 Yeah, thank you for the introduction and Welcome to this talk where I will tell you about results So experimental results on the correlated dynamics in two different settings of strongly interacting quantum systems so I'm from the group of Hans Christoph Negel at the University of Innsbruck and I'm going to start with a slide showing you the different kind of directions we pursue in our group So we have actually three quantum gas experiments two of them dealing with with mixtures of potassium and cesium and rubidium and cesium and are aiming to produce Ultra-cold molecules and particular dipolar molecules with long-range interactions in optical lattice potentials But I'm actually from this lab where we have a cesium experiment a single species experiment in an optical lattice So I have to apologize that in this talk I will talk about particles with short-range interactions But I hope that I can convince you that we can still do interesting physics with short-range interacting ground state atoms in these lattice potentials so let me Start with this little sketch So what we want to explore in in this setting is the dynamics of interacting short-range interacting particles on a lattice and What they can actually do in this in this lattice landscape, which we engineer with laser beams Is that they can tunnel from side to side so they can move Through the lattice through a quantum tunneling and whenever you have two of them on the same side they're going to interact with each other strongly and so in a way, this is kind of a Synthetic condensed matter system that we engineer here and that we try to study and in particular in situations out of equilibrium So I'm going to start with these kind of systems and tell you about Experiments that we did in the past on correlated tunneling dynamics in tilted mod insulating hubbard chains And then I will quickly switch to new results where we looked on systems with driven particle interactions and it turned out that we can create a Hubbard Hamiltonian with occupation dependent tunneling terms and so this will be the second part And then I will switch to a different kind of setting where we look not on lattice system But actually on on tubes of one-dimensional systems With strong particle interactions and strong correlations and in these kind of setting We have recently observed block oscillation often the block oscillation dynamics of impurities that are immersed into the correlated background Yeah, so to correlate this let me start on the first part So to those of you who are not that familiar with these called atoms and optical lettuces Let me recap a little bit the model that we used to To compare experiments to theory so these atoms sitting on a lattice are actually well described by the Bosa Hubbard Hamiltonian And this Hamiltonian consists of two terms the first term describes the motion of the particles through the lattice We are tunneling so we have a nearest labor tunneling process with it with a single particle tunneling rate j and Whenever we have two of them two of those atoms on the same lattice side they interact short-ranged And this interaction energy is quantified typically by By the interaction energy you and then for some of our experiments what we actually do to initiate dynamics in these systems is we apply a Tilt we tilt the whole system and apply an energy offset from one side to the other Which we quantify by e and we do this in the experiment by a magnetic force that acts on the atoms All right, so I'd like to emphasize here that what we have actually in our lap is so the realization of the Bosa Hubbard Hamiltonian with three different parameters that we can tune independently We can tune the the tunneling rate by the lattice depth We can tune interactions by means of so-called Feshbach resonances And we can certainly tune this tilt by varying this magnetic force What we have done in the past in these systems is we looked on quench dynamics in tilted mod insulating Hubbard chain so we started with a System with exactly one particle in each side So mod insulator For which the interaction energy is much larger than the tunneling rate and then the ground state of the system is such an array of atoms were Where each side is exactly occupied by a single particle and then we applied this tilt to the system So we tilted it and you can imagine when this tilt is sufficiently weak and in particular Much weaker than the interaction energy than just nothing happens, but interesting dynamics can now happen in the system When this tilt so this this energy offset from side to side just compensates for the interaction energy Because then you can imagine that when you have a particle for example sitting initially in this side here to the very left It can tunnel onto its neighbor in a resonant fashion and in a resonant way I mean that the energy needs to occupy this this side with two particles Yeah, the on-site interaction energy you is just delivered by this energy offset by the tilt So it's a it's a resonant tunneling process But it's also correlated tunneling process because it can only happen when this neighboring side is initially populated So there's a constraint on the tunneling dynamics, and we have actually Studied many body many body dynamics in these tilted settings on resonance So so particularly we have started in this one atom per side mod insulator And then we have quickly quenched the system on to this point where equals you and then we have counted the number of doubly occupied sites We call it Dublin as a function of time after the quench and what you see then in the experiment Is that these number of doubly occupied sites oscillates and decays? So this is this many body tunneling dynamics in the system where the particles tunnel back and forth on to their neighbor in this resonant fashion and And you can do this also a bit detuned from resonance by you by changing a bit the value of the tilt So this blue line was really where equals you but then you can do this a bit detuned and these Oscillations become faster and that the amplitude goes down. So this was really stuff We did in the past and what I'd like to emphasize here is that these tunneling oscillations these correlated tunneling processes To a very good approximation essentially happen with a rate that is the single particle tunneling rate So this J in the Hubbard model So it can be used for example as a direct measure in the experiment to measure the tunneling rate if you wish but what we wanted to What we thought about more recently is can we actually engineer a system Where is the where the tunneling of the particles does not happen with J? But becomes actually dependent. So the tunneling rate becomes dependent on the number of particles in neighboring sites So in this sense, can we engineer a Hubbard model with an occupation dependent tunneling rate? that was kind of the question and the way we did that is by Using a fast drive in the system and employ the idea of what is now This cold Adam business Kind of termed floquet engineering as we use a quickly driven system periodically driven system to engineer such an occupation dependent Tunneling rate and what has done in the past To remind you a bit is people have controlled in this way in this by by driving the system the single particle tunneling rate And this is often called the kind of shaken lettuces So what you do is you take your optical lattice and you shake it back and forth very quickly And then you can make such a floquet Analysis of the system and you'll figure out that you can engineer and kind of a system where you have a new Effective tunneling rate that is the bear tunneling rate multiplied by a Bessel function and in the argument of the Bessel function You have the strings of this drive. So by the strings of the of your of your shaking You can kind of coherently control the tunneling rate the single particle tunneling rate So this has been done and has been used now in many different labs For example to drive quantum phase transitions from superfluid to mod insulating states To study classical forms of frustrated magnetism on triangular lettuces to implement artificial gauge fields even to implement now topological models such as the Heldain model or to engineer spin dependent Spin dependent tunneling and lettuces. So this is really just to sketch how How why this field of floquet engineering is now kind of explored in this cold Adam? business and what we wanted to add now is tool to Kind of use these methods to engineer occupation dependent tunneling and not just the single particle tunneling rate And we do this not by shaking shaking the lattice, but so to say shaking the particle interactions We look on a system with periodically modulated interactions What what that means is we have our Hubbard use in the the on-site interaction energy and we modulate this now in time With a with a certain amplitude and a frequency with this sinusoidally in the lab and then for When this drive the drive frequency is much larger than the original Hubbard parameters you and Jay You can do a similar kind of look here analysis as in these shaken lettuces and you what you're going to end up is A new kinetic term in the Hubbard model that has this particular form So you you can recognize the tunneling part. So here's the patient creation operators on neighboring lattice sites i and j this was the bear tunneling rate But now you see that the tunneling rate Is now modified again by a Bessel function and in the argument of the Bessel function have the strength of the drive so you think the amplitude of the Modulation but also in the argument you find now the number of particles on the left and the right side that that Contribute to the tunneling so in this sense you can make now this this term really occupation dependent And what that means is that you when you look now at different types of tunneling processes For example when you have a particle that wants to hop onto a side, which is already occupied This tunneling rate will scale like this blue curve with the modulation strength But when this side is occupied by two particles, there will be a factor of two in here And the scaling will be different. So in this sense you can coherently um engineer a system with Well-controlled occupation dependent tunneling parameters And the way we do this is we again start in mod insulator with Single side occupation in the limit of large interactions And then we quickly switch off the interactions between the particles So we make them non interacting and what happens then is that they can start to delocalize in the lattice They can start to tunnel they they are not blocked anymore by their mutual interactions And this will lead to the decay of particles with of of sites with single single occupancy And the build-up of multiple occupancies in the system We use this decay to actually measure now the tunneling rate in the presence of this modulated interactions so What I show here is the normalized number of single single occupancies in the system or single sites in the system And when we don't drive this is The system and you don't shake interactions and you see this quick decay It will be a component by a rays of double occupancy, but the singlons actually decay you extract when you extract a raid you can You can plot this here So this will be this data point and now we do this experiment in the presence of some modulated interactions with an amplitude delta u Some particular frequency and when we switch on this drive now, we can see that the singlon decay is Is significantly reduced so this gives rise to this data point here in the decay rate We can even completely freeze the system although the mean interaction strength is zero But but essentially because of this drive, it's kind of frozen due to Their neighboring particles So that's the mean sign here and gives rise to this data point and we can go on and on and take more more data sets And if you take points also in between then you can get then you get this type of behavior And do this also a different drive frequency that shifts the whole thing it scales a bit differently But essentially we recover this special function dynamic this special function scaling of the tunneling rate and Again, I'd like to emphasize here that this is only because there's neighboring atoms in the lattice Because you have this many body system if there would be just one particle and you drive your interactions It will just tunnel as it With a with a single particle tunneling rate So this is really due to the correlations in the lattice and the fact that you have many particles So it would be nice actually to see now directly the scaling with with the occupation number also Not only with the drive strengths, but also with the occupation number and We do this again by applying our our tilt trick So essentially we start now with an initial state that is not one atom per site mod insulator But that is more or less kind of a random distribution of single single occupancy Some holes and some Sites with two particles on it Then we can Tilt the system so that this energy offset is again equal to the to the interaction energy and then we We can drive tunneling processes where a particle hops onto sites where there's just one atom If we double this tilt to 2u You can see that now a particle can hop onto a site where there's two particles already So this kind of allows us in the in the experiment to differentiate or to to To isolate tunneling processes Of the form where a particle hops onto a site with two bosons or a particle hops onto a site with just one atom And those those tunnel in the presence of this drive now Those tunneling rates Should scale differently in particular there should be a factor of two in here because you have two particles here and not just one And indeed we we we can do this So what is what is plotted here actually is kind of the number After we after we do this tilt that we wait for a certain time And then we plot the number of w occupied sites as a function of this tilt and we see then two resonances One would correspond to exactly this process where we create doublons in the system So one one goes to two zero and the other resonance would be Um corresponding to the process where two particles two one goes to three zero. So we lose doublons This is these resonances now we can do this We we can actually look on the height of these resonances as a function of the drive again And then we see these different scaling. So that's the drive. That's the height of these resonances normalized And then we see the different scaling and we can actually recover this type of special function rescaling or occupation dependent tunneling in the lattice So this was kind of of the first part where we where we kind of engineered Hubbard model with occupation dependent tunneling and that opens now various new Various playgrounds to actually look on the phase diagram of such hubbard models with occupation dependent tunneling which should exhibit phases of dimer super fluidity and and various other regions Or it could potentially lead to New new tools to engineer gauge fields where the gauge field is actually density dependent so kind of the dynamical gauge field with the density dependence in it This has a little Outlook now on this But now I'd like to switch gears and switch to the to the other type of setting. We were recently studying and this was Not these these both are hubbard systems and dynamics in these both are hubbard systems, but actually a race of homogeneous or let's say invariant one-dimensional Tube like systems. So we we do this by two laser beams which are or re-reflect laser beams which are Horizontally propagating and this gives rise to a lattice in which we create these tube like systems isolated tube like systems and what we wanted to to observe in there is what happens if we If we create an impurity particle in these one-debose gas and And drive this by a force and then we were interested in the dynamics of such an impurity particle In immersed in such a one-debose gas Before I show you the the experimental results Let me quickly remind you a bit to to the physics of these one-dee Systems of strongly interacting bosons So What what you have when you have this knob to to to change the interactions between the particles Is that you can engineer a situation in the laboratory where you have these bosons actually non-interacting So the scattering length is set to zero and then you have a non-interacting bose gas And so the principle in ideal gas in one d And then you can crank up these interactions You can make the scattering lengths larger and larger and larger And at some point you'll end up in a regime which is known as the so-called tongs geradogas where the particle where the interactions between the particles Is basically infinitely repulsive And because you're in this one d setting you can In principle think of the that the particles can't hop around each other Yeah, so they they can't get around each other and this leads to the fact that when they are strongly repulsive The effect of of correlations become important. So You basically end up in a regime with strong particle correlations One can actually even map this to a gas of non-interacting fermions where so to say the the the polyplicate Results from this strong repulsive interactions of the bosons. That's why sometimes also called fermionized bose gas and in the in the In the context of these one d Of these one d bosons the strength of these interactions is typically parameterized by a dimensionless parameter Which I label here with gamma which is zero in the non-interacting limit and goes to infinity in the strongly interacting limit The experiment we had in mind was now to be in this regime where particle correlations become important And create a single impurity particle in these tongs gas and then Subject this impurity particle to a force and see what happens And on the next slide I'd like to sketch a bit what we expected to see or what what what Interesting physics can actually happen in the motion of such an impurity particle immersed in this strongly correlated background gas so An intuition what could happen Can be drawn when you look on the dispersion relation or the excitation spectrum of of this many body system You look on it. So what is plotted here is as a function of of the system's total momentum and the energy of the excitations in the system and Turns out in the context of these one strongly correlated 1d systems that the Low energy excitations obey actually such a cosine shaped periodic excitation spectrum and So in particular you have for any non-zero momentum You have you have a gap. So these excitations are gap and when you approach twice The the the Fermi momentum in the system Yeah, so I said before these bosons are very Kind of comparable to free fermions. So you can introduce actually a Fermi momentum Which depends on the density. They have this periodic periodic shape of the of the excitation spectrum And this reminds you Very much to the situation in a lattice Because when you when you put a quantum particle in a lattice You you'll get a this this quantum particle will feel a band structure Plotted here is a single wave packet a single quantum particle That is placed in a lattice potential and then you have your bryoline zones and your band structure of the lattice And if you now restrict yourself just to the lowest band and this This kind of picture is a bit identical similar. Yeah, so you have periodic dispersion relation and if we now Drive this analog further And you have your quantum particle sitting in this band structure What happens if you expose it to a force? Is that you will actually drive it through the bryoline zone and once you reach the zone edge You'll get break reflections on the other side and this motion of the Of the quantum particle in this lattice structure will be periodic In momentum space And so this is known as what is called as block oscillations and The block oscillation frequency actually depends on the drive Strengths on the force but also on the lattice spacing and now you can make this analog on So what happens to our impurity and we drive it with the force you can imagine that it follows this dispersion relation and and undergo some oscillatory dynamics and again I'll go ahead and say then the effective block frequency would be the drive and depending on the drive and the density in the system and But there is some difficulties because differently to the lattice situation there is a whole Continuum of excitations above this low energy spectral edge And this can be excited in the course of the quantum evolution So the question is really although we have no imprinted lattice structure The the dispersion is still periodic Um, so this could give rise to block oscillations of this impurity particle But can they survive actually because there is there is this, um Continuum of excitations on top that can be excited. So we do experiments now by um By actually exciting this impurity in a different spin state. So we apply a radio frequency pulse This is our correlated background gas or bosons, but the black dots and we Try the single impurity in each of these tubes in a different Hyper in a different Hyperfine spin state and due to the different magnetic moments of the background gas and this impurity it will Experience a force downwards That will be accelerated And then we can do time of light and actually map out the impurity momentum distribution as a function of time We can do this um for various different interaction strengths. So this is actually the scattering lengths of our background so background background collisions and collisions between the background and the impurity atom And tuned by a magnetic field So, um This is true that we can actually engineer this uh this interaction parameter by changing the scattering So the simplest scenario would be a free fall so to say, you know So when we um are on a point where the interactions are zero between the impurity and the host atoms And then what we see is actually that so this is um impurity momentum as a function of time just to base a linear evolution It increases linearly with times or basically this resembles a situation where the um background gas is made transparent to the impurity If you increase interactions now what we see Is that a part of this impurity wave packet after some time gets actually break reflected And it gets break reflected by just twice the firming momentum. So this is um, essentially this effective bryolian zone you get in this Fundy fermionized system And if you increase interactions this break reflected part becomes stronger and stronger and in the deep in the strongly correlated regime You'll see that you get really this type of oscillatory motion With these break reflections of the impurity on the background gas on the correlated background gas And we can compare this to numerics and it fits really nicely There are some slight quantitative differences due to Imperfections, but the overall comparison is very nice You can also extract the mean impurity momentum as a function of time and then we see these oscillatory Dynamics also in the mean momentum. We can compare again today to a Miracle exact calculations of the problem and Amplitude and time scales also fit very nicely And actually really now Extract the the frequency of these oscillations as a function of the force to some extent And compare with these simple predictions from this idea that you go like Periodically through this dispersion relation of the coupled system Well kind of in conclusion what we see is block oscillations of a single impurity particle on the correlated Background gas in the absence of any lattice Find that quite amazing Okay, that's the team working on this From the experiment and there's also very A lot of theory input mainly from andrew daily. I like to thank yugin demler michael knap and michael swanoweth For valuable extremely valuable theory input on this work on the block oscillating impurity and with this I'd like to thank you very much for your attention