 recording yes because we have still one minute but this doesn't matter we can start just one minute to wait maybe for the rest of participants okay i think we can start afternoon session and the first the first speaker is alexand kirjenko who will be talking about quantum time crystals from hamiltonians with long-range interaction so the floor is yours sasha yes thank you very much christoph and thank you very much for organizing such a wonderful conference i'm i would be more happy if we are all together in three years but having this online also creates a link to community so what i will try to do today is provide a vision on quantum time crystals from slightly different perspectives that we will usually have and specifically i'll try to explain how can you construct a hamiltonian that contains a time crystalline behavior and for me this question is very much related to the question of how do we imagine quantum time crystals so previously i we had an amazing colloquium by frank wilczyk and frank had a very visionary talk saying what happened in the past but what happens in the future so if we take the same vision and ask what is the time crystal for instance is it the fractal structure as if you google it or maybe it's some weird shape or even related to salvador dali pictures what is actually the time crystal and for me this question is very much related what is the underlying hamiltonian of the system because if i see the hamiltonian i can also imagine how to build this system and to answer this question we need to look at definitions and there are many definitions of time crystals the first one as originally proposed by frank wilczyk comes from the spontaneous symmetry breaking for time translation and that draws exactly from the same translation symmetry breaking for crystals what frank also specifies that we want this system to be closed quantum mechanical system but the definition may change in the future and if we take this definition of closed quantum system required time translation symmetry breaking one opportunity is to use the josephson effect and look at the current in the supracoduct and ring so that's the example which was already discussed but also frank had few comments in the paper and i specifically want to read the one related to the speculation that more elaborate quantum mechanical systems whose states can be interpreted as collections of cubits might be engineered to traverse in its ground state a program landscape of structured state in the hillbill space and that's exactly what i will try to describe right now that we can hope to engineer collection of cubits that behaves as a time crystal so with persistent motion in the superconducting rings there were a lot of discussion is it really time crystal or not why because you cannot have current exactly in the ground state so it really depends on the definition what is a time crystal can you add a little bit of energy do you can you drive it or not so there seems to be one no-go theorem but later there was another no-go theorem formulated by Watanabe and Oshikawa and what they did is trying to define strictly what is a quantum time crystal so if we say there is a crystalline order that is defined by long-range correlations in space you can take some observable phi you can measure what will be the correlation in different points of space and if it is a periodic function of the distance between these two points and this also works in the thermodynamic limit you have space crystal then Watanabe and Oshikawa said if we have the same correlation but at different points of time they are periodic in time for instance density density correlations where you have revivals and it also holds in the infinite limit of the system in the thermodynamic limit then we have time crystal so that one possible definition we can rewrite this correlation function using our order parameter phi capital which will be some microscopic property of the system evolve phi in time and demand that it is a periodic function of time in thermodynamic limit and what they have also found that if we do the algebra we will see that the correlations will be limited by the Hamiltonian of the system namely if we have interactions in the Hamiltonians that decay as a power low even though the power might be very small we cannot have formally time crystals in the closed system and second we also consider the equilibrium case of t equal to zero or some finite temperature but if we violate one of these assumptions we may hope to get the time crystal and I would first explain how you can get it in this stroboscopic time by adding the drive and next I will introduce a different way to bypass the Watanabe-Shikawa's theorem by considering long-range interactions so the stroboscopic formulation as proposed in different systems for instance in atoms by Krzysztof Zaha and Elsebauer-Nayak for spin systems we do not try to break time-translational symmetry in continuous time but instead we introduce a stroboscopic or discrete time and here the definition will slightly change from what we had before because we want some observable to oscillate at different points of time of stroboscopic time we want this to continue perpetually and we also want to see the response at different frequencies that at which we drive so that will be a little bit similar to what Frank Bielczyk defined for the superconducting current there is a second definition which is not non-trivial flock air operator for the system and why do we want this because we don't want the concept of time crystal to reduce to something very simple so we demand that the evolution is non-trivial and if you follow these two definitions we can create the protocol for discrete time crystals the one I would use here is take some initial state apply the pi pulse so just do the rotations of your spins from up to down but then you will also evolve the Hamiltonian with ison interaction type and since it is an eroded Hamiltonian plus many body localization you would avoid heating in the system so using discrete time crystal protocol one can easily simulate this perpetual oscillation of magnetization we can just go and simulate it we see magnetization changes in time and the frequency of response will be subharmonic so you have a peak different from the frequency at which you drive and it will be robust to perturbations because we have interactions in the system so that was the main feature of discrete time crystal the system was later observed experimentally so there are a couple of groups working on realizations of discrete time crystals and that's not a full overview so there are many more advances experimented is that happens since that time so the field was really evolving and currently is evolving towards more sophisticated protocol and introducing new system how you can realize driven time crystals if you look at the advances from the theoretical point of view there are lots of different proposals how can you extend the notion of discrete time crystals and I can see that from the perspective of dynamics it is a very interesting system to work with and I'm working myself on protocols for instance of flock simulation but if we look at any floccase scheme we always ask the question can we find the effective Hamiltonian for this floccase system usually it's possible if you have a fast drive but in general we can also for any frequency of the drive we can try to find an effective Hamiltonian because if there is the unitary evolution it must be generated by some underlying Hamiltonian and my question is what will be the property of this Hamiltonian so that was a general interest and can we find a family of Hamiltonians that give us this time crystalline behavior which can now happen and continues as a continuous evolution and that will be again the answer to my question can we imagine time crystals so how do they look like will it be some spooky image from google and I will claim that for me it's more related to the macroscopic coupling between two entangled states and evolution of these states so to explain how this works I would like to return back to the Watanabe and Oshikawa condition of time crystal and they formulated it for the closed system where magnetization change the correlation function for magnetization changes periodically in time when we average over the ground state and this should also remain true even if we extend the system to infinite size so that's a very strict definition and from the colloquium Frank just said that it all depends on the way how you define the system so here we will choose the specific Watanabe Oshikawa condition and we can do the reverse engineering imagine that this is true that the conditions for Watanabe and Oshikawa theorem are satisfied how can we construct such a protocol such evolution one way to proceed is take a state in naught and couple it to another many body state e1 through the action of magnetization operator so magnetization operator is non-unitary and you will need to renormalize the state these two states can be taken to be orthogonal so if you act with mz on in naught you get e1 and it should be orthogonal to in naught and the Hamiltonian for evolution of the system will be very simple we can say it contains a projector on state in naught projector on state e1 and some other states if we use the spectral decomposition we will also ask these states for these states to be non-degenerate such that we actually can observe oscillations and next how do we build our system how do we get the oscillating correlation function we can rewrite it as an action of mz on in naught and get the e1 state we can evolve with the unitary evolution state in naught so get our projector in the form of some oscillating phase and accounting for normalization of our magnetization we see that the correlation function reduces to the periodic time dependence where the frequency is given by the difference of energies for two states and some order parameter which is equal to mz squared taken as an expectation value over the ground state if this is satisfied we actually formally obey Watanabe or Shekawa's theorem and still get time crystal in continuous time so the key ingredients the energy difference is constants these are not degenerate states the oscillations must survive in the thermodynamic limit that's a very strict condition which again we need to satisfy and the states that a couple will be orthogonal how do we construct these states for instance we can take an eigen basis of the total magnetization operator which is given by different states of spins up and down we can pick only those states that satisfy conditions and one way is take e naught as a superposition for some coefficients c of the computational basis states to satisfy the condition of our orthogonality of two states we will demand that magnetization in total is zero which means the number of spins up and down should be equal and one possible way to satisfy this is take a gz state so gz state will be the maximal integral state geometrical integral state with all spins up plus all spins down with the normalization perfecter and we will have the action of g plus the action of mz on g plus will give us g minus and return us back so these are two couples states through magnetization operator and these are macroscopically integral states so that's why they are Schrodinger ket states now that I have all the ingredients I can write the simplest toy Hamiltonian for the time crystal and say it just equal to the projector on the one of the gz states of course that's not a true Hamiltonian of the physical system and we can ask can we actually make physically can we write the sequence of powerly operators that corresponds to this state so let's try to do it anyone that who ever written the projector on many body state in the powerly operators will observe that it's highly non-local operator so when we rewrite it formally we observe that it contains the strings of the operators that have even length and it also contains the length of size n for sigma x operators with pair y sigma y substitution so this is my recipe of creating the Hamiltonian of time crystal that obeys the what another Chicago condition but how exactly can be constructed there are many possible ways so as long as I follow the rules specified above and add these non-local strings I will get the time crystalline behavior and the trick is to include couplings of the following form where all spins are connected so that's very strict condition because if I say it's valid in the thermodynamic limit how do we even couple infinitely many spins in the single term but that's what formally is required for a satisfying what a number should cover condition and I also should mention just power low decay won't be possible because it falls in the category of no-go theorem so if we want to really construct the Hamiltonian it should really involve macroscopically many spins but we also try to answer the question what will be the most local Hamiltonian that satisfies this condition and we can only answer it for specific problem for instance Hamiltonians that contain gsz state in the ground state and it was solved before in in the paper in this period from 2011 where the authors answered that the shortest range of interaction to have gsz states and to have them non non-overlapping but also non-degenerate you need to couple at least half of spins in the system so you you will introduce the nearest neighbor interaction that makes the two states non-degenerate but you will also couple and over two spins in the system and with this you have the non-local Hamiltonian for time crystals but which is not a toy model anymore we summarize these results with Valeria Kozen in the following PLL paper and we also asked what will be the properties of Hamiltonians for time crystals one property that we can look at is stability to perturbations if we include magnetic fields or maybe two local couplings will we change the response of the system what happens to the correlation function and what we observe that oscillations are stable it's easy to understand because we demand the evolution that is based on maximal integral states that involves all spins so it's very difficult to break it with just single terms in the Hamiltonian evolution second question we try to answer is what happens at finite temperature and if we include finite temperature there will be a part of the correlation function from excited states and that really starts to change our response there will be some higher frequency components and we observe that time crystal can melt if you go to the infinite system size so this way all finite size calculations so it gives us the hint that if you want a genuine time crystal in closed system you need to stay close to zero temperature finally you may ask okay that was very idealized close quantum system but what about environment can we actually have this same physics in the presence of environment and the answer is no because if we actually demand that there are GZ states that will be transformed by Hamiltonian evolution one to another these states will decay exponentially fast in the system size so if you want to have the thermodynamic limit and you have some small coupling to environment even infinitely small gamma will destroy these oscillations so in some sense if you demand ideal quantum time crystal you also need to say how do I implement this ideal quantum system and there are not many that we actually know but one possibility is a fault tolerant quantum computer because if you can correct for errors that will be the example of ideal quantum system and if we look at the way how fault tolerant quantum computers are realized for instance with the toric code we see that they require strings of operators so we have physical operators x and z and the logical operators will correspond to strings of these operators so in some sense the operation of fault tolerance will be very much related to what we find for a idealized time crystals and this is an interesting question for the future research can we relate the two there were also the discussion of should we even bother to write down effective Hamiltonians for time crystals because they are unphysical because you neglect the tradition how can you even couple all spins together and the conclusion was that okay the flocchiatic crystal is the only genuine time crystal my answer will be that if we want to really understand the time crystalline behavior we need to agree on the definition and in fact there shouldn't be just a single definition of time crystal so one you can ask what's the idealized system and if you have a close system like a fault tolerant quantum computer how do you observe time crystalline behavior there what if you actually change the definition and make it operationally useful can it operate at finite noise and what useful effects of coherence will bring to spectroscopy and measurements so these are all the questions we can ask and study from very different perspectives finally I will just mention that the example I have shown is actually related to discrete time crystals because if I study the effective Hamiltonian for the sequence of discrete time crystals I will recover exactly the same shape of Hamiltonian so I will write it down as a matrix and this matrix will couple the states many body states in the form of GSE states so in some sense what discrete time crystals do for spin systems they mimic the effective Hamiltonian which I have shown and include the strings of different spins and with this I come to conclusion I would say that quantum time crystals are fascinating and they can be started from different points of view dependent on the definitions so if we go to very strict definition of ideally closed quantum system and impose what another Oshikawa conditions we can break it if we use long range interactions but if we relax this condition if we add the dissipation and drive we can get some other phases of matter and staying with the idealized system we could also ask the question can we relate time crystals to full tolerant quantum computation and can we use it in some protocols so with this I will thank you for attention and we'll be waiting for questions so thank you very much for perfect timing so please raise your hands if you want to ask questions so maybe let me start let me be the first actually we know that there is a no-go theorem from Watanabe and Oshikawa and for so that means that for systems with two body interactions continuous breaking spontaneous breaking of the continuous time translation symmetry is not possible in the ground state and and you have shown that with actually multi body interactions long range multi body interactions it is possible one of the important ingredient is that you need the gap in your system but the presence of the gap is not sufficient can you can you give us some intuitive some intuition what what is different in your system that that in your case it is possible but in the typical situation even if you have a gap system it is not yes so the intuition is the gap is important because the gap gives you oscillations if the states are degenerate there will be no oscillations for the correlation function but the trick of Watanabe and Oshikawa condition is we want to divide the correlation function by volume squared so whatever oscillates must must be microscopic must involve many spins and if I had relaxed this condition if I didn't divide by the volume but renormalize it in some other way I could live with a smaller range of interaction so not this all-to-all interaction but asking that correlations so your Hamiltonian must update all spins simultaneously that's the condition because only then it survives if you divide it by the volume that's the cruelty I would say of Watanabe and Oshikawa condition that you want all spins to talk to each other simultaneously and relaxing this condition you will actually make it like you don't need to update all spins and I would say it will be more like we'll have more operational mean in this condition thank you so still there is a chance for questions we have we have time so if not I will ask second question and because concerning the let's say the resistance of your system to non-zero temperature it turns out that actually only at zero temperature you can observe time crystal behavior and as far as I understand for in your system what is important is that you don't have that's a ground state that the first excited state are not degenerate my question is if you is it possible to let's say invent such a Hamiltonian also you know by changing this let's say properties of a highly excited state so that your system would be resistant for non-zero for let's say if even in non-zero temperature I believe yes we tried to do it and couldn't prove that it's impossible but also couldn't disprove it so the problem is not even the degeneracy you can come up with Hamiltonians where you you have like space in between levels such that there are oscillations the problem was what happens with the order parameter will it decay as you grow the system larger and larger because if we just do the simulation we observe that the prefector in front of the correlation function was decreasing as you increase temperature so you will you can still you still have oscillations but the magnitude of these oscillations will decrease as the system grows and that's again one more condition by but another she covers that everything should remain oscillating in thermodynamic limit okay thank you very much I I think we have to switch to the next talk thank you Sasha thank you and now let me turn I hope okay the next speaker is Vladimir Eltsov I can Vladimir you can you can share your screen okay so now the floor is yours you can start okay so thank you very much for inviting me to present our work on superfluous time crystals this is done at Alt University in Finland and this is experimental work so our time crystals are actually in stain condensates of magnet quasi particles which exist within superfluous helium 3 and I will explain what are these magnets and how we make a basic condensate of them in a trap within a superfluous and how we observe this condensation its manifestation is that spins or magnetic moment of these magnets the magnetic excitations spontaneously develop coherent precessions so all combined spin or magnetic moment is processing around external magnetic field without any external drive and this breaks a continuous time translation symmetry and so that makes this magnet condensates to be time crystals and we can actually make two of these time crystals in close proximity and they will precess coherently at their own frequencies which are close but slightly different and since these magnet condensates are actually possesses they possess spin superfluidity then due to the interaction through this weak link here we observe the Josephson effect or population oscillations between these time crystals while this continuous precession remains time coherent and we can also arrange such situation that during time evolution the precession frequencies of these two time crystals will actually cross and then we observe some dynamics which we interpret as a Landau's equivalent of Landau's inner transition in this time crystal system so this experimental work was mostly done by my former graduate students and postdocs and the time crystal aspect of it was most important in the work by Samuel Autey who is now at the University of Lancaster and we enjoy theoretical support from Grigory Valovik and his postdoc Yavkan Issey. Yes so as we heard many times already and we all know here that time crystals supposedly break time translation symmetry and in original idea continuous time translation symmetry and to limit the number of possible systems typically only many body interacting systems are considered and I'm coming from quantum fluids and solids community and qfs community has immediately an answer a superfluid in superfluid they can introduce a symmetric wave function or the parameter and the phase of this wave function will wind continuously with the frequency defined by chemical potential but as we also know that if you have isolated a piece of superfluid then its face would be not observable and this is a kind of general we have also general argumentation through this no-go theorem that if you have a ground state of a quantum system and then you can have this perpetual observable motion in it so there were ways to go around it found and one of them which is very very wide is discrete time crystals so breaking of discrete time translation symmetry set by the drive and we actually also have some work towards this direction but today I'm talking about breaking of continuous time translation symmetry so another way to go around this no-go theorem is to relax slightly this requirement for the ground state so if we can make a superfluid from metastable particles so that we will have by the instant on the set of some quasi particles for example then ideally such system will be characterized by two very distinct time scales one long time scale is the actually decay of the number of quasi particles but there will be some much shorter time scale which corresponds to equilibration within the system of quasi particles and if this time scale is really much shorter than this one then at some intermediate time scale you can consider system with almost or constant number of these quasi particles and look for the ground state of this subsystem at fixed number of particles but since this will be not a ground state of the whole system then this no-go theorem is not applicable and our choice for this superfluid made from metastable particles are magnets in between superfluid here on screen so magnets come as quantized spin waves and a usual transfer spin wave is the precession of spin around the equilibrium direction along the magnetic field which propagates as a wave so precession with certain frequency omega which propagates as a wave with a certain wave vector k and formally magnets are they introduced like through calcane primakov transformation from spin to boson operators and this way you find what's the number of magnets operator and then the spin magnets have spin minus h bar and the magnet density which is related to the keeping angle of spin or magnetization of course to have this precession to propagate as a wave one need to have some interaction between spins and in different systems it comes from different reasons and so in helium-3 it appears the following way so helium-3 is a thermosystem so it goes superfluid through cooper pairing but it's unconventional pairing it occurs in a state with spin one and orbital momentum one and so orbital also the parameter is three by three complex matrix responding to three projections of spin and three projections of orbital momentum and in particular b phase of superfluid helium-3 which i'm looking at here the so-called relative spin orbit rotation symmetry is broken so cooper pair they have spin and orbital momentum and what happens in the b phase that the direction of orbital momentum and spin are connected by rotation through over some axis n by some angle theta and this rotation is the same for all cooper pairs and the matrix of this rotation comes into the order parameter and in the absence of spin orbit interaction the energy doesn't depend on n or theta and so these are soft modes of order parameter and actually these nambugal stone modes they correspond to coupled motion of spin and this rotation matrix of n and theta and these are these spin waves in helium-3 they come as collective modes of the order parameter and n as a unit vector has two degrees of freedom and its motion corresponds to transverse spin waves which will be spectra and in the absence of external magnetic field they both will have zero energy zero momentum but if this symmetry is broken by external magnetic field then one of the modes gets the larval gap and it's called optical magnet and that's what this mode which we consider in this talk and what's important for producing Byzantine condensates of these magnets few things first these quasi-particles are very light so there is no problem of getting enough density to achieve Byzantine condensation especially this one anyway need to be at submilical and temperature for helium-3 to be super fluid the second important thing is that that these quasi-particles decay or thermalize to the ground state of the whole system through interaction with the fermionic quasi-particles with bagalubov quasi-particles in super fluid and since helium-3 has gap delta then the number of those fermionic quasi-bagalubov quasi-particles in bulk decreases exponentially and so lifetime really increases exponentially with decreasing temperature and lifetime of 15 minutes have been demonstrated and third important ingredient that actually in helium-3 there is spin orbit interaction and its strength is characterized by so-called legged frequency omega b and that means that energy does depend on the direction of n vector here and that means by manipulating the magnetic field and the direction of n vector we can create a trap for these magnets within the super fluid bulk and that's how our experiment looks like so we have a glass container filled with helium-3 b and using the magnetic field profile we create a trap in axial direction for magnets using Zeeman energy and using boundary condition for this n vector distributions called texture which is vertical in the axis of the sample and have some angle at the surface of the cylinder we create a trap in the radial direction and overall the trap is nearly harmonic so what we do then we create magnets by radiofrequency pulse we tip the magnetization and decrease in the z component of magnetization of spin means that we create magnets and of course after original tipping pulse all the magnets created are coherent so they have the same phase but since they exist in this non-homogeneous magnetic field their precessions start quickly to defase and also this in homogeneous texture has the same effect and so the signal is very quickly lost but what happens later as magnets get collected to the ground state in this trap this precession is magically refocuses and we end in the state where all spins precesses with the same frequency and coherence phase over the whole volume and this state is characterized one can also introduce this macroscopic condensate wave function and it turns out that the modulus of this wave of this wave function is a transverse magnetization of the condensate the precession frequency plays role of chemical potential and the precession phase plays role of the phase of this wave function and so all components here are observable in experiment and so that's how this looks from a real measurement so here we have the pumping and defasing you see it's very short on this time scale and then this condensation on the ground level of the trap happens within this calibration time and what we see here is this sinusoidal signal from the pickup coil which corresponds to the coherent precession of magnetization and by that time of course there is all memory of the pumping pulse is forgotten here so we believe the state is a time crystal so we can have a kind of time crystal checklist so it's certainly made a body interacting system and time crystal formation happens as a phase transition here this buzzer condensation certainly externally observable so the period is internally regulated and robust to perturbations pump or and just in a moment on the next slide about this and it's not a ground state of the complete system but it's ground state of the relevant subsystem of this magnet subsystem in a trap and dissipation doesn't affect the periodic motion it has no relevance to this period as I will explain on the next slide but eventually of course the number of magnets decays so we actually almost never look at our experimental signals in this time domain so what we do we have a signal in the short time window then we make a Fourier transform and then this coherent precession gets this very sharp peak here and then as you see here that actually when it's plotted like this the signal then you see that actually frequency slightly changes over the time it increases here well a little bit on the level of one megahertz of precession but this is exactly this internal regulation of the period with spin orbit interaction which which what happens here is that this spin orbit interaction it acts from texture to magnets but also acts other way around so and this texture orbital texture in super fluid here on three it's not rigid it can yield under the action of spin orbit interaction and so this precessionization favors in oriented vertically here and when we increase the number of magnets in the trap then actually the trap gets wider and the chemical potential lowers and the chemical potential means the precession frequency as I mentioned and so that means a larger number of moments precession frequency is lower and then it's increases and dissipation has nothing to do with it so this time increase magnum bc time crystals turned out to be a very useful tool to measure various things in in this super fluid here on three so they are sensitive to fermionic quasi-particles so one can probe for example this surface states in the topological superfluids they're sensitive to to the bosonic collective modes through these decay processes and then there is one particular collective mode which calls light kicks so can absorb this way they're sensitive to the quantized vortices so we have been using them to measure quantum turbulence so tangle of these reconnecting vortices moving to this condensate region and changing signals and also they can actually move around the sample carrying this trap with themself or the actual trap with themself and in this way they actually simulate implement exactly the Hamiltonian of one so-called cubal models in high-energy physics so about the thing which which which which is I want to kind of discuss here at the rest of this talk is interaction between time crystals so as I mentioned we have these two time crystals and or we can create two traps for for the magnets and we can fill them simultaneously and then we have these two traces from time crystals here sorry for different color scheme so for this amplitude of Fourier transform and as I mentioned we can extract various properties here frequency of precession which would be chemical potential phase of the precession and also the number here or the number of particles in this condensate that's I will show in the next slide and well basically these two time crystals evolve and I think special here but but you see here the side bands so so and these side bands we interpret here as you know in Fourier transform if you have a modulation amplitude of frequency modulation then then this appears as a side band and so we interpret those as this population oscillation between these two condensates so in in the very general weak link model yes between between two two states with the wave function corresponding to bulk bulk and surface condensates with some coupling key it's rather easy to get that there will be this acid josephson acid josephson effect when the population of there is a current from one condensate to another proportional to sign of the phase difference but this phase difference evolves increases with the difference of the precession frequencies and that corresponds to periodic oscillations of population of the condensate to acid josephson effect and the distance between the side band in Fourier transform corresponding to the to the modulation to the main carrier frequency is frequency of the modulation and as you see the frequency of the modulation is the difference of chemical potentials of the acid josephson effect and for this time crystals the sorry the for this time crystals the difference of chemical potentials is just difference of the frequencies of precession so we should have this frequency to be equal to this frequency and we can check this and that's indeed is true so this side band appears because the window Fourier transform is longer than the oscillation period we can of course analyze the signal on the time scale which is smaller than the period of this acid josephson oscillation and then in the bulk we have this nice population oscillation with a proper period as you see but for the surface condensate we observe this very strange thing which is actually have twice period of frequency so here we observed some new type of josephson effect where one of the components oscillate actually with double frequency it turns out that it's not an explanation it comes from the fact that when I was saying that our signal is proportional to the amplitude of wave function so to square root of the number of magnets there it was over simplification naturally the spin which is closer to the pickup coil will produce a bigger signal and so also geometry with respect to NMR coils enters into the picture and what happens is that when this number of particles in the big bulk condensate oscillate it also changes the trap as I explained previously not only for itself but also for the surface condensate and that changes the geometry of the condensate with respect to pickup coils and changes the signal in the pickup coils so what we did we did the simulation of all these three-dimensional textures of the wave function in the straps and the signal they involve in pickup coils and impose the this expected AC josephson oscillations there with the same magnitude and opposite phase to the surface and bulk condensate and then we found this doubling of the measured signal so that's the interpretation of the signal but the josephson effect is just normal so in a sense our time crystals they are doubly superfluid so they exist within the superfluid but they also demonstrate spin superfluidity by themselves so in the previous picture the frequencies of these two precession frequencies of these two time crystals were separate but since the trap for the bulk condensate is more flexible and for the surface condensate it's more rigid due to presence of the free surface which stabilizes this surface trap we can arrange so that during the time evolution the frequencies of actually of these two time crystals they cross and that's that's how this row for sliding Fourier transform look like here so this is bulk condensate which is here on this side and here on that side and this is surface condensate where frequency is almost independent on time so what happens here so we have here like two level time macroscopic two level system made from these two time crystals and what we can expect here that there is an aborted crossing here and that can be confirmed by solving appropriate equations and now if we actually look at the populations of this lower energy state which is first corresponds to bulk and then in the surface and of the higher energy state which first can spend to the surface condensate and then in the bulk then what will as a function of time then we will see that this there is this population of the lower energy state and so that's it's almost smoothly transferred from this bulk condensate to the surface condensate here but there is a small small part of population is actually going to the excited state here this is square root that's why this this change here is so much different so that smells like 1,000 in a transition the only thing here is a complication that if I actually calculate this probability in this particular case we can figure out this one seems that one can figure out this frequency change from this plot and coupling constant either this splitting or for the amplitude of this side band then we get complete mismatch in numbers so in experiment we get like one person transferred to excited level while according to this well-known formula they should be essentially no transfer of population due to this very slow evolution of frequency or chemical potential and to understand that we actually did the simulations of this two level time crystal system and so this is a slightly different experiment where only lower energy level state is populated and then everything you see here in the high energy state is comes due to this transition and this is simulation which actually reproduces the very well the behavior of the experiment with the coupling being hitting parameter here and also the so-called feeling factor for NMI measurements so how much actually this psycho-use experimental signal also hitting parameter and looking for simulation results we actually find what's what's what's the problem it's exactly comes to the fact that this precession frequency here and its change is internal property of the time crystal Vladimir five minutes left yes I am I'm next slide is conclusion yes so so and then exactly what what what happens here is that when frequencies of this two time crystals comes very close to this old rubber region where rubber region where this frequency difference is smaller than the coupling then they start this very fast radio oscillation and these couples through the trap creates very fast actual change of frequency and now if one put this into the Landauziner formula then one get the expected kind of transfer to the excited state which one see in the experiment but if one actually look at this slow change here that really gives wrong result and so I'm skipping the movie and so I'm coming to the conclusions so but then same condensate of magnet quasi-particles which is forming on the ground level of the superfluous here in three is manifested by this coherent precession of monetization which spontaneously break continuous time transportation symmetry and represents a time and interacting with time crystals they demonstrate the josephson effect conformity spin super fluidity and I stress it during all this time evolution they do this 10 millions precession periods keeping the coherent phase and and this two level time crystal system show dynamics which is kind of very often occurred in two level time systems such as Landauziner tunneling and the fact that this precession period here is internally regulated through the time crystal properties plays essential role in controlling probability of transition between levels and given that these things are keep the coherence over a long time that you can have josephson effect and some features of two level systems there the question is could one use them this question has been also asked before during this day could one use these features to invent some quantum devices based based on time crystals and one nice feature about spin coherent time crystals is that they probably exist even in room temperatures there are claims that there are some magnetic materials where the similar phenomena can be observed at room temperature and then of course that will be very nice for quantum technology so thank you very much for your attention thank you so please ask questions please raise hands if you have I can't see my hands okay maybe again let's let me start asking questions okay in your system first of all the number of magnets are not concert because this is on a global scale it's not conserved yes so but within this say observation time here it is essentially conserved but of course in in in in reality it's not conserved and as far as I understand you know there is a strong interaction between these two time crystals they at that corresponds to the nearly the same frequency of the precision of both of the condensate yes and this is my question is because one can also consider other system other coupling of of different time crystals for example even discrete time crystals in this morning the actually in angelo talks we saw that it is possible to couple discrete time crystals by let's say by something let's say they could interact do you expect that they the effect of the interaction will be also the strongest the closer frequency of the driving this to to separate time crystals is or or this is of course it's difficult to make this general prediction I can only say that that maybe I should clarify that this coupling actually between these two time crystals it's it's changing during evolution when frequency change frequencies change but but its magnitude is not the strongest at at this when frequency are the closest it's just that the interaction which may be the same where the frequency are far or nearby have the strongest observable effect when when when the frequencies are close by in our case so so so so maybe maybe that that what I can maybe that can be projected to other systems so yes if you have interacting time crystals then it's it's kind of maybe expected that when the frequencies are close by then the effect of this interaction would be the most profound okay thank you we have a question okay Vincent Liu please unmute and ask a question great very exciting talk so I just want to have a question something you might have talked about but I catch that so what sets the time scale of the emergent period of the meganon time crystal you said is the internal right yes so it's it's a competition let's see so basically it's it's a ground level on this trap yes and so so so the kind of the main the the trap is of course is prepared by experimentalist but but then the time crystal itself can make a small adjustment to this trap by modifying the texture so this this 800 kilohertz precession frequency is set by us by experimentalist but but but but then the time crystal is adjusting its frequency depending on on the number of magnets you put into it's another way to let me backtrack a little bit so it's very nice to see the measurement to test the super fluid which is associated with the u1 symmetry broken which is associated with the approximate conservation of particle number right so it's another way to test this time crystalline symmetry breaking or some effects due to that absolutely absolutely so thanks for this question so so because I can slide after this conclusion yes so that let's see it's yes so so there is this symmetry breaking so we can expect this an unbogal stone mode yes which would be we can call a phonon in in in a in a in a in a in a time crystal yes and yes this mode exists so it corresponds to oscillation of the soft variable of this phase of precession and it can be observed on the experiment this is like with double excitation of demodulation techniques you can observe the standing wave of this mode in the sample and then the next excited state so yes it certainly can be observed thank you okay thank you I think we have to stop at this moment now we have a break nearly half an hour and at 5 p.m. we will meet again during the poster session there will be breakout rooms associated with each poster so we can travel between different posters and okay we have a break thank you