Chetan Nayak, "This Time will be Different: Time Crystals in Quantum Systems"

let me turn to this afternoon speaker Chetan Nayak is another longtime participant in the Aspen Center for physics and an avid hiker and outdoorsman he comes to Aspen a lot and he's done things which leave me in awe he's done the four pass loop in a single day he's climbed pyramid in the bells multiple times but much more importantly he's one of the world's great creative minds of visionary whose understanding of the weird properties of quantum mechanics which get evermore weird as the more we look into them has changed the way we think about things and indeed his work also has related these weird properties of quantum mechanics to things that can be measured and designed Chetan was got his PhD at Princeton he worked with Frank we'll check who was then at the Institute for Advanced Study he did a stint as a postdoc at the institute for theoretical physics in Santa Barbara then he moved to UCLA and then continuing with the Santa Barbara the the Southern California theme he was snapped up by Microsoft Research Station q well he's part of a team working to bring quantum weirdness into everyday life through quantum computing quantum metrology and beyond and today he's going to tell us about a new visionary idea time crystals in periodic systems so please join me in welcoming chuttan thank you very much thank you for the kind introduction and thank you all for coming here today it's really a pleasure to be here what are we telling you about is some recent work on understanding some new states of matter and they're interesting cooperatives and by way of introduction which i think is appropriate for Aspen I want to start out with the beginning of the fourth movement of Dvorak new world Symphony which looks like this so two notes an arrest two men two notes and the rest let's imagine we have an orchestra playing that but we did something very boring which is to say they just kept on playing just that instead of going into the rest of the that member of the symphony they just kept on playing those two notes and rest over and over and over again okay which would sound something like that this over and over again like a metronome okay and let's suppose we had many musicians playing this in fact many orchestras playing the same thing that I'll be playing in tune well actually during the the playing of that kind of boring piece you're sort of tuned in in the middle you wouldn't know if they were playing the two notes you wouldn't know if they're playing AC rest or fear resting first and then playing the two notes okay unless you knew what gladly when they started and you can imagine that you know some of the musicians maybe lost a concentration or whatever they would end up playing the wrong thing which would say they might rest first and then play the two notes okay and end up you know being you know off you know relative to the to all the other musicians because they'd be resting when everyone else was playing and playing when everyone else was resting and and if you read and you know that's going to sound not like what it supposed to sound like if you have some musicians playing out of phase the other musicians you end up with something but let's say a minority you would end up with something like that [Music] okay you have most of people playing this okay and if you playing this say if you playing this then you would end up with well the other was something sounding like the music of Jaws okay but that's not really what we're looking for here okay and the reason that you hear that is because the sound waves don't really interact very strongly they basically just add so if you've got a bunch of musicians playing and some other musicians playing out of out of phase you just hear both of those sounds okay now in real life of course the musicians would see each other and hear each other and realize what's happening with fix fix happen let's suppose that they were all inside of boxes they couldn't see each other they couldn't use each other they wouldn't know that they were played somewhere playing out of phase with each other and then you would just hear what I just played but on the other hand if there were some way that the sound waves could interact okay then you know maybe they could self correct now of course musicians can correct but you know there's a lot of maintenance involved in making a musician able to do that you know positions generate a lot of entropy and there's a lot of training and you have to keep them alive and feed them but um but you know but if the sound wave could just interact and self-correct wouldn't that be great I mean then you would end up hearing something like this oops you would end up hearing [Music] you would hear you would hear those two musicians playing out of phase and they would get softer and softer and you would go over to the right thing would not be great well actually it turns out that that isn't such a crazy thing because things like this happen in nature magnets for instance have this self-correcting feature here's a block of iron and in this iron design urns magnetic because it's got little microscopic magnets inside of it these electrons and their spins which is you think of a small microscopic magnet inside the iron well there's been imbalance between those pointing up and those pointing down now those fluctuations all the time and those fluctuations you know sometimes it's spin flips because after all this isn't at zero temperature and those fluctuations are a lot like actually it's that when some of those musicians are playing out of phase okay you get some fluctuations you get some errors if you will but actually the magnet self-correct okay and it actually maintains approximately the right imbalance between the up and down spins crystals also have this kind of feature so here's our Greg Euler table salt you've got sodium and chlorine and they form a regular pattern and there's a preferred distance between the different sodium atoms but you know there's always some fluctuations I mean these things are bouncing around a little bit they aren't sitting at any given instant right and those lattice sites however they bounce around and fluctuate and if you look at them on average they actually self-correct and the distance between sodium atoms stays the same including sodium atoms are very far apart okay these are both examples of what physicists call spontaneously broken symmetries okay Ferro magnets and crystalline solids are two examples okay superfluid helium it turns out is another example in these case and all these are examples of situations in which the ground state or low temperature state of the system less symmetrical than the system itself for meeting less symmetrical equations that describe that system for instance in our magnet there really is no preference for up or down they're both equally good but once one is chosen there's actually an energy penalty to reverse spins there'll be a domain wall between the reverse bins and and their neighbors and that energy penalty favors fixing the errors that occur okay I'll give you another example okay which is actually more similar to the main topic of today's talk so here's the surface of graphene okay which if you were to exfoliate it you would have justice sorry this is the surface of graphite which you were if you were to ex foliate it would be a single graphene layer okay it's a honeycomb lattice of carbon atoms anduse a methane gas atom okay well one thing that can happen is that methane gas can get observed on the graphite and if we edit the surface is exposed to a gas at the right density then actually it can absorb many graphite so many methane atoms now if the density is right they'll end up occupying alternate sites on this honeycomb okay which your older ones in red that's where the methane gas atoms have been absorbed absorbed now you'll see there was an arbitrary choice here which half of the sites okay it's kind of a checkerboard pattern but checkerboard on a honeycomb lattice rather than on a square lattice and both choices are equally good okay with a spontaneous choice okay and if all of them had shifted over by one lattice spacing to the other sub lattice that would be an equally good choice but if part of the system chooses one sub lattice and part choose the other then there's a domain wall here separating those two choices that is an energy cost and that actually suppresses those reverse regions and so as result although one sub lattice is that just as good as the other sub lattice once the system chooses one of those two it prefers to stay on that sub lattice okay this is the manner in which spontaneously broken symmetries lead to a form of rigidity which would say the system wants to choose the same thing everywhere and that's really the self-correcting feature that I was hinting out earlier with the music that I play for you now as I mentioned there are always fluctuations okay so even if you know once the system is chosen this is preferred sublattice you know there always be some fluctuations at any given moment some region might get misaligned with the rest of the lattice and there'll be some energy penalty associated with it but as it fluctuates around it'll bounce around and on average it will all stay on that sub lattice okay but if we heat the system up enough and you have enough fluctuations then you can end up in a liquid state where really this this crystal on top of the surface is melted but in that liquid state small regions will momentarily look crystalline so if you look at this region here inside the dash line its misaligned and you look far away you'll see that this is not even sitting on the same sub lattice as this one but if I look just at this small region it would look like a crystal okay but if I look over long enough times okay what will happen is on average that will all wash out and the probability one of what I'm trying to depict with the kind of transparent methane atoms here is that if I look at any site the probability of seeing that thing there is not is 1/2 okay and that's a liquid state okay but if I can really take any snapshot as I showed here you might in any snapshot in any small region see something that looks crystalline okay and that probably won't be surprising to any those of you who either accidentally or on purpose have done a belly flop into a swimming pool kind of painful the swimming pool feels pretty solid right and here's another demonstration of that that it's actually quite subtle to distinguish a liquid from a solid here is assuming purlettes been filled with custard okay so mostly water and cornstarch and you can see that it's liquid okay but if you just probe it on very short times it actually feel feels very solid and you can see he's going to walk on it and he doesn't think okay because on very short times it seems awfully solid okay just as the belly-flop err to the swing pool but once he stands still and stops moving and you look at it over longer timescales guess what happens it starts to sink in okay and over longer time skills you can tell this liquid now actually a lot of trouble getting him out of there because the first excited to pull quickly as I said on short times filled is pretty solid so if you try to pull them out quickly it's just going to hold them in like he's fixed in concrete so they actually have to pull them very slowly out and if you do it slowly it's a liquid okay so it is actually a subtle distinction between a liquid and solid and I'm sure enough timescales something that is act very much like a solid may actually be liquid okay and only by looking over long enough times can you really tell the difference okay but as a matter of principle there is a very clear difference between them as demonstrated you know with with the honeycomb lattice which is that either you have equal probability on all sites or you don't okay so you know our self-correcting sound wave oscillation if such a thing could truly exist well that would have to be like methane on graphene in the sense that okay are you know self-correcting thing where the you know people were playing out of you know with the wrong rhythms kind of their sound got fixed and you headed over to the right thing well that would be like something like this okay where the methane is dissolving is sitting on half the sites and well you could get some misaligned region just like the people who are playing wrong but then the whole system would self correct now what we were calling wrong of course that was a little bit arbitrary because if you're kind of listening in the middle of this you really can't tell you know unless you know right where you're starting you can't tell the difference and that's like the other choice they're really both equally good as long as everyone's playing the same ok but once most of the people have chosen one you really want to self-correct and everyone else to play the same way on the other hand if you sort of have 50/50 then you end up with something like this instead which is analogous to the liquid state which is the thing that sounded like the shark we're getting really close to us right so that's the analogy I'd like you to keep in mind okay but you should also distrust it a little bit because that analogy is assuming that time and space are really very similar ok because you know this periodic oscillation which is what this music is well that's an oscillation in time whereas the periodic structure here is occurring in space and there's a question it really is really time really like space ok well is it different well you know Einstein's theory of relativity unified space and time and terms that actually to understand for instance events trajectories of particles even the issue of simultaneity we need to think about space and time on the same footing and combine them and even more so in general relativity for instance here with black hole formation time and space could all twist it together so if it were true that time and space really could be treated on the same footing then we would have an analogy which is that just as a crystal is something that breaks a spatial translational symmetry which means what the world doesn't have any specific preferred places but the crystal arranges itself in a specific pattern that something called a time crystal would be the analogous thing in time so just as the crystal houses a preferred periodic arrangement in space you would have a spontaneous oscillation in time and this is an idea that my former PhD thesis advisor Frank will check kind of enunciated crisply a few years ago and asked whether this was possible and and and suggested that it actually was okay that was controversial at the time and and and criticized and many people kind of shot holes in some of those arguments culminating in work by my friend Misaki yoshikawa and his junior colleague Haruka watanabe who showed no time crystals don't exist okay that that idea doesn't really fly time and space aren't really the same but you know sometimes when in physics when there is a no-go theorem and you prove that something can happen really it should be viewed as a challenge to figure out what the loopholes are in that theorem and in this case one of the assumptions was assumption of thermal equilibrium okay and once you assume thermal equilibrium it's really kind of an azimuth to the idea of a time crystal because equilibrium really is in some sense the statement that things aren't really changing that they're that they're stable in time okay there's a little more of the argument of that and it's fairly technical but that's kind of at the heart of it now I think most people myself included the time thought that this was kind of the end of the story because that's a pretty good assumption assuming thermal equilibrium if one departs from thermal equilibrium well one can have all kinds of oscillations and all kinds of unusual behavior but what you wouldn't say is that it's at all analogous to a ferromagnet or a crystal which all are phenomena that occur in thermal equilibrium and thermal equilibrium carries with it all kinds of good properties that one would want to hold on to if you were trying to draw an analogy okay in particular for instance you can happens like this you can have in Rayleigh Bernard flow one can have periodic Asil Ettore phenomena for instance when you take a pot and you heat it up so you from the bottom and and the and then he was escaping from the top well that was set up periodic flows but this requires an energy flux through the system only occurs in open systems doesn't have this generalized rigidity that we is a property that we'd want to have that crystals has at ferromagnet cells and so on similar things happen with oscillating chemical reactions may have heard of something called the Johson effect occurring in superconductors when one drives a current through the superconductor that's sufficiently large that it generates a DC voltage you get an oscillating current associated with that but there's a net DC current flowing through the system in general heating occurs so these are all situations in which you're not really in equilibrium and don't have the kind of properties that we'd like to have in thermal equilibrium and so these are not the kinds of things one would ordinarily call a time crystal so you know what's another know Chicago's proof really said well yes there are things like this that can happen but if you are looking at thermal equilibrium things are analogous to spatial crystals to throw magnets to superfluids and so on time just was on can occur okay now okay but that's not really the last word on any equilibrium it turns out that in spite of that it's a little bit too restrictive okay to restrict ourselves to thermally clear in the following way it turns out that what we now understand is the culmination of some of work over the last 10 years is that there is this non-equilibrium systems that actually have all the good quote unquote good features of thermal equilibrium systems and the reason that they have those good features the generalized rigidities and so on is that the equations describing these non equilibrium systems can be transformed to look just like thermal equilibrium or another way of saying it is that these systems though outside of equilibrium actually it looked at in the right way really are just as good as thermally Librium God and I like to call these systems quit their equilibrium crypto meaning hidden at the very hidden equilibrium the non equilibrium systems by hiding inside them really there at the heart there like equilibrium systems and it turns out that in crypto equilibrium time translational symmetry actually is a symmetry just like any other and you can have or you can start asked more reasonably questions like the time crystals exist okay and in recent work with a graduate student brilliant graduate student Dominic else and colleagues a lab our what we discovered with it yes in fact in crypto equilibrium Congress tools do exist and what we showed is that in a series of papers that time really is just like space in these systems and time translation is just like any other symmetry and just as crystals break spatial translational symmetry and ferromagnets break the symmetry between the spins pointing up and down similarly time crystals break a time translation symmetry and so this led to various things in the popular press that captured some of this flavor but not entirely accurately it did correctly say you know time crystals might exist after all it's not quite an open-and-shut case one of them said well Microsoft thinks time crystals may be viable after all okay which may have been a backhanded compliment and a motherboard just said well what's the time crystal so in slightly more colorful language so so it is all about okay well um came up with a theoretical model and okay the technical term which I'll hint out a little bit later for this type of time Chris told basically where we start out with a chain of spins or in other words like little microscopic magnets okay and this model is going to involve some manipulation of this and we're going to see that it has that self-correcting feature that I mentioned which makes it analogous to crystal in a specific lag okay and this thing can be manipulated in a couple of ways the two ways that we're going to take advantage of or we're going to apply a magnetic field that takes these spins and rotates them okay and we're going to rotate them by approximately 180 degrees actually doesn't have to be exactly 180 degrees if we rotated by exactly 180 degrees if we did it twice we'd get back to where we started and that wouldn't in a huge surprise but if you rotated by 170 degrees okay you'd rotate them to rotate them twice and you wouldn't expect to come back to where you started you wouldn't in general okay so but we're going to do this kind of approximate rotation the other thing we're going to do is we're going to allow these spins to interact with each other fellow magnetically means they want to try to line each other up and we may or may not apply in addition some a random magnetic field to these spins pointing in the same direction in which they prefer to lie okay and these there's a history of thinking about systems that have been manipulating this way periodically driving them using these kinds of these manipulations going back to some very interesting work that I guess it's cut off unfortunately by physicists in Slovenia named Thomas frozen who's not well known but done a number of really impressive things and you know down to work by gil rafael cruz here at the Aspen Center right now that really kind of pointed this in the right direction for thinking about time crystals and then some beautiful work by the group in Dresden and a group in Princeton developing these ideas and that what we're going to do is take take these manipulations okay and apply them periodically so for some period of time t1 we're going to rotate these spins by applying a magnetic field okay and again I'll be approximately on in 80 degrees okay and then in the next sequence we're going to let them interact and aadya fly a little random field slightly different field to each spin I've never just going to keep doing this again go back and do the rotation do the interaction and so on like this T 1 T 2 T 1 T 2 and so on and the period of this manipulation the period of this drive is capital T which is T 1 plus T 2 ok and question is when we do this what happens okay well there are roughly three things that can happen okay the sort of generic is the thing that I think most people thought was the only thing that would happen is something that this is called the eigenstate thermalization hypothesis which is just a very complicated way of saying well just going to heat up to infinite temperature you keep driving it periodically you're pumping energy into the system that energy gets thermalized and spread over the degrees of freedom the system and it just keeps on heating up okay it doesn't heat up the instant temperature hopefully you realize it's heating up and you stop okay but it heats up as it continually heats up while you drive in okay well we learned in the last 10 years or so starting with some really beautiful work by colleagues of Andes at Colombia ego Elena and Bohr cell solar is that there's another possibility called many-body localization and in those in systems that have this property okay it's never heats up okay in fact it always the system regardless of what initial state you start in it actually always looks as if it was at zero temperature okay now if it requires a lot of impurities okay which in and buying purities I mean anything kind of random like the random fields that I was describing earlier so it's a little bit special in that sense but nevertheless very interesting as as a counter example to what was the conventional wisdom and then there's something called pre thermalization okay also relatively recently appreciated and this is a system that actually does heat up the infinite temperature because of the drive but if the frequency of the drive is sufficiently high but it actually heats up very very slowly but exponentially slowly so as a result because of the exponential slowness for a very long period of time the system doesn't heat up in temperature and in fact these two cases over here are examples of what I would call crypto equilibrium even though these systems are not in equilibrium there being periodically driven this one in fact looks like it's at zero temperature which is an extreme case of thermal equilibrium and this one it turns out also looks like when looked at the right way or without exponentially long time during which it doesn't heat up also looks like a system in equilibrium now you may object and say well this one is heating up albeit slowly but it takes exponentially long time for to heat up and as Caine said me on the long run were all dead so the fact that it actually heats up maybe isn't something we should worry about too much yeah so if we were to take one of these two roots to equilibrium that's how we could potentially get a ton crystal okay so what happened say well you know we take our system we take our system of little magnets you know which is running recalls you know which I call spins and we do rotation by 170 degrees okay so you can see the magnets of little spins here rotated they haven't rotated by exactly 180 degrees 170 degrees okay then you let them interact and sometimes when they interact well that causes nearby spins to kind of tip away from each other sometimes the those balls will exchange the spins with each other and so you get some further evolution of this you then do another 170 degree rotation which rotates this 170 degrees it's not getting back to exactly where it started because after all the 180 degree rotations and the spins interacted in some complicated way you have two spins interact again and you can see you've ended up with some state like this and you keep doing this and what you expect what you expect to just scramble everything okay what I mean by these hours pulling every direction is that if I look at any of these spins on average anyone who spins at equal likelihood of pointing in any direction okay so it doesn't really have any preferred direction it's more or less it's actually not more like it it's forgotten what state I started out in it's all washed out and again this is sort of the the you know kind of the standard assumption that we would have made about a system that was being periodically driven like this okay and this is a lot like well I'll return to what it's a lot like in a moment but first let's ask does this really fit the only things if it really happens okay with this what it's a lot like is it's a lot like a liquid state okay because you've washed out all of the memory of what you start out with you've manipulated it done 170 degree rotations and so on and by the end of this it can point with equal likelihood in any direction and there's no difference between the end of an even period and odd period because I go one more period do one more hundred seventy degree and one more interaction and well they start out that by the time I've gotten to where they have equal likely at the point in any direction going through one more cycle doesn't change anything it's still equally likely to point in any direction and that is just like this liquid state of methane armed graphite it's the same that even in odd multiples of T here same probability to be on either a lot of sides okay so this is really what a liquid state in time would look like which is here I'm showing it in the pre thermal case which is that you start out with some initial state and you start out and it's indeed oscillating as you start out because you do the hundred seventy rotation you letter interact a little bit you do another hostage rotation and it's going to bounce around but after some relatively short time that all washes out and the red here is what's happening at the e at the end of an even period and yellow the gold is what's happening at the end of an odd period and although they are different initially they'll wash out and you'll get this long time over which basically they look the same okay that's like a liquid state so if we want think about a time crystal well we really figure out is something to look like this instead which is there's some initial all transients over which the system forgets some of its initial state but not all of it and as you continue into this long time regime it now oscillates between red and gold between even and odd cycles okay so that would be a time crystal now how can we get this well if you think about it what we need is we need those interactions okay to be stronger to stable like this in step two okay that's how the spins can try to lock together and in such a case what would happen we do 170 degree rotation okay spins would not flip precisely in the opposite direction so only 170 degree rotation you then interact that jump scrambles them up a little bit okay do another 170 rotation and you've not quite reversed them you let them in Iraq that scrambles them a little bit you can see here you've ended up not really exactly opposite of where you started which you shouldn't expect because after all 172 rotations but then you do this more and more and more and at the end or not the end but at some much later time once you've done a number of cycles you may find that it hasn't all just washed out and it's still if not it's not forgotten where it started and it isn't equally likely to point in any direction okay and what happens in that case which is a time crystal state is that if I then go one more period it's actually rotated by exactly 180 degrees relative to where we started okay so it actually has a self-correcting feature even though I only did 170 degree rotation or it could have been 175 or 178 or something like that because of the interaction step what happens is that eventually the system locks in and and every even and odd are alternating perfectly and this is like the crystal state of the methane on graphite okay the off being opposite even odd is like this choice of sub lattice okay now here kind of a cartoon limit where the reds are always on one sub lattice now of course it would still be a crystal state even if it were 75% likely to be here and 25% chance of being here as long as there's some unbalance between those two okay so even the only situation in which we really call liquid is when it's 50/50 and equally likely to be on either and similarly here the system can forget some of its initial State but whatever it retains at late times will oscillate exactly binary degrees which is sort of what I was depicting over here that it does forget some of its initial State but then there's this long time over which you get perfect oscillation of whatever's remaining okay okay so the oscillations self-correct okay in other words it really ends up sounding like this okay where you have some errors occurring here but in spite of those errors what happens is that the initial you lose you you forget some of the initial state but then you lock in eventually so that you go in exactly honeybee rotation which is really like saying AC rest AC rest and so on Gazza universe so you know we cooked up a model that has this property and then I found and colleague at Berkeley normally I'll got very excited by this and talked to his friends Kris Munroe okay who's an experimentalist at the University of Maryland who works with South ions and Misha Lucan at Harvard and came up with two different experimental realizations of this theoretical idea okay one of them they said involves trapped ions so here is a trap in which utility of ions are trapped in a line okay so this picture is taken with a special kind of optical camera but it turns out that they actually give off light and you look into the trap through one of the windows remarkably even though you're looking at a single you turbulence you can actually with the naked eye see them and these ions can be made to rotate by 180 170 degrees or however you like and they also can be made to interact with each other okay the interactions that we need could be just between neighboring ions or they could be longer-ranged and ions could interact with their neighbors and second neighbors and so on it turns out that when we're making a linear chain of these it's advantageous to have longer range interactions and what they found when they modulated the evolution of the ions in the periodic ways that I described was that indeed when the interactions were off or weak what they found is that this kind of beating pattern which means that the system was very sensitive to how much you deviated away from 180 degrees a way to quantify that is to take its Fourier transform which is to sort of look at the periods the frequencies are inside and the fact that there's two peaks here which vary depending on how much you deviate for modern-day degrees is a sign that the system isn't locking in okay on the other hand when the interactions are strong even as you deviate away from 180 degrees there's just the one oscillation frequency which is a signal of a time crystal the other experimental realization okay turns out to be with what are called env centers in diamonds so these are diamonds that have some flaws in them okay so now flawless diamonds and the kind of flaws they have are there so diamond is this kind of lattice of carbons and some of those carbons are missing okay that's the V and NV it's a vacancy another thing that can happen is that the causing could be replaced by nitrogen and when you have a situation where there's a nitrogen in place of a substitution for carbon sitting next to a vacancy okay well in that case it turns out that that effectively acts like one of these spins that I was talking just like in the ion case okay these have been of great interest recently because the streams associated with envy centers in diamond can be manipulated and imaged and so on many beautiful ways what Misha Lucan and his group tip was one of these diamonds that has many many of these a very high density of these flaws often call black diamonds because it actually looks black it's a different kind of black diamond than we're used to talk about nasty em and you know subjected it to a periodic protocol in which they post it in the waves we just discussed during these rotations that were in some cases 180 degrees in some case deviating away from hundred eighty degrees and as a result and then allow these or actually induced interactions between them and what they saw was very similar than what we see in the ions totally different system go totally different system but yesterday saw was very similar which is to say that when the interactions weren't sufficiently strong you didn't get any locking in and you see these two peaks in the Fourier transform which your signal of the fact that it's not really perfectly locking odd and and oscillating and conversely when the interactions are strong enough what they saw was that everything locked in okay now on the other hand what you'll notice in this plot as in the plot that I showed you earlier was actually that although there is indeed this oscillation you can make out it's actually getting weaker as it goes on which is not what we'd expect naively at least from a time crystal so there are things about these experiments that we don't understand I think in the case of the ions the reason for this has to do with the fact that it was not a very large system of ions initially and in the next generation of experiments they are looking at larger systems and what appears to be the case is as you make it longer this decay goes away okay in the diamond and V centers it turns out the it's probably more complicated physics going on in here that's not in the model that we don't understand yet okay so indeed I think these experiments really are consistent with the stories about time crystals and I think one might even say yes time crystals exist but lots of characterization does still need to be done okay because although they broadly agree with what's predicted there are some things we don't understand and I think there's more characterization there's some interesting ideas floating around about how time crystals might be used for metrology okay the idea being look if you want to measure lengths you wouldn't use a liquid to measure length you would use a ruler that's a solid okay and similarly if you want to measure times or in some cases time differences you simply want to use something that locks in at a certain frequency or certain time period as time crystals do and it turns out that time crystals in some sense with the tip of the iceberg there are many other states that can occur in crypto equilibrium that realize even more exotic states of matter some of which have analogues in actual honest-to-goodness equilibrium systems some of which have no such analogs and involve things like topological phases of matter and things that perhaps even are interesting or useful for quantum computation so I hope that over the course of this lecture I've been able to introduce you to something that to me is very new and exciting in terms of understanding and manipulating states of matter which even just a few years ago we all presumed did not exist so thank you very much for your attention I'd be glad to answer your question okay thank you so the floor is open for questions yep yep that's a great question and actually in fact often when I've given talks on this topic to thesis the most common type of question I get is is X a time crystal well X could be a laser X could be spontaneous parametric down conversion it could be the AC just in effect it could be those Rayleigh Barnard flows that I talked about so that is really an excellent question and kind of one of the first questions I think comes to mind I think the answer to that is no and I think the reason is that all of those systems that that I just rattled off our systems that do not look like equilibrium systems in any sense they don't possess the properties of equilibrium systems and in reality all those systems would really have fluctuations and those fluctuations would eventually cause their phase to wander it may be that the fluctuations are really small and so over any reasonable period of time that we want to apply it to they would they would phase wouldn't wander but it would actually wander but they often have stabilization mechanisms that usually involve the system being open and that is an interesting and and and you know different phenomenon but I wouldn't call it a time crystal and I think when you have an open system lots of interesting things can happen that are not you know such as in an open system while the entropy can decrease why can the entropy decrease well you just you actually increase the entropy and slow the extra entropy out the window and it looks like in your system all that extra entropy has you know is done away and in you can have in open systems if you have some fluctuation that's inconvenient well you can throw it out the window okay because you have an open system you have a big reservoir a big bath and there are states of matter that rely on the openness and the fact that you can sort of expel unwanted fluctuations and lock in the day if you want they don't behave like equilibrium systems I'm not to say they're not interesting and useful but they're not really analogous to time crystals Leah let me yes yep okay okay I know it yeah so let me explain it again so so pre thermalization occurs in periodically driven systems when the drive frequency is very fast so remember the in the particular case we talked about you rotated with the field you have enter a core to your legend tract and so on and basically there's some period for this for that periodic driving if you make that period very short to do everything very fast then actually if you think about it if you're doing oscillating very fast if you look at it from a distance you can't actually you know if you have a slow oscillation like this kind of easy to tell that it's oscillating if you have a really fast oscillation like this from a distance it actually might just look like a straight line because the oscillation is so fast and indeed that's what happens when the in the high frequency limit because the oscillation is so fast in the drive it actually pretty pretty it looks to very good approximation like a system that's actually static it's not being driven at all now a quick it isn't static there really is if you look at it closely enough in oscillation but the interesting thing is that that actually only shows up at exponentially late times you might have naively thought well okay I just kind of step back and you know when the time is sort of comparable you know to maybe an amplitude or something like that I'll notice that there's action oscillation but it's not it's an exponentially long time and so that very quickly can get you know much longer than the lifetime of any experiment or observation and so it's not it's really not analogous to you know the guy who was walking on the custard it's it's a different thing yeah so that was a non-newtonian fluid that by walking on the custard certainly but but this effect is not really an August to that okay other questions you know there are some papers that talk about that time quasi crystals and so on I would say that you know just no experiments yet there have been some theory papers and I would say they're not to me that convincing so I think there is something still to be worked out there yes okay so good question the answer is of course I I don't know but I will I'm going to speculate here okay which is you know as I mentioned these are examples of states of matter that don't occur you know in equilibrium found for certain types of quantum computers you want to exploit novel states of matter that have some kind of rigidity associated with them some kind of self locking features that let you get certain quantum gates okay very accurately and it turns out that many of these ideas carry over as I was mentioning I mean for these little bit of just a buzzword but I'll say it you know topological states are matter you know which could be very useful for quantum computing it turns out that in the PIV driven context you have analogous to time crystals topological states in mountains that don't occur in equilibrium and they allow you to have some kind of locked in gates that you couldn't otherwise get to our modern understanding of electricity and magnetism his laboratory was visited by william ewart gladstone zalewska british prime minister and Faraday showed him the various experiments in Gladstone said to him in essence sir what good is this Faraday looks at him for a moment and says someday sir energy are there any that can just watch wait Palmero good question yeah so let me go draw over it maybe hang on so what you said is absolutely true but I just want to kind of draw this analogy a little bit which is in this particular type of crystals mentioned here where you have the methane adsorbed on graphite there was already waiting for the methane this periodic structure of the graphite now the methane still had a choice here which is you could choose to sit here or sit here okay we could spontaneously did but there was some intervention human or otherwise that lay down this honeycomb lattice on which the methane could could play out it's spontaneous choice of which sub loves to sit on so in our time crystals there it is our periodic Drive time is analogous to the periodic structure that we've laid down in space for the methane okay so that's that make sense and I'm gonna get to the second part your question in a moment but before I do does that make sense yeah okay yeah exactly so what we're doing is we're letting out the lavas and it turns out that heat adopts the periodicity that's allowed us in time and it adopts the periodicity that's different from the period I'm not introducing lattice by a factor of two in this case but it could be three or could be anything okay just like here the methane has chosen an underlying periodicity is different from the periodicity of the graphite in this case because the density is half it's it's only on every other carbon atom by the potential would have been the creative element in every third or something like that okay now that still leaves open the question you asked which is if I have an unwritten system could such a thing occur and so the answer is I think the only case that I really believe this can happen is it turns out there is an analogue of pre thermalization that occurs in undriven systems also okay and it requires some special I mean there are some special features associated with it but there are in I believe that such a thing could occur and there were actually experiments back in the 80s that were you know NMR that we're looking at nuclear spin that may very well have they didn't use the word time crystals in those days but may very well as inadvertently chanced upon something that was rather like a time crystal now so the answer is I think it can exist I think it's a little less generic because in undriven systems pre thermalization requires some extra I don't want called fine-tuning but it does require a little extra work to get into it because pre civilization is a little more easily spoiled in undriven systems for reasons that are I can explain in more detail but it's a digression so so I think there is a non driven version of the story but it's sort of a little more special a little less generic okay all right so I'm coming up on 6:30 Aleph is there one more question why well if oh I'm sorry Chandra I didn't say one thing one has a sense of both backward and forward one can go X and minus X in these systems can you speak in any way for going backward in time I don't know what it mean means to go backward in time so Oscar is the answer to the question this gentleman asked related to the fact that time and space are not the thing takes time in something always goes forward hmm well I agree time and space are certainly not the same thing there is I mean look there's a causal direction here right there's we believe there's causality I guess what I'm saying is that in some respects time and space are actually the same is it and the fact that these symmetries can be spontaneously broken and marred is actually quite a bit more structure underlying this in which time and space act the same even though they're not really the same or I might think on that note since time is going forward thank you [Applause] [Music] [Music]

Channel: Aspen Physics

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Keywords: ACP, Aspen Center for Physics, crystals, quantum, science, physics, lecture, time

Id: g0d9CtRT0ss

Length: 55min 34sec (3334 seconds)

Published: Thu Aug 17 2017