 It was good. Let's go on with our workshop and now it's the turn of Julian Leonard with the frontiers quantum simulations with optical lattices Yeah, thank you very much. And thank you To the organizers for having me here. It's been fantastic so far. And thank you all for for listening for being here My talk fits actually perfectly in with the introduction that Anna gave this morning on on quantum simulations with optical lattices and This is the one platform for quantum simulations that I've been working on during my Time as a postdoc in the group of Marcus Griner at Harvard. So those these results that I'm going to present are mostly From there and I would also point out when we had some overlap with machine learning techniques Which we use to interpret or better understand our data sometimes So afterwards or since since recently I've started my own group at to to mean so that's also why you can see the Affiliation there and I'll also briefly show you what we are up to there Which I think also fits very well within this workshop here So in general when you're looking into performing quantum simulations And there are two different reasons why we want to do that and the first one is to is a more technological interest So we have certain platforms that we Would like to understand better to use them for for example industrial applications that includes some having for example better Materials high-temperature superconductors having better sensors better quantum technologies. So being able to Compute some problems compute with a physical platform some problems Would help us to solve those those technological technological issues on the other hand there's also fundamental interest because of course we also want to know how these systems behave from a very Physics point of view so there's an intrinsic value for us to understand that and that also means that we often want to go Beyond what is actually physically relevant and now study models or parameters Parameters that are outside of the physical reality So that can of course be useful to benchmark certain numerical techniques to have a better understanding which physical effects are actually at play here So they go beyond of a pure Computation of a physical system For this inter-industrial application, but actually also from a very fundamental point of view and there several ways how we do deal with these and always it starts from very very well understood fundamental building blocks, so we want to understand our individual legal blocks and we want to Then combine the interactions and once we understand the individual one once we understand the the rule with which You can bring two together We hope that the complex structure that we will find at the end is something that we will observe And that we can trust because we understand the individual rules very well And there are several platforms that I want to highlight here. Of course, there's more but there's a few key players here One are the trapped ions that have been very successful early on the optical lattices which I use the neutral atoms in the in the Also, ripped back atoms in tweezers, which have become very prominent over the last years have Have also working with the new atoms and then we have superconducting devices and this talk here will mostly be about optical Letters, it's also a little bit about tweezers not not so much about ripped back But a little bit about tweezers. So this is essentially what we are we are going to talk about today And these are both dealing with neutral atoms. So you can really tell that neutral atoms are really one of the very promising platforms in general to to access quantum simulations in today's today's physics In this talk, I want to talk about three different things first. I will give you a little bit of an introduction how this actually works with the essentially our our version of of quantum simulation with neutral atoms I know you already got a very nice introduction by Francesca last week at least those who were here last week I'm sorry. I'll keep it throat and focus on what's what's special for our system And afterwards I want to talk about two different Kind of problem sets that mimic a little bit these two different approaches that I mentioned before One is a bit more condensed matter oriented to actually understand How certain material properties can work in that that's where optical letters is originally started from and where they're very powerful And the second one will show you how with a little bit of more of a programmability You can actually also Study phenomena that maybe go beyond a pure material science application and have a more fundamental interest No, let's let's just start right away The the key to having a good quantum simulator is that you start with an excellent Initial state preparation that you have control over how you want to evolve the state Which means that you have control over as many possible Hamiltonians as possible and then finally that you and just I think we run out of battery Okay, I think I see to be wants me to do a blackboard talk now. Okay, we will see And and the third thing is that you can read out with a high fidelity and Luckily with these neutral atoms we can build on this huge toolbox that quantum optics has been Provided us all the all the quantum opticians of the last half century have developed for us And so we can prepare these states with a really really high fidelity And we can we can we can prepare them by optical pumping and cooling techniques We can then for the evolution we have very very high control over potentials because these atoms are always attracted or repelled by Lasers and so proportional to the intensity we can build Potentials and that's where you are useful and we can also control the interactions With actually a range of techniques that we've been developed for example, fresh butternutrients Resonances photon-mediated interactions work interactions dipole-dipole interactions, so there are many many different ways and Then we can have a very high resolution state Or a state readout down to the individual degrees of freedom of the atoms with Fidelity is I think the record now is a four nines ninety nine point nine nine Detection whether there's an atom at a given position or not So we would extremely high fidelity we can also know read out all the microscopic use of freedom of these systems So a very nice toolbox that we you're going to use this A few a few challenges here So one is that all these atoms you have to first make them actually interacting to have actually useful useful Quantum simulator they use some interactions and then also the second part is something that was very Challenging for the last decade or so for our community to get to the point where you have individual control over all these large numbers of atoms So having not a number of atoms is something that's easy. I pointed it out here on the left So actually it's fairly easy to have hundreds of thousands or even tens of thousands of atoms What's the difficult part is can I also get to the point where I have microscope to copy control over each of those atoms? So I think that's that's kind of the the balance that we've been learning a lot over the last 10-15 years In our system, this is what it looks like and so you can see here the this little line here separates the vacuum chamber from outside And this cartoon you really find that there's essentially a microscope that is half way outside a vacuum half inside a vacuum chamber So the last lens of the vacuum sits in the last lens of the microscope sits inside a vacuum chamber And then the physics happens right underneath this microscope lens So that right underneath this last lens and we can use it in both ways We can use light that we focus down in arbitrary patterns by shaping this light this light beam up here with the dmd We can create arbitrary patterns here and in particular also this optical lattice, but also variations there on there off on top of that And then we can also collect fluorescence from the atoms and actually image these atoms and can you can see here the pictures and So here's a bear picture and the Zoom in and then you can binarize this and with the high fidelity We know which which site was occupied or not so these are techniques that are by now 10-15 years Also, that's not something very new, but this is exactly how we do it in our experiment and that yeah It's a tool set here And I mentioned earlier that atom numbers are not intrinsically a problem So you can see what it looks like if you load all the all the atoms in our system So these are now tens of thousands of atoms and you can zoom in and it's indeed the shot that I showed you before So each each side here is on the letter side is either occupied or not occupied So it's a projective measurement that we take off these pictures of these atoms So the measurement is projective Projective that also means that the wave function that we evolve at the end will be in a in general in an entangled Proposition so it could be that we detect the atoms like this or like this or like this So although it's always the same quantum state each individual outcome will look different I sometimes call those the snapshots in this clock I will call it the snapshots of our quantum state So if we realize our system once and we take a snapshot of course the other the state will be projected into one particular Fox state basis and then I Throw away the state I restart over and I will prepare the exact same state Evolve it and since I have the exact same state my next Measurement will be just a different projection of the same side So this is in general how it works and this allows you to access a lot of Parameters a lot of observables and starting from density correlations and density is of course first order relations But also higher order correlations in the densities You can also measure local currents and you can also even access more complex Observables such as entanglement entropy quantum state purity and others So there's a huge range of Observables that are addressable with these kind of systems due to the single-site manipulation and detection techniques that we have Yeah, so with this I'm finished with my deduction. I hope we are all on the same page now. What's how it's going to continue Let's continue with the solid state Phenomenon that we're looking at and this is something where the optical lattice is actually original originally Was the original motivation for for building of the lattices and this stems from this analogy that in a solid We have the ionic cores of the Particles and the valence of electrons can now hop from side to side In this potential that's formed by the body by the ions of this of each of each atom that the that the solid is assembled from and we have you a very small length scales on the order of angstroms very very small Very small time scales of course because these electrons will hop very quickly now And accordingly you can afford to be at fairly high temperatures fairly high means in the Kelvin regime to actually see physics there and In contrast in optical lattices we could just get rid of the ionic cores and we say okay This is the static potential that electrons move in and this is what gives me in the end all my transport properties So I create this by a standing wave optical potential And this is now in which I place my atoms and this could for example now be fermionic atoms That move now from side to side again by hopping By tunneling from from side to side and then they interact And in this case now my lettuce constant is much much larger than the solid my time scales accordingly I'm much much slower, so it's accessible with standard electronics And my densities accordingly also of course much much lower and what does mean is that if my densities are lower now? My temperatures also have to be much much lower to have a comparable to have a comparison to solids And this is something that we are still struggling with to actually reach exactly those temperatures We are still a little bit higher, but we are still we are cold enough for a lot of phenomena But for some of the solid state phenomena phenomena, so we are not quite cold enough yet And this is an ongoing ongoing work But overall we are we are in a similar regime So there's a different quantum regimes the deploy wavelength is much much larger But in the end comparable in the same comparable to the lettuce constant in both cases in the same way and so therefore This is a system that is just much more controllable much more much more manageable than a solid But in terms of the physics we should expect the same results and This is one of the early results that were obtained when people started to load fermionic atoms in these lettuces And here if you increase the interaction strength they start here from a metal to a band insulator Where you can see that each atom each side has exactly two particles In this case the shop is empty So since these are fermionic atoms of two spins that means there is exactly One spin up and spin down on each side and then if you increase the interactions then these particles They start to repel each other so they're not on the same side anymore And it's that we end up with a mod insulator which is a charge or that's so exactly one side each side Occupate one atom and then people started to look into also magnetic ordering and by lowering the temperature below the super exchange you can now look at the Antiferm magnetic case and indeed if you then look at this spin ordering here You find these kind of nice spin correlations that as a as a function of the distance you find this nicer checkerboard pattern of ups and downs Of the spin correlation here so a big step towards simulating real real solids But as I mentioned again, and we are not really quite cold enough here to go all the way down To the to the regime maybe to explore this full face there I come here And what we now did in our experiment was to add a different flavor to this by going towards magnetic phenomena And this is something that's a little bit counterintuitive because of course the difference between our between real electrons and our neutral atoms is that Our neutral fermions they or atoms they would just repel each other through to S wave collisions Whereas electrons actually repel each other due to their charge and so all atoms since they're not charged They will also not see a Lawrence force so there should be no effect to a magnetic field But there are tricks so I can do that and essentially what happens is that you engineer piles phase through a ramen process that is different on each different lattice site or from each different pair of lettuces of lettuces and that means that if I now hop on a little plackette here I can accumulate a phase that is identical to the face I would accumulate in a pile space so like an electron on a on the lattice on a Solid in a solid state that is and it's even possible to tune this at will So you can really go from zero magnetic fields to all the way to essentially infinite magnetic field And I put it like louder than 10,000 Tesla because this would correspond to a pie phase on an individual an individual a placage So there's no point in going beyond that so essentially you can You can reach all kinds of magnetic fields that you could even not even dream of in a solid state system So that allows us now to because a new tool to also look at magnetic phenomena and One of the first things we were starting to look into was a Laughlin state Laughlin states are the permanent paradigmatic class of states that describe fractional quantum physics And what I do in a very nice way is that they are they are very strongly correlated And they combine both the cyclotron motion that a magnetic field would like to impinge on the on these atoms and at the same time repulsive energy kinetic interaction energy By bringing these particles apart and you can see that if you just would take a snapshot of a Laughlin state So this is a just a simulation where you see that normal particles if they would just Repel even if they would repel each other they were still somewhat somewhat random here So this would be a non topological state not a Laughlin state But maybe for example a superfluid state whereas the Laughlin state You can see that particles tend to try to be far apart from each other So there's there's some correlation going on where particles they don't want to be close to one another But a little bit farther and in the Laughlin ray function This is incorporated by the kind of a cyclotron motion where which particles do around each other So you can really think of the Laughlin state as one as a state in which All pairs of particles dance around each other So each particle is in its position of encircling all other particles And therefore it actually has its cyclotron motion built into the wave function But at the same time also it never meets another atom because it's always going around the other one and therefore the interaction energy is also minimized so that's why it's such a good state and it's also well it turns out to be a ground state actually and so that's it that's important and it's it's a good state because it's very simple and it's a very simple and that's and that's that's also Influential about this and we were thinking how can we prepare something like that in our in our system now that we have the magnetic field built in and Our first approach was to say, okay Let's put the let's take the smallest system possible and then try to understand this and build up from there The smallest system possible is two particles And in our case actually we're working with bosons here And so the the subtlety for Laughlin state so the they're always appearing at half flux So the even denominators one half one quarter are bosons It's a good for bosonic particles and then the odd ones for fermions And so in our case we're expecting to reach the one half Laughlin state here So one half flux which means we have twice the number of flux quanta in the system compared to the number of particles and that's Here we're starting so we're starting from a mod insulator one particle on each of these lattice sites So that's a small box. There's no harmonic potentially. It's just a small box four by four Sites one particle on each side and then we get rid of all the particles except for on those two sites And then we start the state in the as an initial state and we perform an adiabatic ramp Such that the initial state is the ground state to a certain Hamiltonian and then we change the metronian parameters Such that as an initial state remains the ground state throughout the entire evolution until the very end when we are Ending up at the final Laughlin state And then we can characterize this to snapshots So we may take a lot of pictures of this final state and we prepare take a picture Prepare again take a picture and so on and from that we can then characterize what the state looks like if it has the features That we expect from a Laughlin state We can even do something more we can Invert this final ramp and bring it back to its initial state And then if we end up with the same initial state of this So with the same same state that we started from then we know that during this evolution We actually stayed in the ground state and we can also even more trust that these snapshots here were actually taken from a ground state How does the sense of showing that yes adiabaticity is indeed working in the system? And these are the main results that we obtained here So you can find on the left side what would Particular top is experiment bottom is a theoretical prediction on the left side is a normal state And we are looking at the two-point correlation So not at density but the two-point correlates within these two particles and you find the left side that actually has particles They are happy to be at each they happy to meet each other So there's not a strong avoidance whereas on the right side We can really find that particles tend to be away from another so this is really this vortex structure The particles tend to encircle one another is much much more built into this right ray function So here down here is the radial average and you find this vortex core essentially in the two-body correlations And again, I want to emphasize the wave function itself is actually flat So similarly to this picture that I showed before with these many many black dots If you take would take this picture many times and then average over them it would be flat Right, it's just built in the correlations of the particles, but not in the actual wave function So it's not a crystal per se. It's really just a Pattern that appears only in the correlation and then we see exactly this pattern here in the two-particle version of this You can even go a little bit beyond that and actually verify that it's a one-half Laughlin state So the one-half Laughlin state has we expect to have a transport properties that correspond to a Laughlin state And these transport properties are showing up in terms of the fraction whole conduct connectivity Which you can probe by checking the variation of the bulk density with respect to the flux And this is called straight-up formula. So there's a variation of the bulk density So if you increase your flux by a little bit then the bulk density chain is a little bit And it increases a little bit and this increase is exactly proportional to the whole conductivity So from the ground set properties You can actually infer the transport properties of the state and indeed it's consistent with having about one half Of a fraction whole connectivity. So that also fits with what you would expect from the Laughlin state I want to point out that we are now exploring how to go to larger systems So this is an in collaboration with Tizia and that's and I know about so Tizia is also here in the audience If you want to learn more about us, he developed a Bayesian algorithm to actually optimize this preparation ramp that we were using And now we with this ramp We should be able to actually do the factor of 10 faster which in turn also means that with this optimized ramp We could now go to not four by four systems, but maybe eight by eight systems should now be within the same time scale and reach So we should be able to remain adiabatic because usually when you would go larger than of course adiabatic Particity is harder to to maintain and So if we can actually have an approved ramp then with this now we should be able to get much larger system So that's very promising and something that we are excited to explore in the future. Yes Exactly, yeah, and it's even the topological phase transition Which means it's very nicely for both protect protect it So you have to be very creative with your ramp to find a way that Keeps the gap maximally open. So essentially your finite size gap should be you want to be always as large as possible given by your finite size and That's easier for four by four than eight by eight system that that's correct But that's that scales fairly favorable if you take the right ramp So the trick is to have asymmetric tunneling during this ramp So these are some details that I didn't talk about now But there there's an optimal ramp which actually allows you to reach the final state without an extra gap closing But always a get an avoided crossing which is of course limited by the final by the final size of the system That's why it was so important for us to optimize this ramp before going to larger systems Because we only have a finite coherence time in the systems particularly does this artificial magnetic field Is it is a driven system? So you have to be make sure that you separate your energy scales and so well which works But you still have to this is all fine at coherence time We did on the order of 100 tunneling times and if you want to be adiabatic with a gap That's on the order of like it's less than a less than a tunneling energy. You have to be you have to be careful Yeah, but just to say that there's some promising new New work in this directions and this also motivates us to go to larger systems And so in Vienna we had actually now building a system Where one goal one of the goal is to actually explore these systems where these physics with other systems And what we want to do here is to to protect the lattices in a more flexible way Which will also enable us to have these fractional quantum Hall systems in in larger boxes We are in the very early stages now So here you can see a picture of the vacuum pump down as we did last week We also developing to these tools for this wave length So holographic protection of these lattices, but yeah, these are very early stages So but I'm very very excited that we hopefully soon will be able to to just build on this work and and look at more physics concerned concerning fractional quantum Hall states Yeah, with this I would like to move to the last part of the talk the non-equilibrium dynamics Are there more questions at this point? I'll show you one A few hundred usually a few hundred Yeah, and in the end most of these things scale like one over squared n is your error bar so if you want to have a reasonable data point Usually on the order of a few hundred starts to be interesting Yeah, so to probe non-equilibrium dynamics particularly in a more controlled way We are making heavily use of the light shaping that we had built into the system here And so typically we start from the smart insulator as we also did for the preparation of the previous state And then we apply local potentials to cut out certain regions Within this mod insulator that will be our initial state So here for example what you can do is get this two by four system here as a starting point Oh what we did here was to create exactly one particle in each row and this for example We use this as a test and for calibration purposes and for to check out the coherence in our system But it's kind of a cute little experiment So I thought I'd just show it to you so we have exactly one particle in each row and these are so these are copies So there's no vertical tunneling only horizontal tunneling so as soon as we should switch on the horizontal tunneling we expect to have a quantum walk and If we now tilt the system then there's a defacing that is proportional to the lattice side So there will be a refacing after a certain times of particle tend to go back again Of course only if everything remains coherent It's kind of a real space analog of law oscillations if you like yeah So you apply a force in this case by a tilt Which is a potential gradient that we apply and that now lets these particles to to kind of oscillate and after one Time scale which is given by the energy difference between two sites So after all sites would re-phase all particles would come back to the initial site and need that that's what's happened So here you can find snapshots after different evolution times So they're spread out and then after some time they come back to the initial site almost perfectly And that shows us that it's a very coherent process and we can let these run for for long times up to about a second So that's that's that's one thing we can do with these systems in this case That's really a single particle quantum walk And now it becomes of course more complex once these quantum walks are not performed from a single particle But actually from multiple particles at the same time So think of a starting of a one-dimensional system now with the one particle on each data site We're in the repulsive both are habit models of particles like to hop on neighboring sites They can occupy many particles can occupy each site and we have on-site repulsion And we start from a completely pure state So we know that each side has exactly one particle and we know that the state is globally pure So globally pure and locally pure in that sense Now as we let the system evolve after a certain time these particles have tunneled around So we are in an entangled state which now locally does not look pure anymore So locally this should approach now a thermostatistics So for example for the observable of the number of particles I would detect on a given lattice site I would expect a distribution that follows a statistical ensemble And at the same time of course we still have this globally pure state So the system has followed a unitary dynamics. So I know my global state remains pure We can actually check that the state is globally pure by interfering with a copy and you find that The purity remains need constant over time and there's essentially unity and you can also look at this purity on subsystems Which then essentially is the The the renee entropy of the subsystems and you find that very quickly they reach their thermal equilibrium And then the this entanglement entropy remains constant and if you look at larger subsystems Okay, it takes a little longer and there's some finite size installations so these are these are some things one can do to probe whether your system is thermal or not also as a Mutual information that can can be probably systems And we were wondering if one can actually use this kind of dynamics because it explores a lot of your orbit space Maybe there's a way to efficiently use this to actually learn the Hamiltonian which you are And that's a work that we've done in collaboration with Agnes Valenti and Eliska and and Sebastian Huber So it was she's also here. You've heard a talk about yesterday So the idea is that you use this non-economic dynamics to have an efficient way to figure out the parameters of your Hamiltonian and indeed even with a basing base algorithm You can be fairly fairly good But if you do use a neural network you actually just with a reasonable number of snapshots You can get knowledge about the Hamiltonian parameters down to the promul level We're just very encouraging to us because these are some of the bigger big problems Well, it's it's something that is difficult to calibrate sometimes to actually know exactly these parameter of the Hamiltonian It's typically something that reaching a percent level is fairly difficult It's it's it's easier to keep your system stable than actually to know your individual parameters So this is just a very nice way how how we can get our Calibration of the system essentially for free from from these snapshots Now the next step that we were applying That we were going here was to introduce disorder in the system and we know that this picture of of Thermalization and and locally thermo and globally pure that this should fail as soon as we go into a strongly repulse Strongly disorder system. There's this concept of many body localization that occurs here So essentially particles start to become localized because all their All their hoppings are exponentially suppressed so all these amplitudes of actually moving away they're exponentially suppressed so particles remain exponentially localized and There's this prediction Many body localization tells us that also in the limit of Interaction interacting systems. Although there are more many body resonances. I should still remain exponentially local So we have two competing exponentials here, right? We have on the one hand we have Anderson localization Which would tell us particles should remain exponentially localized on the other hand We have an exponentially growing here but space now because we have not only more particles But also interactions so the question is they compete and how do they compete and who which one does win and the framework of many body localization tells us that yes, actually what wins is the is the localization and over the recent years This has this review has shifted a little bit and now over very long times We believe that maybe there's still a little bit of the localization going on but on shorter timescales there indeed is localization is predicted and This also means that we are now in a system where statistical physics fails because we are not exploring the entire Hubble space in the system anymore Although we are very very far away from the equilibrium. There's a lot of energy in the system We would like to explore the entire space But there is destructive interference that we would do so many destructive interference of the many body processes in the system That prevents us from doing this and to our knowledge is really the only system that does not do that so many by the localization is really the exception to the rule and the exception to this paradigm of of Quantum thermalization, so it's very interesting to understand the conditions that are necessary to actually do so So in our system the way we probe this was very similar to the previous experiments except that now what we do is that we we apply disorder to the system a very strong disorder and Here what we do is we calculate now the the classical entropy Of the half change so it's actually count particles in one half for our system And if that remains at a constant value that means there's no more tunneling going on over the barrier Yeah, so we count the particles on the left side here Then we compute Pn log Pn to compute the entropy associated with that and then we see that really here on a logarithmic scale here These are many orders of magnitude thread on a logarithmic scale very quickly we reach a plateau here So from 10 to 100 tunneling times essentially nothing happens anymore And then we can also look at more complex processes in the system because there is still there still interactions present in the system So there should be some difference to a non-interacting system and turns out that this difference Manifests itself to the phasing of these localized particles or think of one particle being low in a localized orbital here another one here They're still talking to each other through these exponential tails because they're just exponentially localized. So Exponentially suppressed processes will actually lead to entanglement between different particles and that should Show up as an exponentially Logo-rhythmically slow growth of the entanglement entropy in the system and in our system here We probed the quantity that's related to the entanglement entanglement entropy and what you indeed find this this year There's a log scale again So we find the logarithmic growth of the entanglement entropy in the system Consistent with this picture of of a slow formation of entanglement. That's non-local in the system So this was the the second observation here in the system And now we went farther than that now and asked okay, what happens in between how can we characterize now the Thermal region and this localized region so as a function of disorder strength for weak disorder We know that the system should thermalize for strong disorder. We know that it's localized So what happens in between and other maybe some observables that should peak there Not something that just goes down or so but actually what tells us where the critical point should be what tells us with which point am I thermal at which point am I not and What we just looked into was the higher order correlation function in the system So we said okay The state should be the most complex in the middle because we know many body localization is weakly entangled It grows only logarithmically slow a little bit So it's a weakly entangled state a thermal state is also a simple state because all the correlations are completely Shaft into the global degrees of freedom So the the critical state should be the most complex one in terms of it's many buddy look it's many buddy correlations and so here we compute the multi-order correlation functions the connected correlation functions of two three four five and so on order and Check how strong are there they as a function of the disorder strength and what we find this This is the result here. So here the blue is the strongly Disordered regime and the yellow is the weakly disordered regime and in both cases We find that the second order correlation functions are present But everything else is very quickly decaying and becomes essentially negligible to describe my state and In the intermediate regime with strong with intermediate disorder I see that the higher order correlation functions. They stay high So you see the circles are the data points and the bars are the theory So and you have good good agreement with the theory that the higher order correlations matter And we went here up to the 8th order was essentially what we call computer and a laptop and they are they are really relevant We need them to describe the state and they are really peaking at this intermediate disorder strength and Also here we were trying to understand this a little bit better with machine learning techniques What does it mean to thermalize and how can we maybe narrow down this critical point a little better? This was in collaboration with Annabelle board at Regensburg And we tried several techniques For example just simple classification We also sort of tried to understand to learn the dynamics by essentially asking a network whether the It can still distinguish the state from a thermal state and if it can't distinguish it then we it would be a thermal state And so that was another method and we also tried a confusion method that was pioneered by by ever to is I think I don't know if he's already here, but he's over here where Yeah, it's a different technique where you essentially Guess whether there should be a critical point or not and not and from that in an unbiased way try to distill your critical point and These are just different approaches that we try to understand our data better And that allowed us to narrow down this critical point without going into the higher order correlation functions We are now going beyond this and trying to engineer in Vienna in a new experiment is non-local correlations in a more direct way and instead of actually Waiting exponentially long times. We are doing this by mediating the These inter entanglement these interactions between the particles over non-local Over long distances to light and so this is to an optical cavity that we have built around Individually addressable and detectable atoms and now the slide field now allows us to Connect any any other any particle with any other particle in the system In this case, we can even switch them on and off through this single addressing so you can in a programmable way Let these atoms interact throughout this entire system So this non-local couplings you can even do this dynamically switches on and off It also allows you to do non-destructive measurements for example for error correction protocols of our new observable so like weekly weekly perturbative measurements And also this allows us now to be much faster compared to these quantum gas microscope measurements that I've shown you before This is what it looked like before we put optics around the setup So there's our vacuum chamber here just to show a little bit of the update here's our little cavity that we put into the vacuum There's operating in the regime of strong coupling between each individual atom to the light field So not a collaborative effect, but each atom individually is strongly coupled to the light field and here's we Traffing these atoms in a tweezer array that we load from a 3d mod So it's a that allows us to be much faster Yeah, so with this I would like to close You can find a summary here So we talked to you about the solid state phenomena particularly for the fractional quantum Hall effect that we were able to observe for the first time in optical Lettuce is now here in particular this vortex structure that really shows us that Repetition of Laughlin is also what we find here and then that we were engineering this or measuring this entanglement dynamics in non-non-necribum systems in both in the thermal states and in the non-thermal states and Trying to understand a little bit more the conditions that you need to to get there So this is the team that I've had a pleasure to work with here the team at Harvard in the group of Marcus Griner and the theory collaborators that helped us a lot to understand and Interpreties data in the better way and this was a really fruitful collaborations and here's the new team at Tobin That I'd also have the pleasure would work with now for two years almost Yeah, and thank you all for your attention Okay, thank you Julian for the very nice talk I'm here Please go with questions. You are an enlist. Don't worry. Thank you very much So in the kind of one of the last slides you mentioned that you can now also like probe like longer-range systems and stuff like that Generally for long-range systems iron traps are considered like a Much better option. So how does it compare in simulating like parlor decay interactions and stuff like that? This Yeah, so indeed there's some some similarities with with iron traps in this kind of setup to have them in the string and then Mediating the directions in all case not to phonons, but to photons. I think the difference is that we don't use the Photons to trap the atoms simultaneously So in an iron trap the photo or the phonons or essentially the trap and the phonons the motion are coupled, right? So and that's that's exactly what limits the iron traps to actually still have these simulations going on in a faithful way When you when you go larger and larger, so I hope that with this system by splitting this off by having Fixed individual atoms that are at fixed positions trapped to light fields that are not the light fields that you use for talking to each other We actually have a bit more control We are also not limited to power-law interactions But actually we can go to any any kind of any any kind of so we're not within this range of what is it? 0.8 to 2.7 or something They have just deficit I don't I don't give a wrong number here But I'd have this range where they would have you comfortable, right? And I think we are we in principle can go to any other range We could also even think of an interaction that would increase and decrease with distance So you're not really limited to any power law even so that there's there's more flexibility But of course we have just pioneered this right now. It's not working yet. So we will see So being for the very nice talk I was wondering that plot the 3d plot that you show the the different regimes for the multi-partite correlation Yeah, multi-particle correlation. I don't know if you could just go back there because it's easier to explain Yes, exactly. So when you mention the critical Behavior that if you find that it's still high But I was wondering whether it's important the fact that it's no monotonic in the very end If it's there some Yes, that's a good question some specific when face transition we've asked as our as ourself Maybe we already see The onset of the finite size here because these were 12 particles on 12 sites So it could be that this is already like kind of the globalist degrees of freedom Which you put some into your free information because it's a finite evolution time, right? We are always probing here to find evolution time in this case after 100 handling times Which is much much longer than you need for the thermal and dmbl charge sector to Stabilize but in the intermediate region you're not there yet, right because otherwise it would not be like yet It takes very long and and so we are we're wondering if that would be reason, but I think it's not 100% answered Are there other questions Comments, so I have one. You know, that's now there is this quarrel if mbl exists or not Does your experiment help to? Critify this point. Yeah, we actually did another experiment on exactly this question Which I did not want to talk today about because I thought that's that's a bit too much information But there they are so There on the theory side I think there has been a little bit of a shift over the last years and the critical point has been moved upwards by I don't know a Factor every year. I think now we are somewhere at thousand instead of five or so so things go up And we believe that there's no true mbl in the low in the low digital regime Which is where low means below thousand tunneling energies or something like this So it's not quite clear if there could be a rematch super super high disorder strength Or if there's actually no true mbl at all now when I say no true mbl I mean that that there's still charge motion on the double lock scale So very very slow very extreme. It's not only exponentially slow But actually very slow. Yeah, and so that's something that experimentally I think you would not be able to address in this limit now the dominant factor that is believed to cause this very slow Dynamics is called the avalanche dynamics So essentially what happens there is that you have a small local Thermal bubble and that will help you now to to delocalize the neighboring spin or the neighboring site and the larger now This local bubble becomes the sort of local thermal bubble It acts as a bath always to the neighbor and then you have this avalanche process that De-stabilizes side-by-side your entire system eventually and so that would mean one bubble is enough to destabilize everything and It's just a question of Stochasticly how often do you have these bubbles and that's suppressed with this sort of it's always there and We were looking into this mechanism whether we can kind of artificially create such a bubble and then look at the dynamics And we did could see that there was this avalanche dynamic dynamics happening So that sense we can contribute to this But seeing this lock-lock dynamics over very long scales I think is something that like what you would expect in a really strongly disorder system long long like really big I think that's something that experimentally will not be addressable in the near future also not theoretically But is this this idealized models where you can understand the processes? I think that's something where we have already and also in the future that may be more experiments along these lines Yeah, okay. Thank you very much Let's thank Julian again