent optical properties, individual addressability, and long spin coherence times. The NV spin state can be manipulated both optically and magnetically, and the quantum control operations can be performed with very high fidelity (>99%). Due to these uniquely favorable properties, quantum dynamics of a single NV spin can be investigated in great detail. I will discuss quantum dynamics of the NV centers, and the decohering effect of the spin bath (made of atomic nitrogen impurities) on the evolution of a NV spin. I will demonstrate how the decoherence dynamics depends on the experimental conditions. Further, I will discuss how the modern techniques of quantum control and dynamical decoupling can be employed to preserve coherence of quantum spins. Using a variety of analytical and numerical tools, we can characterize and optimize the factors which limit controllability. Finally, I will demonstrate how the theoretically optimized protocols for quantum control have been used in order to extend coherence time of individual NV spins, and how dynamical decoupling can be integrated with the gate operation in the prototype hybrid system, the electron-nuclear spin register.

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