Time Crystals: new states of matter, by Frank Wilczek

so welcome everyone to a very sunny Wednesday here of Sola and to this excellent opportunity to have a presentation by the professor start condition this presentation is hosted by the Department of physics and astronomy and the broad foundation so it's very nice to be here in oxalá right had many happy experiences and friends and I'm pleased today to tell you about some unusually exciting developments I think in the exploration of a new class of states of matter these are time time crystals let me introduce the question to which time crystals are the answer so symmetry is a dominant theme in modern physics it was very helpful in leading to the fundamental equations we use in the description of nature's basic laws it's also very useful in classifying states of matter and exploring possibilities for behavior of material systems in both those regards equally important is the question of symmetry breaking we often like to postulate that the underlying equations of a system have a higher degree of symmetry than the solutions of interest and this is in a very very fruitful theme in physics as as you probably all know among symmetries perhaps the most fundamental of them all is time translation symmetry unfold strangely not that doesn't seem to have at least in English a less than seven syllable name so since we'll be talking about it quite a bit I will need is convenient name for a taco it's simply town maybe in Swedish there's a shorter description although I very much doubt it so tau is the principle which instructs us that we can discover eternal laws it tells us that the form of laws doesn't change with time it's also connected through a mean urges fundamental theorem to the conservation of energy so it's a pretty basic symmetry of nature now the spontaneous breaking of spatial translation symmetry of course we also have spatial translation symmetry which tells us that the laws are the same at different places and is connected to conservation of momentum is often broken and in fact almost many common materials most common materials like to form crystals at low temperatures in which space does not homogeneous there are certain places where atoms are and other places where they're not and it's an ordered arrangement so an infinitesimal translation of the body will take it into something else which is to say that the body doesn't obey spatial translation symmetry but only a discrete version physicists are accustomed to making analogies and connections between space and time of course theory of relativity is the ultimate in that but also in our equations some their exes and there's 80 therapies and you can see that they play similar roles thus it seems natural to ask whether there are states of matter that correspond to crystals and time and that's time crystal so here is an ordinary crystal which is an ordered array of atoms a time crystal what should that be well atoms don't come and go ordinarily but we can talk about events that are periodic in time that would be a time crystal so materials which somehow pulse a or have structured behavior in time in the most general sense are time crystals made in the most general sense of that word so in that by that criterion a beating heart is a time crystal it speaks and so marks time any clock at the time crystal but we don't for purposes of physics and invoking all the machinery that goes with the concept of spontaneous breaking of symmetry we want to be a little more selective about what we call a time crystal a beating heart is not very precise it requires feeding and maintenance and it's complicated we'd like physical time crystals that are worthy of the name that exhibit spontaneous symmetry breaking and associated phenomena like soft modes Nambu Goldstone modes and transport properties associated with those sorts of things needs needs to be better in all those respects they have to be self-contained we want them to be simple if they're not simple and not in its chemistry or biology not physics and we want them to be precise so that leads to the question is there a reasonable sense in which Tao time translation symmetry can be broken spontaneously are there material systems in which that happens this turns out to be a very subtle question which has however recently borne some spectacular fruit which I'll describe to you and I think it's fair to say that the answer is clearly yes this in fact is a picture of time crystal actually it's not a picture of the time crystal it's the picture that accompanies the announcement that time crystals actually exist last October in science alert and here is kind of the more official version when the discovery papers were actually published in the knife very recently in 9 March 2017 issue of nature which has a beautiful picture also completely fictitious of a time crystal but inside it has two discovery papers and also two news articles technical and less technical about those discoveries usually discoveries in physics take several years sometimes decades before they reach commercial applications but time crystals have short circuited that process and they're already for sale [Music] so let me discuss physical time crystals our first survey what's out there and then make a more detailed specific description of these new experiments so there are three classes I would say of existing time of time crystals that I want to discuss Josephson time crystals glow K time crystals and pre thermal time crystals so I will discuss those oh and a fourth open time crystals which is closely related to the pre through time crystals so I'll discuss all those in turn an inspiring example which really was at the front of my mind when I started thinking about time crystal the possibility of time crystals is the eight D Josephson effect I put an asterisk next to the example for reasons that will appear then through the discussion let me release me remind you what the AC Josephson effect is we have two superconductors and an insulating barrier between them so that they are almost independent but not quite there's a so-called weak link a weak coupling between them due to tunneling of the Cooper pairs nevertheless we can describe them as having independent phases and independent numbers of Cooper pairs then you can write down an effective Lagrangian that describes this physical situation the simplest possible minimal description of it is that you have a number which is the number of relative number of prepares on the two sides and the relative phase is conjugate to that according to the basic principles of quantum mechanics and so you can incorporate that conjugacy by having the number difference multiplied by the time derivative of the phase that establishes if you like that one is the p and the other is the Q dot in the canonical description then there's the energy coupling which is if the the energy is minimized when the phases are equal but the two things are weakly coupled so that they can vary independently with a finite cost in energy and then finally when pairs move across the barrier if there's a potential difference between the two sides if there's this electric potential energy so all the rich phenomena of the Josephson effect follow from this very simple of Ranjan you vary with if you vary with respect to n abs are vary with respect to Delta you get this equation of motion this is the equation since this doesn't have V this is what you get even in the absence of a voltage but if you have a voltage it appears in the equation you get by varying n the which is basically the Schrodinger equation for the phase of the condensate wave function relative phase of the condensate wave functions in the two superconductors if you combine these two equations it's very easy to solve them and and if you solve them you find that the phase the relative phase changes with time in a way that's linearly proportional to the voltage and then that the resulting current according to the first relationship is some constant times a sine wave this if you think about it at grade level it represents an oscillating current so there's a physical quantity that's changing in time even though the underlying system is not changing in time so it's a spontaneous braking time translation symmetry and in the scheme of titania symmetry breaking one signature is that there should be a soft mode or an ampoule Goldstone mode a thing that can vary within the manifold of possible solutions that are related by translating time by different amounts okay so the underlying since the underlying equations don't care about that if one time is a solution and time plus a constant is also a solution that's your soft mode and there it is and the form of Delta zero it's possible to play many variations that many variations on the AC Josephson right and that's a fruitful source of different kinds of phenomena that very different in their realization physically but embody the same fundamental idea for instance you can have condensates of neutral particles in the liquid helium superfluids or in cold atoms superfluids and there are many studies of analogous effects in those contexts we can also vary the geometry okay so coming back to the asterisk there are several reservations that one could express about this example and which have been expressed I'd say all that one is answerable and let me very briefly go through them first of all it's not an autonomous system there has to be something supplying the voltage and this brings me to this reminds me of this is the famous discussion of Bill Clinton where he says well it depends what the deposition of it is if it the system includes the battery and the whole thing is that system so that's autonomous it isn't self sustained that is the battery will eventually run down if you close the circuit somewhere there'll be resistance and the battery will run down well you don't need this battery just have an ideal capacitor or a spherical Junction so that it doesn't radiate or use the neutral analog and this can minimize or theoretically completely eliminate dissipation it requires additional symmetry some people have objected on that ground because but so what it can't be is all of the reason that that perhaps objectionable is that if you want to see the flows those represent flows along the broken symmetry direction so the symmetry really isn't broken you can't observe those flows if so up to observe them you have to probe symmetry breaking and so if you observing them all the time there was no symmetry but you just if you observe them intermittently that's not a problem either so I don't think any of these reservations are well-founded however there's one reservation which is very well founded which is that this system is too familiar we've known about the Josephson effect for a long time and guess it's interesting to observe that it breaks time translation symmetry but in some sense it's a repackaging of things we already knew we want examples that are different that are new states of matter not the Joseph's not things that are so similar to things we've known before so let's keep going the recent breakthrough experiments that were advertised on the cover of nature concerned what are called locate on crystals so let me explain what those are in those systems there's a periodic driving term so time translation symmetry is broken from the get-go however what happens is that the response of the system is even less symmetric than the driving force so in the two different examples and in the experiment one has a driving term with some period t and the response is period doubled so the response is at twice the time interval so translation through t is no longer as big t is no longer symmetry only translations through twice that period and in some of the experiments it's also tripling three times the period so we violate the discrete version of time translation spontaneously here are the two papers they are quite different in detail in an interesting way the first one is a totally controlled ten spin system so you know exactly what the Hamiltonian is but the in fact the interactions are these are separated atoms so they really don't interact very much at all if if you if you leave them alone but if you shine lasers on them bringing the atoms into resonance and clever ways you can dial you can manufacture hamiltonians basically to order and that's that's what's that's what's done in this ten spin system the other is much more naturalistic less controlled it involves what are called nitrogen vacancies in in diamonds so you have diamonds and that's that and you infuse nitrogen into it and the nitrogen takes up some spaces in the in the diamond and leaves a dangling spin and in this these systems you have millions of spins that are interact and they're not so closely controlled obviously so there's a nice description in the nature non-technical article that I would like to co-opt of the simpler of the ten Adam experiment but the principles are not that different for the other experiment so I'd like to borrow that description in introducing you to the experiment so if you have spins and introduce what's called a PI pulse then you can if the spins are in the Z direction you can flip them over to the minus Z direction and vice versa so you reverse the spin in the Z direction by applying basically e to the I PI Sigma Y as a unitary evolution operator for exponential of a Hamiltonian so this is well known in magnetic resonance you the typos and if you just have a spin and apply a PI pulse and it's precisely aligned in the Z direction it'll be plus the plus minus plus minus plus minus the period will have doubled so that's already less symmetry than the underlying situation but it's kind of trivial and unstable so it doesn't deserve to be called a time crystal because if for instance the laser is slightly detuned so the PI pulse is not quite politely Epsilon then the ordering is completely washed out the system does not obey this doubling and I'll show you precisely what happens but but things go go haywire so that nice simple behavior is not stable however in a time crystal you have additional interactions so that the different spins want to synchronize basically and then even if you get things slightly wrong because as it's typical of phase transitions because the interactions are dominating external fields if the fields are small enough you get this spin flipping as a stable phenomenon and as a symmetry breaking for this to happen thermal equilibrium has to be not established that is not normal thermal equilibrium the system in thermal equilibrium should have a unique state as a function of time but here we have two states that get interchanged after you go through a cycle so let me explain this in I'll explain this in more detail so these systems do not thermalize in the normal way to have extra structure there are two distinct possibilities that occur even in exactly the same physical circumstances with exactly the same history of things they've been exposed to so how can it be that the spins managed to synchronize even though the pulse is roll it's not a particles well because of the interaction a ferromagnetic interaction they all want to point in the same direction and you also need some disorder in the system so that although your typical spin is in the Z derivative e Direction doesn't have the right Pizza period to match your faulty dipoles there will be some spins because of the disorder which do and those things can lead to this can lead the synchronization so the interaction gives you the desire to synchronize the disorder gives you the ability to synchronize that's the closest I can come to a an intuitive discussion of what's underneath is structured equilibrium here is a picture showing the physical situation in visual form so you have spins and you have an external magnetic field and then you have also the pipe pulse which flips them and this is what it actually looks like you have an array of atoms and Chris Monroe's one of leading experiments experimenters on this atomic time crystal this is what the diamond looks like it's very pretty with the lasers that implement the effective magnetic field and applied pulses and the red objects are that the nitrogen vacancy centers being probed by a different frequency of laser light so let me now go from diagrams and pictures and words and arm-waving to things a little bit more formal description of this situation a flow cave system by definition evolves according to a time-dependent local Hamiltonian that's periodic with some time capital T some period capital T in that case if you look at the evolution that takes you not through an infinitesimal time but through the complete period Big T that's a unitary operator that you're applying over and over again in the evolution of this system in the tentacle form so it's a unitary operator you can diagonalize it and therefore you get low K what are called sloquet Ivan States if you look at the flow K eigenstates they obey this kind of property and if you take expectation values of anything within these flow ki ghen States they will be periodic so for a time crystal behavior somehow you have to talk your way out of these eigen States that they don't get realized so a complete state of flow K eigen States always exists and if you could diagonalize and use that basis you would no time disappear but they meant as be physically reasonable states they might involve specifically coherent superpositions of macroscopically distinct pieces that is they might be as different as dead and alive shorting your cast they are things that don't arrive in practice they can't be prepared experimentally nor realized by reasonable experimental procedures dynamics this consideration is central to spontaneous the concept of spontaneous symmetry breaking in general it would always be possible in principle to say in a crystal to consider the crystal displaced by different amounts infinitesimally to take the superposition of all those as a quantum mechanical state and the symmetry wouldn't be broken it would even lower the energy but those are not realized in principle in practice because there's your superposing States better microscopically different so physically reasonable states have to satisfy a condition that captures the idea that they're not short your cat States and this is the so called cluster decomposition property here which says basically that if you take observations at far separated places you don't have to worry about their Karla there are no correlations okay we don't have to worry about what's going on on the other side of the moon or consistent we make measurements here we don't have to worry about what's going on very far away so for instance specifically we're talking about the ferromagnet as an example of spontaneous symmetry breaking we could have a state which is up with all the spins up or get out of state with all the spins down these do satisfy the cluster decomposition property you can easily convince yourself but they're superposition does not if you consider specifically for instance the possibility of observing a spin up here and a spin down over there then the product operator vanishes in either the up state or the down state as does the product of the single operators but in the up plus down state although the product vanishes the single particle expectations don't vanish so that does not obey the cost of decomposition property and it's a physically unreasonable state because obviously the you would have to make non-local operations to change the Upstate into the down state and those are not realizable in practice do not change work on an infinite number of spins at once so the basic flow kate i'm cristal recipe in this language is simple one uses two-step what is called stroboscopic driving so one plies one Hamiltonian for certain interval and a different Hamiltonian for a second interval okay if you apply one Hamiltonian consistently that would be normal time translation symmetry if you apply them in blocks then it's only the combination period the total period that isn't that is invariant in the first step so for the first block of time you apply what I'll call eighths of mb l mb l stands for many-body localized localization and it's a certain kind of Hamiltonian that has very interesting properties which I'll come to there is I ghen states are locally ordered with respect to the z direction of spin they are it's a Hamiltonian that incorporates these ingredients of ferromagnetic interaction and disorder that I intuitively indicated were what you need to get at a crystal and then of this kind and then secondly and the second step you applied to PI pulse but the normal spins so this is what it looks like concretely H MBL is the sum of h1 plus h2 which has interactions ferromagnetic they could also began type ferromagnetic it's simpler to think about ferromagnetic and some disorder and then the PI pulse is what you would have for this h3 epsilon with zero by definition you apply it for such a time that you get applied calls it epsilon or zero but we want to consider something more general we want to have a system that's robust that's that's the interesting case of spontaneous symmetry breaking they can be realized stable that is a legitimate phase of matter not a not not a pencil standing on its end we want to consider nonzero values of this epsilon so since the H the many-body localized Hamiltonian involves only the spin in the Z Direction its eigenstates are definite configurations of Z spin and with any configuration you can flip them all and get an eigenstate other definite energy but still an eigenstate and when you apply the PI pulse what you do is take one configuration of the Z spins and flip them all over so you relate one of these eigenstates to the other and so the Floquet eigenstates the eigenstates of the product of those two operations is can be just are just superpositions of those two states with the spin and the spin in the other direction it's 1 plus or minus the other however if those two states are macroscopic be distinct if they don't obey the cluster decomposition property if that is the superposition doesn't obey the cluster decomposition property those loci I can States will be unphysical they'll be shrugging jurkat States they are not the physical states that are realized the physical states will have time translation symmetry broken they will be the eigen states of of H n BL which is not which is not in there which is not invariant it's not equal not equivalent to its flipped version on the other hand if you flip twice of course you're back to the same thing so it's a period doubling in the nitrogen vacancy system they've also following a slightly different protocol and observed period tripling here is numerical evidence of the phenomenon you begin with a mostly spin up state use that Hamiltonian that I showed you and apply that for a while and then apply the PI pulse do it again and again and again and what you find is that the spin in the X direction and the spin in the Y direction do thermalize but the spin in the Z direction does not it exhibits a stable oscillation from one macroscopic value to the other as you go through the two phases of the double period and this appears to go on forever in the numerical experiments so it never approaches thermal equilibrium it Staveley exhibits is symmetry breaking so that was theory or numeric to me when their actual experiments that takes it to another level so let me show you again from from that paper in nature a very revealing set of results first of all let's turn the interactions off this is a totally controlled system but atomic system we can turn the ended atoms off for clarity and observe what happens and if you so then we just have a system of free spins with different magnetic environments that this order is well under if they don't have different magnetic environments if there's no disorder then what you get if you drive it at slightly the wrong period his beats okay they start with some alignment you go through this cycle they have different initial values of the seed Z direction and that fall out of phase and you get beats because you're not get applying exactly a PI pulse things fall out of sync and that's what's exhibited on the left if you put on disorder then you don't get beats because they the behavior is not repetitive they just full they just randomized completely now turn the interactions on and something remarkable happens if you just go a little bit off the PI pulse then instead of getting beats instead of getting the no interaction behavior you find that you get these guys behaving as if they're one giant stand with the right frequency whereas if you do a large detuning so the driving frequency the driving frequency is far from apply pulse then it just thermalized or actually in this plot I'm sorry you can't tell by the naked eye but there still is some structure some stable period I've double the doubling period behavior the thing keeps going up and down you can sort of see it stabilizing by varying the detuning and varying the interaction you can get a phase diagram and this to me is the most dramatic demonstration that we're legitimately talking about a new phase of matter that you can discuss a phase diagram and phase transitions you can study as a function of the detuning and as a function of the interaction when this behavior disappears and when it on sets and when it transitions to different kinds of things so the time crystal occurs if the detuning is not too big and if the interactions are not too small if the detail but also not too big if the interactions are too big and then then thermal equilibrium the normal kind will be enforced by the interactions if the interactions are very small that's like the uncoupled where you get beats and no a trivial insulator formerly these many body localized states are alike integral systems it's as if you have the reason you don't get thermal equilibrium is because there are extra emergent conservation laws but these conservation laws are robust unlike in ordinary integral systems ordinary immutable systems are very very special Hamiltonians that have an infinite number of conservation laws but if you change the Hamiltonian a little bit all those go away but the MDL states if you perturb them a little bit the conservation laws change but there are still conservation laws so the existence of conservation laws is robust even though the non but the conservation laws change their nature and they're in general non-local complicated things hard to follow in detail you may wonder what this kind of localization has to do with localization of a more conventional kind in condensed matter physics Anderssen localization Andersen localization is the phenomenon that in a rant assists of a lattice with some random interactions some randomness particles get can get trapped they don't necessarily diffuse through the system there whereas in a perfect crystal the eigenstates are spatially extended the block states and Anderson when you have disorder even though on average things or periodic the eigenstates are localized in space that vocalization here what's happening is very much like that except that the vocalization is occurring in phase space so your system doesn't explore all of these things it doesn't have normal or ghatak behavior it doesn't diffuse through phase space so for our purposes as if it doesn't diffuse through phase space thermal equilibrium is not obtained in the normal way you have incomplete thermally quickly so that is an introduction to these experiments and that established the possibility of these new phases of matter under broader circumstances one can have not things that don't go on forever but in terms of time crystals that behave for a very exponentially long time even though they eventually reach complete equilibrium these are called pre thermal time crystals and they are firmly predicted theoretically using hamiltonians of a similar kind and theoretically numerically these are established so you have a very very long time in which you get this period doubling or more general kinds of behaviors with and but eventually if thermal eise's eventually the system keeps absorbing energy from the pump and goes crazy however these systems can also break continuous time translation symmetry if you might ask what sets the period the period is set by the internal straw the Hamiltonian as yet there are no experimental examples of pre thermal time crystals but I'm very confident they'll be coming soon they have been established numerically now the kind of closed systems that leads to pre thermal time crystals when coupled to a system that can take out the energy that's being pumped in by the drive to form another class the open time crystals so the the idea of lokay time crystals that we talked about establish a kind of quasi equilibrium with the drive so they don't absorb energy but keep going in this structure at equilibrium that has two facets but in a more general circumstance the quasi equilibrium states keep absorbing energy so unless you take it away they are pre thermal time crystals don't last forever but if you take away the energy that's being absorbed in the right way you can have systems that go on forever and these two have not yet been observed but I'm confident that they will be at some level all time crystals are open time crystals because if nothing else oscillating systems will emit low-frequency electromagnetic radiation that might be very slow but it's enough to take away energy if the energy is not increasing rapidly if the increase in energy slow okay so this is how a open time crystal looks schematically you either have oka heating or noise the steady-state is a flow cave or pre thermal time crystal and if you take away the energy the flow K time crystal will remain unperturbed an acetal still behave as if located on crystal the pre thermal time crystal will go into a stable forever time crystal including the possibility of breaking continuous time translation symmetry okay so that's that's a tour of what's out there at present and I think in the near future now I'd like to describe some more general considerations about the nature of the theoretical description of these objects which is quite interesting it would be useful in has been very useful in theory of crystals and theory of solids that's based on earth transport and so forth it's based on those things to have a coarse-grained description where you don't have to discuss the Hamiltonians in detail but can just discuss the symmetry structure in the spirit of landau-ginzburg theory at first sight this looks like a non-starter because if you have a dynamical system described by a Hamiltonian these are the dynamical equations and if you minimize the energy the right-hand sides are both zero so nothing changes the energy if you minimize the energy respect all the position and all the momentum variables nothing can move however Kwasi paradoxically if you look instead of the Hamiltonian you look at a Lagrangian description that seems quite different take this Hamilton this Lagrangian which is the analog of what you discuss in symmetry breaking for conventional symmetry breaking not involving time sombrero Mexican hat kind of potential just not with time derivatives the energy function is easy to work out and it is minimized at a non-zero value of the velocity what's going on we just cool that that couldn't happen well the point is that even such a simple looking Lagrangian leads to a Hamiltonian which is quite unusual if you look at Hamilton ergy function of that form what you're supposed to do to get from our Lagrangian to our Hamiltonian is express that energy in terms of the canonical momentum which is that this thing I've written down here and that's not so easy to do if you want to write this that energy in terms of that variable you ask Mathematica to do it you can't do it by hand you're in when you ask Mathematica to do it you get a surprise what you find is that the solution is not single valued it has this kind of Swallowtail multivalued and cus P behavior so this is not the kind of Hamiltonian you typically find in mechanic's books people shy away and horror from this especially when they wanted to quantum mechanics what do you do when you have multivalued hamiltonian cusps and there's a large literature showing that you can't make sense of these things but in fact you can so getting back to our little theorem that nothing could move that was based on saying that the derivatives were 0 the gradients were 0 but now we know that there are cusps so the derivatives are ill-defined and so there's no real paradox it's just that we were hasty in drawing the conclusion that the energy minimum can't have non-zero motion as I was alluding to it's an interesting adventure to quantize systems like this but that's a better subject for us for a seminar than a colloquium and I won't try to describe that here let me just say that those kinds of lagrangian's arise naturally in the affective theories of accessible systems in view at the time I won't belabor this just to say that one such system is a particle in a strong magnetic field where if you think about it we're familiar with the idea that things keep moving in the Hall effect when you have an electric field and very strong magnetic field the charged particles move that's an example here that kind of Lagrangian arising with higher derivatives others occur I think in an exciting development in the description of circuits when you have circuits that contain things called gyrators that are the least-known passive circuit elements that kind of generalized transformers that in the analogy between mechanical and electrical systems introduce the angular momentum if you have those things and nonlinear elements you can get these kinds of lagrangian's for circuits and circuits are things that you can build in a laboratory explore at temperatures and bring out quantum phenomena so this is going to be a legitimate playground for exploring the consequences of these unusual lagrangians suggested light on crystals okay so I've showed you I think an interesting question some interesting answers now I'd like to go back and discuss a new generation of questions that we can pose with greater interest knowing that the domain of discourse is not empty that we're actually talking about something when we think about generalizing time crystals and exploring new states of matter associated with spontaneous breaking of time translation symmetry what are the thermal and electrical properties of these new states of matter generally in the discussion of thermal and electrical responses of solids a key step is identifying the quasi particles and then in their response and their interactions here the quasiparticles are something new they're not simply things that you get by diagonalizing the energy they're not the energy eigenstate because energy is not conserved anymore what happens what's different about that mostly virgin territory when and where will the pre thermal and open time crystals be observed can one characterize the different phase transitions get critical experience things like that and in fact in a few cases those have been derived I don't know that they've yet been measure they they can be are there time liquids once you start thinking in these direction you could have events that have a fixed long-range density but not necessarily a fixed periodicity those would be time liquids are there time quasicrystals okay and go on every time whatever pick your favorite word and add time and you have an interesting question but you can also add a word in front of time which is imaginary time and this is something that captured my imagination even in the very first paper on the subject in quantum statistical mechanics when you want to set up the partition function at a finite temperature you want e to the minus H times T the usual evolution operator I'm able to give you minus H times theta the usual time evolution operator is e to the minus I H times T so what you can get from one to the other by making time imagine so in the description theorists will notice in the description of thermal equilibrium imaginary time is a very useful tool and so time in that sense gets on the same groups gets gets on the same status as space specifically in a relativistic system if you had when you go to imaginary time the distinction between space directions and and the time Direction is very obscure the metric is the same in all direction and so if you have period periodic structure an ordinary crystal in this higher dimensional system that corresponds to an imaginary time time time crystal so and they're interesting phenomenon potentially associated with that another observation which I think is under exploited and came as a revelation to me just in the last few months is that imaginary time turns the Schrodinger equation into the diffusion equation okay so if you take I beeps I by DT and take the I into the T you get a diffusion like acquaintances and spontaneous pattern formation and oscillation in reaction diffusion systems is the very rich well-developed subjects with things like the the BZ chemical oscillator system and and many others and for that matter the beating heart which we originally I can exhibit very interesting patterns which you don't want to get into that lead to heart attacks and disrupts them they result from disruption in the normal time structure of how the space-time structure of how the horn beat and the analogy between reaction diffusion systems that have been very focused studied and and time crystals in their in the physics sense of quantum mechanics I think can be can very much illuminate these kinds of several kinds of questions that are extremely interesting we can we realize more complex time crystals with several kinds of atomic events if you do and you can under more than one kind of events and more than one thing to monitor than just the spin in the Z direction one can also then one can start to have very close analogies to the reaction diffusion systems and structure in space in in the existing experiments the spatial structure is kind of submerged which is looking at overall growth properties of the thing but in principle you could have correlation of space and time structure and traveling waves of emerging and and here's the particularly where the litter of existing literature in reaction diffusion is going to be very fruitful you can study the defects and topology in these more complex space-time crystals and as I mentioned one of the topological defects that is interesting in the beating of the heart is connected with the onset of failure so finally there's a question which journalists are very fond of asking about time crystals what's their use and the honest answer is I don't know but the semi honest answer is a little bit different the one I actually give is that time crystals might provide nice global clocks or even substrates for quantum computing if you have a quantum computer just like for an ordinary computer it's very useful in algorithms to have a global clock so that everybody can all the operations can be synchronized but quantum computers are very delicate the clock has to be very precise it has to be gentle to be quantum mechanical and time crystals are just what the doctor ordered for that application metrology just everyday measurement this climb mic that when you want it to be really precise might benefit from relatively simple room temperatures super pac's and you can have big ones that operate and are very reliable and operated room temperature and or macroscopic from a larger perspective what especially the recent locate I'm crystals show is that by studying this question of spontaneous tile breaking we're revealing shortcomings in what people thought about equilibrium equilibrium doesn't lead to a unique state in this kind of circumstance the the this structure in time even when we've reached equilibrium when things have settled down and notably that includes the emergence of robust self organized quantum structures and noisy randomized system that's what happens in these time crystals instead of things settling down and being uniquely correlated with the draw if you find that this extra structure in time period doubling or period tripling that emerges spontaneously so major pioneers in this field have been inspired by visions that Dutch self organize self orchestrating structures could provide powerful quantum sensors this is particularly what interested me shal Lucan or infrastructure for quantum computing which is particularly what inspired norman Yahoo elaborating very slightly on the sensor idea in a time crystal you have blocks of spins that are acting in a correlated way in the nitrogen looking with developing and is developing these nitrogen vacancy systems as delicate sensors for temperature or magnetic fields with a variety of applications in mind if you can make the system dense have lots of the spins in the same place that and yet those spins are acting as if all in synchrony all together as they do in these orders time crystal state then you get more sensitive detectors find a factor of how many spins are correlated in the quantum computing set scenario as I alluded to already long-range order can be used to synchronize and stabilize the behavior of qubits if they start to fall out of synchrony and the thermalization or D coherence of quantum qubits it's a major challenge facing quantum computing so the possibility of getting everybody in think by putting them in contact with an underlying time crystal is a really tantalizing possibility in that context so I hope I have convinced you that time translation symmetry is a very interesting question to ask that it's especially interesting now that we know that the answer is interesting and has been led to from startling experimental developments and that there are many many open questions and even potential applications of these two states of matter [Applause] [Music] [Applause] diction following certain kind of a sort of a crystallite and maybe different questions of very black - yes in the Arizonian we've all seen the electromagnetic field is acting on the state let me remind myself what h3h3 was there's that PI pulse defense yeah well the way that this is actually implemented if that's what you're asking is by applying laser light to these things but in principle clozapine external field yeah it's the it's the magnetic component of the light that makes the spin move not necessarily if you make a short enough pulse it can be high frequency yeah what's what matters is the integrated strength if you like these yeah oh yeah absolutely those are called and here is its instead of momentum everybody has in the case of crystals you have momentum changed into quasi momentum and you have pain structure and so forth here you'll have exactly caramel phenomena but now involving energy so you'll have only quasi energy and you'll have bands of allowances reduce reciprocal time as energy yeah so yeah so the in the exploration of things like Brillouin zones and the transport properties and what the quasi particles and transport properties I think is is going to be very interesting now but I don't know where I don't know what's going to emerge how-how's how robust is it well you know it depends on the realization that that's that is the kind of question that the phase diagram answer is it tells you how much how much you can bury things with without without going to another phase now so of course that only envisage is certain kinds of perturbations you could have okay if you if you allow any kind of perturbation then the only state of matter that you should be talking about if the black hole ultimate remove equilibrium but so the question is what kinds of perturbations you wish to consider that do justice to the experimental situation and I think in practice here you can basically well in these controlled small number of atoms systems you can control the Hamilton comeon pretty pretty well however there's always coupling to the electromagnetic there's radiation possible when things are moving around that has not been included here and I think it remains to be really carefully studied that that's what the effect of that is that's related to this question of open con crystals when you couple things to a bath my intuition is that that not only will be harmless but actually will be helpful in draining well certainly in the case of locate I'm Chris Silver's be helpful in draining the energy that may be slowly being pumped in in the case of well maybe I should leave it at that okay yes so it's it's an open-ended question I guess it depends what what you want to consider part of the system and what you want to consider as it's coupling to the environment but basically I think with reasonable definitions of those things you can get pretty robust systems that's that's a big answer but it created a question oh yes absolutely no there is long-range order in time here it's very important that the phase structure the the correlation does not die out at the time that's that's the essence of the net so you know we had this too low structure even over very very long stretches of time they don't fall out of sync and even if you get as I said even if you get the the flipping frequency slightly wrong they still stay in sync so they were busting the long-range order is a very very deep and characteristic property here which distinguishes it from things like a long time ago Faraday discussed area doubling when you take a dish of mercury and shake it up and down and look at the wave that developed you can find period doubling in that circumstances of the mechanical system but that doesn't last forever it dermal eise's and also it is not not phased synchronized over a long period of time yes yes yes those are reaction you better ask that again but but let me ask the first question answer the first question first which is I would say that these reaction diffusion systems and in simple mechanical systems display some of the properties we'd like to have in a physical time crystal but not the full array of properties that we normally would associate with spontaneous symmetry breaking in physics so math whether you want to call them time crystals or not as somewhat a matter of taste and I don't think it yet there's a general agreement about what the exact definite made there may never be exactly exactly what the definition is but I think you know the criterion is the rough criteria that I outlined you want something that's autonomous nice and simple well that's that that and and that has soft modes and so do some of the more detailed things critical exponents those things are the best examples that you know they sort of the Platonic ideal time crystals but then there are other things that are kind of debates versions of time but I'm really hoping actually that we can the the pure cases will exhibit well well we can study in the pure cases phenomena that have already been illuminated from the mathematical point of view in these impure cases in particular I'm discovering now as I look at the literature of these reaction diffusion systems that not only have they studied time-dependent I'd information that also defects in the time-dependent conic formation and so these are kind of like defects in space-time and that kind of ordering and those I died and now that kind of analysis that style of analysis will also work for of course with the physical time crystals and I think will be very very interesting so we get that we get to steal a lot from the chemists and biologists yeah yeah we know from the exterior sophistic there are some women Thank You Bree from my side although a resolution asking to the promotion comes and if I consider experiments then we have some responding Antonio to describe resistance or things with long tails well it's a different subject I'm not sure but as far as I know I mean there are very there a variety of mathematical methods to describe statistics of long tails some of which have a physical kind of overtone in terms of instant tones that rare event subject but as far as I know that has not grown in ideas about spontaneous symmetry breaking of any kind let alone time translation symmetry song so there may be something interesting here and I don't know what it is [Applause] [Music]

Channel: David Burman

Views: 39,332

Rating: 4.7928286 out of 5

Keywords: time crystals, physics, symmetry breaking, symmetry, time translation symmetry

Id: JYZMqtDxrYg

Length: 81min 13sec (4873 seconds)

Published: Sun May 28 2017