11:58:21 Okay, great. So, the title of my talk today is programmable interactions and emergent geometry, and an array of atomic ensembles it's about some work that we're doing in my lab on advancing control over interactions in systems of laser called Adams, and
11:58:39 And I don't think I need to convince you particularly after your talk, that cold atoms are wonderful tools for studies of quantum physics, with, you know, some of the kind of recent developments are astounding levels of single particle control and single
11:58:54 particle detection, but also these are systems where there can be well controlled interactions.
11:59:02 And I've shown kind of a couple of examples here of various systems where one for example sees Andy Farah magnetic ordering either of for me ons and an optical lattice due to their contact interaction, or in this case of some spins that are encoded in
11:59:23 Rydberg Adams with long range Vander walls interactions. So these are some of the tools that are available to us and systems of cold Adams.
11:59:28 But one of the kind of limitations that most experiments in this field face has to do with actually the connectivity of interactions. And so in these examples I've shown you.
11:59:39 You know where we see this anti Farah magnetic ordering it's coming about from some local interactions where, you know, interactions between nearest neighbors dominate.
11:59:47 And there are a number of reasons why you might want to be able to go beyond building systems where interactions are constrained to be local and, you know, one way you can see that in the in the sort of classical world is.
11:59:59 Isn't it amazing in this era of zoom that we can talk to each other, irrespective of the fact of we're, irrespective of physical location, right. So we know that connectivity governs the flow of information, and the fact that the internet gives us non
12:00:13 local connectivity, really changes the way that, let's say scientific collaborations form. So in the quantum world. Similarly, the conductivity of interactions governance for example the types of quantum state many buddy states that one can realize.
12:00:27 So if I had, for example iz interactions between nearest neighbors on a lattice. That's a natural way of dynamically generating a cluster state, which is a resource for computation, but if I have the same form of interaction and every atom talks to every
12:00:41 other that could generate a squeeze state that's a resource for enhanced precision measurements.
12:00:45 If I have some random graph of interactions. That might be a way to explore the phenomenon of fast scrambling of quantum information, where locally encoded information very quickly becomes hidden in complex correlations among many degrees of freedom,
12:01:02 and that in turn could be a toy model for what happens to information in a black hole.
12:01:07 Or if I have sufficient program ability of the interactions between the constituents of my system.
12:01:13 For example, I could take some classical computational problem and map that to the problem of minimizing the energy of my quantum system.
12:01:22 But that requires some program ability of the couplings. So, the sort of vision that we have in my lab is having versatile control over the graph of interactions in the quantum system.
12:01:34 And just to give a little bit more motivation.
12:01:37 Building on sort of the theme of quantum dynamics that's of interest to many of you, I think, let me sort of zoom in on this example of what would it take to realize a fast scrambler of quantum information.
12:01:52 So, Kate and, and for us this is this was actually kind of a motivation for some of the experimental development so I'll talk about today.
12:01:57 So say I want to study kind of fundamental limits and quantum dynamics, a fundamental limit to how fast information can spread from one to many degrees of freedom is.
12:02:12 It was sort of pointed out, coming from the study of what happens to information that falls into a black hole on that there's a fundamental bound on how fast information can be scrambled or localized across the system.
12:02:23 And that fundamental limit involves an exponential spreading of information from one too many, which wouldn't happen in sort of a system with local interactions, but does happen in some toy models that one can write down on paper, such as this syk model
12:02:39 with all to all random couplings are also actually some sort of early toy models for fast scrambling involved systems of billiards on expanding billiards on tree graphs for example, so here interactions are local but in some very exotic geometry.
12:02:56 Okay.
12:02:58 So if you'd like to start to explore some of these things in the lab, let me kind of draw some inspiration from the example on the left. We can't realize we won't realize precisely this syk model.
12:03:08 But we can sort of do some things that are similar in flavor.
12:03:13 In the spirit of sort of having the ability to have particles that can talk non locally in our system the particles are spinning cetaceans. And in order to get them to sort of hop over long distances.
12:03:26 The hopping process is mediated by light. So we have a physical system where we can, if I sort of think of a spin excitation as a particle on a site. Then if I can make a spin exchange interaction.
12:03:36 That is non local that would correspond to the sort of non local hopping.
12:03:41 The way that we do that conceptually, here's kind of a simple example if I have to level atoms, and I want to generate some non local spin exchange interaction.
12:03:52 What I can do is I can convert an expectation in this Adam on the left, into a photon right if the atom can flip it spin in the middle photon and this that photon is absorbed by another atom that allows me to have a spin exchange interaction that is sort
12:04:06 of as long ranged as the mode of the light that mediates the interaction is spatially de localized. And so this gives away of giving sort of effectively non local interactions over some volume within an optical resonator where there is strong, Adam like
12:04:24 the interaction in RX. So, so we in the lab, we have essentially an optical resonator it's really just to mirrors five centimeters apart. That allows us to have strong Adam light interactions and within that resonate or we Trump, an array of, in our case
12:04:42 little clouds of Adam so these aren't individual Adams but we have an array of about, typically 20 sites, each with some thousands of atoms.
12:04:51 And the idea is that photons should be able to mediate interactions between arbitrary Adam pairs in the system. And we'd like to also get to the point where we have some program ability of the structure of those interactions.
12:05:04 So before I kind of show you data I'll tell you a little bit more about the atoms in our system in our system.
12:05:11 Each atom has actually I sort of gave the spin half example earlier but each atom actually has a spin one. So it has these three magnetic sub levels minus one zero and plus one.
12:05:21 And one of the ways that we like to probe the system involves initiating the atoms in the zero state. And in that case in the simple case of two atoms, the process that you would expect to see is one where, if you send in a control laser, a photon can
12:05:37 be scattered by the first atom which flips it spin from zero to the minus one state, and the second Adam re scatters that photon and gets converted to the plus one state.
12:05:48 So I drew it here in kind of an asymmetric way but really you should think of this as a way of taking two zero atoms and making this superposition of one atom being in the minus one state or the other in the plus one state.
12:05:59 Okay. So that's the basic mechanism that we're going to use to kind of probe the interactions and the dynamics in this system with non local photon mediated interactions, and we won't look at two atoms will look at the system of many little clouds of
12:06:15 atoms. And the first thing that you can do to kind of sort of see these atoms interacting is start with all atoms and zero state, turn on some light that should turn on the interactions, and then measure after some fixed time, the populations in these
12:06:29 three internal states.
12:06:32 And so what I'm showing here are some pictures, where each row is just a different iteration of exactly the same experiment, so this is 30 repetitions of the same experiments.
12:06:49 You, there's in each column I have actually sort of position in this array is the horizontal axis, and we have the populations for these three internal states that we image independently.
12:06:55 And what you'll see is that from shot to shot, you'll see some large fluctuations in the populations.
12:07:02 But you'll sort of notice those fluctuations are correlated right so some shots we have more atoms in the minus one state and also in the plus one state.
12:07:13 And, and this is starting to be a signature of this process of the light mediated interaction that generates these correlated Adam pairs and the plus one minus one states.
12:07:22 Okay, so far. One thing you'll notice is there don't seem to be any interesting spatial correlations, more or less, if there are more atoms in the minus one state you see that kind of uniformly across the atomic cloud across the array of atomic clouds.
12:07:39 So we would like to this is kind of showing all to all interactions mediated by the light, and we would like I said to have also some control over the structure of these non local interactions.
12:07:53 And in particular, you know the dream might be to have arbitrary control over the connectivity will be slightly more modest and say, Can we start to have control over any translational invariant form of interaction.
12:08:05 So our goal will be to have sort of any dependence on that we want of the structure of interactions as a function of distance in the array.
12:08:13 Okay. So how might we do that.
12:08:16 Um, so the first thing that we do in order to have this control is actually to break down the all to all connectivity.
12:08:24 By applying a magnetic field gradient.
12:08:27 So ordinarily every atom to talk to any other but if we apply a magnetic field gradient across the system. Then we have a scenario where the process of creating a plus one minus one pair is only resonant for two atoms that are sitting on the same site.
12:08:41 If the atoms are some distance apart, right then.
12:08:46 That process is not conserve energy and the magnetic field gradient and correspondingly.
12:08:50 If we stuck if we do the same experiment start with all atoms in the zero state. Turn on the interactions and measure at some fixed time. What I'm showing you here are basically spatial correlations between population and the plus one state on site I
12:09:05 and population and the minus one state onsite Jay.
12:09:09 population in the minus one state on site J. And you can see the correlations are strong on the diagonal, indicating that these interactions are local and are giving rise to just these short range correlations on each site.
12:09:20 OK, so now though, we can take this one step further, so I showed you, we can get all to all connectivity, we can get local interactions.
12:09:29 And now it turns out that if we want to say turn on interactions at some particular distance, all that we need to do is drive our resonator with to laser frequencies that allows the atoms to an atom to absorb a photon, have one energy, and another item
12:09:46 to emit a photon of another energy and that gives a way of sort of bridging the cost of creating a plus one minus one pair at some distance.
12:09:55 Okay and so here you see these correlations appearing off the diagonal.
12:09:59 In this case, showing that we've turned on interactions at a distance of 10 sites in addition to the local interaction.
12:10:06 Okay, and and that you can vary. So essentially what we're doing is really intensity modulating the laser field so that there are these two frequencies present, and as a function of the modulation frequency.
12:10:17 If we look at spatial correlations so horizontal axis here is basically showing correlations versus distance vertically we're varying the modulation frequency, and you can see that the distance at which the correlations are strong tracks the modulation
12:10:30 frequency.
12:10:32 So that's showing program ability of the interaction distance and we have very fine control we can really see discrete peaks for interactions at 10 sites 11 sites web sites.
12:10:42 And now you can imagine generalizing this, it's actually quite easy in the lab to control the spectrum of the laser field. And that should allow us to control, and then essentially arbitrary way, the interactions of the function of distance.
12:10:56 Okay. So to give a little bit more of a picture for sort of how I like to think about this.
12:11:02 You know I sort of gave a picture in in real space, where the frequency separation between sort of two teeth of my dr field sets the distance at which the interactions are on.
12:11:13 Um, it's also kind of nice as a complimentary picture to think about this in momentum space. So if I take a Fourier transform.
12:11:21 I can conclude that actually the, the waveform and time of my laser field. I'm actually sets the energy as a function of momentum. So it's that's the dispersion relation for spin expectations in the system.
12:11:37 So that's another way I can think of this, my writing my Hamiltonian momentum space.
12:11:40 This energy versus momentum is set by the temporal waveform of the dry field
12:11:46 in our system actually.
12:11:50 And there's a there's a minus sign in front so minimum intensity corresponds to maximum energy.
12:11:56 In this particular system of this spin one physics.
12:12:00 It turns out that the peaks in a sorry the the energy minima are also maximally unstable to creating these correlated Adam pairs. And so one of the things that we can see actually is if we analyze the time evolution, or plot the time evolution we can
12:12:19 look at it in real space or in momentum space in real space as a function of time.
12:12:26 In this case I turn on interactions at a distance of three sites. I'll see correlations sort of spreading from a distance of three sites six sites mine sites as a function of time or equivalent in momentum space, I can think of this is some peaks appearing
12:12:39 in the structure factor at a momentum that corresponds actually to a peak in my modulation waveform and this is really coming about from the fact that the modulation waveform sets the dispersion relation, and the energy, energy minimum or maximum the
12:12:55 unstable to creating these correlated that in Paris.
12:12:58 Okay, so that's the time evolution. I'm one of them and it sort of corroborate to this picture that I can engineer the dispersion relation with the modulation waveform at the DR field, one kind of interesting subtlety.
12:13:12 That was actually pointed out by one of my students is that well this is a you know finite size system. So really, if I'm thinking about sort of engineering the dispersion relation.
12:13:20 This should only be defined that discrete points and momentum space.
12:13:24 So if you take that literally you would say maybe I shouldn't be driving continually my laser maybe I should actually be posting it on at discrete times.
12:13:32 And it turns out if you do that you precisely realize the dispersion relation for the finite size system with periodic boundary conditions. So that shows up in this plot of correlations versus modulation frequency as saying that for example if we have
12:13:45 interactions at a distance of two sites. We also have interactions at a distance of the length of the chain minus two sites.
12:14:03 So that starts to show you that the geometry of the interaction ground doesn't have to be the same as the physical geometry in our system.
12:14:10 even though physically, the system is, it's just a linear chain.
12:14:12 And one of the things that we like to do to kind of actually directly from the data see what is the actual geometry of the graph that we've engineered, we can actually directly go from sort of the measured spin correlations, to ask, you know, we think
12:14:28 we've engineered let's say this ring with periodic boundary conditions.
12:14:33 Do the data agree.
12:14:35 And so we can for example take these measures correlations and say, What is the best sort of geometrical representation of the different array sites to explain the measured correlations if we adopt some concepts that correlations decay with distance,
12:14:50 and some effective geometry, right, so we're going to try to find some effective coordinates that explain these measured correlations.
12:14:57 In our case it's natural to adopt a Gaussian opposites. And if we do that, what we find in this case of nearest neighbor interactions and periodic boundary conditions, is that in fact this sort of reconstructed geometry by this black box techniques right
12:15:12 from the experimental data looks a lot like, all right.
12:15:15 And here we've actually drawn all possible bonds.
12:15:19 And there are passes it is set by the correlations, specifically extracted from the inverse correlation matrix. And so it really what pops out is the ring and okay so that kind of corroborates that we have that graph.
12:15:34 And now you can kind of play with different waveforms and see what geometry pops out and just just as a few examples you can make this ring, but you can also make a movie a strip.
12:15:43 You can make an anti fair, a ladder geometry, a cylinder. And these are just by different sort of coupling graphs that we program in with the spectrum of the dry field.
12:15:54 And one other thing I'll highlight here is the color of the bond indicates the sign of the correlations, and just by sort of a phase that's either zero or pie in the modulation waveform we can control or the interactions and the resulting correlations
12:16:09 Pharaoh magnetic or anti Pharaoh magnetic.
12:16:11 So those are all tools that we have, and there are kind of a number of different directions that one can take these.
12:16:20 One thing I highlighted here for example are the ability to have an effect on magnetic interactions that are of interest for studying frustration for example, realizing potentially class, frustrated, classical xy models and asking whether the quantum
12:16:34 system can help to find the ground state.
12:16:37 Sign changing interactions could be interesting for studying spin glass physics. Some of the graphs I've shown you can realize in other ways with local interactions.
12:16:46 So we're particularly interested in kind of what are the unique things you can do with these exotic non local interactions. And that brings me back to this sort of topic I mentioned earlier with Ken one realize some kind of toy models for phenomena such
12:16:58 as fast scrambling or models inspired by by quantum gravity. So, in that vein for quite a while, actually, before realizing this level of control in the lab we have been dreaming about what are some of the things we might be able to do with it.
12:17:14 And we've been thinking about sort of what would it take to observe exponentially fast, spreading of information across across a quantum system.
12:17:24 And one sort of toy model that, in principle out to allow that in the system is one where you have couplings. So, in our system that couplings will be translational invariant.
12:17:36 But imagine that you have couplings that are at distances that are powers of two. So, 124 and eight sites in a chain of 16.
12:17:54 For sort of any site to talk to every other in a number of steps that's logarithmic in the system size. So we had to kind of been thinking about this toy model you can add one more ingredient which is some power lot exponent that decides, do the interactions
12:18:05 decay with distance or do they grow with distance.
12:18:06 And if they decay with distance the coupling graph looks like what I've shown on the left, it's not that different from a linear spin chain.
12:18:13 If they grow with distance.
12:18:18 Then, then that looks a bit more exotic right the strongest bonds are between for this neighbors.
12:18:22 You can kind of actually rearrange the ordering of the sites compared to the physical order so it starts to look a bit more local, and I'll try and convince you actually the right way to think of this system is that the sites are arranged on some sort
12:18:35 of a tree graph.
12:18:37 Okay and the conjecture is that actually at some point in between these two geometries. Everything is kind of strongly connected to everything else and this should be a fast scrambler.
12:18:48 What we're focused on so far is actually the the sort of right side of this slide, can you realize this weird tree like geometry.
12:18:55 And so, you know, we can just program in that structure of interactions there at distances that our powers of to and they grow with distance, if you measure the correlations in the system.
12:19:04 They have some rather exotic looking sort of non monotonic dependence on distance.
12:19:12 And this starts to look a little bit more structured, if you reorganize the sites in this analysis so I plot these same correlations, but I reorganized the sites according to their position on that tree graph.
12:19:24 And then you'll start to see kind of a hierarchical structure and the plot of the correlations, there are some blocks that start to appear.
12:19:31 And if you ask actually what are the correlations as a function of sort of the actual measure of distance in the tree, which has to do with sort of how many steps up the tree you need to go to connect to sites, then you actually see a smooth the K of
12:19:51 correlations versus distance in this sort of exotic new geometry. We are kind of intrigued by this because this tree graph is actually considered. It is a sort of a toy model for the idea of holographic duality, where I have some physical system that
12:20:04 lives on the boundary of a higher dimensional space that encodes something about the structure of correlations in the in the physical system on the boundary.
12:20:13 So, this is this idea that there's sort of one expert I mentioned with with curvature that might come about from gravity.
12:20:22 That gives a notion of of distance thats related to the correlations and the system on the boundary.
12:20:29 So in this particular case.
12:20:33 In contrast to other graphs I showed you where we really engineered let's say a Moebius strip here, the tree isn't physical, but the tree is supposed to capture something about the structure of the correlations in the quantum system.
12:20:45 So if you want to sort of really directly.
12:20:49 Check that is this tree graph a good description of the system.
12:20:53 We can sort of adopt the procedure I showed before where we first asked, What is sort of a good geometric picture for thinking about the positions of the sites in some effective geometry or correlations decay with distance and doing this here actually
12:21:08 for two cases.
12:21:10 One is the one where interactions interactions that came with distance and it's not too different from a linear chain. This is the case where interactions, grow with distance, sort of more exotic regime.
12:21:20 So the first thing is we reconstruct sort of the site positions in 2d, some effective positions that explain the correlations. And then we adopt a course grading procedure where we draw bonds between sort of the most strongly correlated sites so we measure
12:21:35 correlations between the spin on site INZJ we draw bonds between the most strongly correlated sites we treat those as a larger site and repeat the process until everything is connected.
12:21:45 And if you had the sort of interactions that decay with distance. This kind of looks trivial, you end up with this ring.
12:21:52 But if the interactions are in this model that grow with distance you actually see this tree graph and will emerge from this kind of course grading procedure.
12:22:01 So, that is kind of a neat toy model for this this idea of holographic bulk geometry. But the other thing that you can ask is now, we have these two kind of radically different geometries that you can tune between with a single parameter, that's this
12:22:19 power light exponent.
12:22:22 And if you do that so so here we're actually varying that exponent, s, and asking, How strong is the correlation between kind of two halves of the system, if we cut the system in half.
12:22:36 And so for example if you have the SS less than zero so interactions decay with distance and you cut the system according to the physical geometry.
12:22:47 Then the correlations between the two halves are relatively weak and similarly if essence, greater than one, I should cut according to the tree graph in order for the correlations between the two sites to be week and it's shown in the two sides to be
12:22:59 weak, it's shown in green.
12:23:01 But if Actually, I go in between I set this exponent to zero so interactions are sort of strong and all length scales there's actually no way to cut the system so that the two halves or weekly correlated, and that is potentially sort of the the right
12:23:14 starting point to be able to explore.
12:23:18 Perhaps fast scrambling in the lab.
12:23:19 Okay. So with that, I will just kind of conclude and say that I've shown you a pretty versatile toolbox for programming interactions in the system of cold Adams we can control the graph of interactions the sign of interactions.
12:23:34 We have a way of reconstructing some effective geometrical description of the system, directly from experimental data.
12:23:42 And this would be nice to take these tools and go deeper into exploring the the dynamics How do the dynamics depend on the interaction graph.
12:23:55 Can one. Are there situations where this kind of picture of a holographic bulk geometry give some insight into or a nice way of thinking about the transport transport in the system.
12:24:06 And lastly, also, we're interested in kind of exploring applications of these programmable graphs to problems and optimization or generating new spatially structured entangled states.
12:24:19 So with that, I will just kind of thank the team of people who made all of this happen. And I will take any questions.
12:24:30 Thank you very much.
12:24:32 So, Nicole.
12:24:35 You have a question.
12:24:40 Sorry I was on mute.
12:24:42 Thanks for the very, very fascinating talk it's amazing to see what you realized in the lab.
12:24:47 I was wondering about the ring structure that you showed seemed to have one.
12:24:53 Non uniformity one sort of defamation. And I was wondering Is that just some artifacts that isn't very important. I was just wondering why it isn't homogeneous.
12:25:02 That's a great question, and it is an experiment and experiments usually aren't perfect. What is the limitation in this case, in this case the defect actually is between the two ends of the chain and the physical geometry.
12:25:18 And I believe that is from some combination of the atom density being a little bit lower at the edges of the system and the intensity of the cavity mode also being a bit weaker at the edges, and in principle, there are ways to compensate that.
12:25:34 But, so, yeah, so this this is there is a bit of a defect. On the other hand, actually in the case I showed towards the end with this.
12:25:44 The model, where I was showing the bulk geometry for the tree, the reconstruction of the, the opposite limit where it was more like a linear chain actually look very almost perfect so and you know that was a different data set in a slightly different
12:25:57 interaction structure so yeah I think to me this is I think in this case it may be related to this in homogeneity at the edges of the system. But I would say it's probably not fundamental to be addressed.
12:26:10 So, yeah, thank you.
12:26:17 Go ahead
12:26:17 and proceed experiments. I have one, one question. So you. Why do you use that ensembles, instead of single atoms because on one advantage of December's will be that you can you know look at full distribution functions and see the statistics.
12:26:33 In addition to just you know labeling either be one or zero or minus one.
12:26:39 Yeah, so, um, why do we use. So first of all, the sort of main reason actually why we use the ensembles, is that we do benefit from a collective enhancement in the atom light coupling so we're in the strong coupling regime for single atoms but sort of
12:26:56 barely.
12:26:59 And so we win a collective enhancement. And I think there's an kind of interesting direction of pushing towards, you know, really maximizing the single atom coupling and going to single atoms in the cavity, but right now I would say there's as you say
12:27:11 there's a lot of rich physics already with the ensembles.
12:27:15 And you're right, actually we could look more closely at the full statistics, right.
12:27:20 There's probably a lot of information there were interested in. I haven't proved entanglement with the data I showed you, but we've got something we're currently kind of working on in the lab is measuring entanglement and also asking sort of what can
12:27:32 you do when you can program the spatial structure of correlations between these ensembles.
12:27:37 And then, yeah, and so actually, it's maybe worth mentioning in terms of kind of the outlook ultimately for some of these things like, you know, studying fast scrambling, this would be most interesting in the regime where it's really kind of a quantum
12:27:49 single quantum spin on each site, in the sense that, that's sort of the the regime where you really can't calculate it and have to do the experiment for us, for this sort of early time dynamics with many on the site.
12:28:02 Some semi classical methods work quite well for modeling modeling the experiment so it's where it's interesting where we expect to be generating entanglement, but still in a form that is kind of amenable to some numerical simulations.
12:28:15 But again, for some, some directions like this question of can you use the system to solve some optimization problem that would already be really interesting to study actually in this system of ensembles where there seems to be some kind of the dynamics
12:28:28 naturally give rise to actually kind of low energy states of the classical spin model. So, yeah. And so I think there are really interesting directions and both machines.
12:28:41 One quick quick, did you look at other higher order correlations and factorization and things like this, we haven't looked at higher court order correlations that, um, yeah, really, I think direction or in the quantum corrections, you know, yes.
12:28:55 Yeah, so I think this is something that would be great for us to think about in the future. Yeah. Yeah. And maybe this is something we should learn from you about.
12:29:04 So, yeah, it's a great time, you know, anytime. Yeah.
12:29:10 Okay, don't share all the programs you want.
12:29:11 If you want them.
12:29:15 Great. Yeah. very nice. Thank you for.
12:29:18 For this I I just did maybe to spike the questions. So, did you try creating a two dimensional lattice with local interactions by choosing your long range interactions in a way so that it mimics that or is that too hard, because it won't be then it, it
12:29:36 won't have this forum, it won't be like on a function of i minus j, if you want to create, to the local systems by starting with your.
12:29:48 Yeah, so I'm actually let me see whether I have one slightly different slide, sorry let me I just want to actually show it a different slide if I can, but I have to stop the share and restart it
12:30:05 think it will help answer your question.
12:30:23 you're right you're looking at it I mean I can be to stand up. Sorry, I will. I'm just gonna say it in words. Sure, sure, sure. So, basically like in these examples.
12:30:36 You saw you can see this again right the gallery of graphs. So, These things like the movie a strip and the cylinder are essentially like, you know, 2d systems plus periodic boundary conditions.
12:30:46 I mean, in this case, I mentioned it's pretty short. But the way that we do it like the the movie strip, for example, the way that we actually make it is we have 18 sites and we have nearest neighbor interactions and we have interactions between nice
12:30:59 neighbors. Right.
12:31:00 Precisely.
12:31:03 So, but but how large Can you make.
12:31:06 Can you do like I don't know 10 by 1020 by 22 relapses oh yeah and so for us I think in terms of kind of limitations on how many ensembles we can fit into the cavity.
12:31:17 It's probably hard to go above like order 100, total number of sites in, I was in our existing scheme and I think it's probably an interesting question to ask.
12:31:28 If you really push things how hard, how far you know, can you use a second dimension physically to also fit it package and kind of more racially.
12:31:40 I think there are directions to scaling that up more but I would say 100 is about what's naturally.
12:31:46 Yeah, I was wondering whether out there. For example, something like they could die of honeycomb model or anything more exotic which has.
12:31:53 I mean, that to be, yeah, maybe I would say that actually, in my opinion, in some sense, for some for these local lattice models.
12:32:02 It's not clear to me that this is really the best way to do it, I think, I think there are systems with let's say Rydberg Adams were that are really naturally suited to studying like spin models with local interactions.
12:32:15 And so for me the strength of the system is more the ability to go beyond that and have this really versatile control. Right.
12:32:24 Okay, illness.
12:32:28 Yes, we can also thank you very much very cool experiment. Very nice.
12:32:33 So the one thing I just wanted about because you talked about food controllability and you want to use it for say community optimization. So how are you going to prepare, low energy state in the system, because at the moment I think it's more like a propeller
12:32:47 driven disadvantage states, which is a really great question. So, I'm good to me.
12:32:52 driven disadvantage states, which is a really great question. So, yes, and I kind of glossed over this, so you can start to see so I kind of hinted at this a little bit, when I said what the physics of this pair creation is basically something where if
12:33:05 I can think in sort of momentum space, there's kind of an amplification of certain momentum modes that are at the correspond to the minima of the dispersion relation, but kind of another way to think about this, that.
12:33:17 Yeah, because it's not all obvious right I suddenly turn on interactions Why should I generate a low energy state. So what's kind of going on here is we have these three internal states and there's a quadratic same on shift, which means that, creating
12:33:27 a plus one minus one pair actually has a small energy cost in terms of the internal state energy. And that actually allows the system to lower its interaction energy.
12:33:39 By increasing this quadratic name on energy.
12:33:42 And so for example, like when we engineer one of the graphs we engineered is this anti Pharaoh magnetic ladder.
12:33:50 And we just really, again, it's just dynamics.
12:33:54 But what happens is that we do in fact see Andy Farah magnetic correlations.
12:34:01 And that, that actually match very well to what you would expect, which is a roughly sort of hundred 20 degree ordering on this lattice so you can see that if you look at sort of correlations versus distance or also if one looks at kind of the structure
12:34:14 factor.
12:34:15 There are sort of peaks that correspond to the phase of the spins winding by sort of 120 degrees per site, as I sort of go along this ladder. So that's a really kind of neat.
12:34:27 Almost unexpected thing about this system is it does lower the energy of sort of the x y and the action by increasing this quadratic same on energy.
12:34:39 Yeah.
12:34:40 Okay.
12:34:42 Mama.
12:34:45 This.
12:34:47 Hi, thanks for the nice side. Actually, my question is maybe related to the previous Scotia I'm not exactly. Can you make the Hamiltonian cowgirl in the sense that you would have flip flop, but not fluff live interaction.
12:35:02 Um, I think so.
12:35:04 Let me make sure that I'm thinking of the right thing. So one of the things that we can do is actually and it's related actually to this quadratic name on energy.
12:35:13 So, it turns out that we work in a regime where this quadratic same on shift is relatively small compared to the interaction energy.
12:35:23 But in general, actually even on this plot. It's not entirely net negligible and what you'll see is there's a slight shift of this peak that ideally is at zero, it's slightly shifted, you can see a little bit of a sort of side feature on the right.
12:35:40 And that actually has to do with the fact that if you sort of take this to a place where there's a stronger quadratic Zaman shift, you could actually engineer something where you can create like plus one on a given site and minus one on the site to the
12:35:57 left, let's say like that you can make that be the resident process.
12:36:03 related. So that's actually going to be on her mission. But that's that's okay, right yeah okay so is it also Cairo or no, it's, yeah. I mean, I guess it transports particles one day so it's called on her mission.
12:36:19 Yeah, kind of like this asymmetric exclusion processes or something like that.
12:36:25 Yeah, yeah, I think, in principle, that's the message I'm getting principal decibels. Yeah. Um, and then the other thing you can do that might be related is you can control the phases of the couplings right so we can put in any phase we want to put a
12:36:39 couple links as well.
12:36:44 And you know if you do.
12:36:47 Hey, guys, thanks for the nice talk.
12:36:51 I have one question I have is, at no point you consider dissipation right through. I'm wondering if just sort of defined a devotee line with you really don't care about it because you're copying activity is large enough, or is it something that at some
12:37:06 point I should worry about. Yeah, so definitely at some point you should worry about it and this is in some sense, kind of related to your next question like why do we work with many atoms for us we do benefit from having a large collective cooperative
12:37:25 on each site. And so for the collective dynamics, the dissipation.
12:37:29 It's not negligible, it sort of at longer times there's sort of two processes that can hurt. One is, instead of having these flip flops you could have just as sort of single spin flip and the photon leaves the cavity.
12:37:42 And then there's also three space scattering that can redistribute atoms between different internal states.
12:37:48 And so, neither of those is negligible we do sort of our longest experimental times there is
12:37:55 some substantial fraction of the atoms actually have scattered of photons. So, and the these collective dynamics are relatively robust to that.
12:38:05 And so it's sort of right now at the level where for example if you want to ask sort of how quantum is the system.
12:38:13 We would expect based on our parameters, to be able to measure, squeezing for example as a measure of entanglement by sort of for each individual ensemble.
12:38:24 If you sort of turn on this gradient you could have, like, you know, this this array of ensembles and each of them has 10 dB of squeezing for example.
12:38:32 Or you could control with the spatial structure of the interactions, you know, the entanglement and some other structure of the collective modes.