 Let's start, let's welcome Jesper Lepusen from Monash and I think I know you see me, you might get, let's see, Jesper Lepusen is a PhD at the Schwarz Institute and then he, no, he's a master, and he did his PhD in Boulder, Colorado, and then he was a post-doc in Paris, right? And then we went here, oh, I stopped by Cambridge, you were a post-doc in Cambridge? Yes, yes. Then he was a post-doc in Cambridge, then he was an old student in a barn study working with me and Mira, and then, okay, now it's getting fuzzy, then you went to Australia. Yes. Yeah. And he's now a professor in Australia, together with Mira, and they are a powerhouse in Colorado Physics, a few-body physics, a post in Tommy Gass is, recently they've also spread it to the Solid State platform, and I've had the pleasure to work with them on a couple of occasions, it's very nice, it's also stressful because it's always too against one. Go ahead. Thanks, Theo. Very nice and honest introduction. So, yeah, thanks everyone for coming today. It's a pleasure to be here and to be back in August to present some of the work we've done in recent years, and thanks to Jan for organizing this also, and it's really good to be back. I also wanted to say if anyone has any questions at any point during the talk, just interrupt, please. I'm very happy to take questions. So, what I talked about today is quantum impurity problems, and like Theo was saying, we've been working on these both in the context called atomic gases, but also more recently in the context of dope semiconductor. And these are really, it's the same kind of problems just appearing in different contexts. It's the same formulas we use to describe them, and the results, although they look different, they're just often just plotted on different axes, because we have different observables in the different systems. So really a lot of the phenomenology is common to these systems, and so that's part of the reason why a lot of theorists are working in both fields now. Okay, so, and I also wanted to introduce Monash University, so we have these kind of crazy buildings at Monash. So this year is a chemistry, as you might have guessed, from the shape of the building. So it's a very new campus, we have lots of new buildings, and it's kind of an exciting place to be actually, because we've hired just in the seven years that we've been at Monash now, we've hired more than 10 new people in physics, so it's really happening at the moment. Okay, so what impurities actually don't even only appear in cold atomic gases and semiconductors, they even appear in neutron stars, where you have, for instance, you have a smaller mixture of protons in a neutron medium, so there you again have more or less the same kind of formalism should apply in these systems in the inner crust of neutron stars. They appear also as these absorption peaks in semiconductors, where you can really change an applied voltage here, and you can look at, essentially, you know, you change the photon energy here, and you get these kind of absorption features as a function of essentially how many electrons you have in the system. And this is related to how, when you shine light on the semiconductor here, you excite what is called an exciton, an electron hole pair, and it gets stressed by the electronic medium in this system here. And you can, essentially, you can have an attractive branch where you attract all the electrons, or you can have a repulsive branch where you repel the electrons, and that gives rise to these two different branches. But really what I want to emphasize is that actually apart from, you know, all these various systems here, it's a very fundamental problem because you can think of it as just being the question of, say, I have a single impurity in a medium, I turn on interactions between the impurity and the medium, what happens, how does the system behave, what are the properties of the ground state, what are the dynamical properties, etc. So we really want to describe this object here, which is an impurity interacting with some big medium. Okay, I think I've already said all this here, but the key idea is that we want to describe essentially this system here as what is called a quasi-particle, so it behaves like a particle in some sense similar to the original impurity, but now it has changed properties because every time this impurity, for instance, moves in the medium, it will drag excitations of the medium along with it, so that introduces the concept of a quasi-particle. Okay, so I have quite an ambitious outline, we'll see if I get through everything, but essentially what I want to discuss first are different probes of this system here. These are two different probes that have been applied in the context of cold atomic gases, so-called radiofrequency spectroscopy, where you really shine light on your system and you change your impurity atoms either into or out of some interacting state and you look at the response of the system. But what you can also do is you can essentially consider your impurities as some two-level systems where you can have Rabia installations between the different levels and now you look at these Rabia installations in the presence of interactions with the medium, and so what happens. Then what I'll discuss afterwards is some questions about the nature of the Fermi-Polaran. So first of all, I want to talk about how it evolves with temperature and what we can tell about the nature of the ground state even though experiments at a finer temperature. And then I want to focus on the so-called repulsive-Polaran, which is quite interesting because it's a metastable branch. So remember how I said we have two different branches, we have this repulsive branch and an attractive branch, and the repulsive is a kind of metastable excited branch and so there has been a lot of debate about the origin of its finite lifetime. And so what I want to talk about this is in the context of two different experiments, both an ultra-cold Fermi gas and an atomically thin semiconductor, and both how these two things are similar and also some important differences. And finally, I hope I'll have time to talk briefly about Polaran-Polaran interactions again in the context of semiconductors. Okay, so let me begin by setting the scene here. So let me assume that my impurity has two different spin states. And we call them spin down and spin up. So these could be, for instance, two different hyperfine states of an atom. Now I can imagine two different scenarios for, for instance, radiofrequency spectroscopy. I can either go in, go from this non-interacting system to the interacting system, which is called injection spectroscopy, or I can do the reverse thing here. Essentially what injection spectroscopy is, it probes all the possible kind of states that have a finite over that with this initial state here. Whereas ejection spectroscopy probes essentially this strongly correlated many-body system here, but it's again, you know, I'm projecting it onto this non-interacting state. And we have these radiofrequency pulses that can drive these transitions. And the rate of transfer as a function of the frequency of this transition here gives access to the impurity spectral function. And there have been several experiments on this here, both in terms of injection spectroscopy. For instance, there's this paper here. I think Geo was on this paper back in the early days of impurity physics. So here, again, we have, this is a cold atomic gas, where we have its potassium impurities in the lithium fermi gas. And again, we have this attractive branch here, and we have a repulsive branch here. And we see how this spectrum here probes both these two branches here and some continuum in between. So this is as a function of interaction strain. But we can also imagine, for instance, sitting at a fixed interaction strength and probing, for instance, the temperature dependence. And this is what was done at MIT in the group of Martian sphere line in this ejection spectroscopy measurement, where they observed essentially how the spectral peak moved essentially from this value here at around minus 0.6 or 0.7 or something like that to around 0. And so they saw it by kind of abrupt change as a function of temperature in this experiment. Okay, so you can do both of these things here. And what we realized a couple of years ago is that actually these two spectroscopies in the ideal case where your impurities are completely uncorrelated, they're actually related to each other. So this is kind of a, it's a detailed balance condition, but it's a detailed balance condition where these two different things are in thermal equilibrium, but it's a detailed balance condition where the injection and ejection rate are related. And what we see here is that they're related by this factor here. This is a constant factor. So first of all, there's some exponential pre-factor and we flip the sign of the frequency. But there's also this constant factor here. And it turns out that this constant factor here is just difference in free energy between this strongly interacting system here and a non-interacting system. So this really tells you that if you're in the ideal case where you can do linear response at low impurity concentration, then actually these two spectroscopies here should be completely equivalent. So is there a assumption here that yellow impurity only interacts with the surrounding blue atoms when it is in opposite states? Yes, yes. And indeed you can actually, you can generalize this here to the case where you have different interactions in two cases as well. But this is sort of the ideal scenario that cold atoms is probing. Okay, so that's, I think, an important result for RF spectroscopy and it would be important also in the following, but I wanted to talk also about another probe here. Because what we can also imagine is that we now put on a rapid drive of experimentalists do this between these two different impurities spin states. So we can flop between spin up and spin down at some rate here. And again now we're probing, you know, essentially we're probing these two different scenarios here. And what we'll find is the population in the system here as a function of time now, you know, is flopping between the two different states. But depending on the interaction strength here we see that there's both a dampening and a change in the frequency here. So this is an experiment from a few years ago. And indeed the frequency of the oscillations here is related to the bare rapid drive here with some coefficient here which is just the overlap between the interacting state here and the non-interacting state here. So indeed you can actually from this dynamical probe here you can probe properties of the equilibrium state of this system here. So that's kind of also interesting. So essentially what you're doing is you're coupling these two different kind of of spectral functions. Of course here you just have a kind of trivial spectral function with a more complicated spectral function here. And now by applying, you know, a range of let's say reasonable assumptions on the problem here we can find a kind of simplified expression for this behavior here which shows that we have a certain damping in the system which is related to the width here of your repulsive polar and peak. So this is specifically the repulsive branch that we wanted to probe. And you have this factor here which is originating from this and that's actually a strong correction to the frequency related to the damping and so. Okay, so before I actually go to the results I'll just talk very briefly about how we model this kind of dynamics. So like I said we have our impurities here with some dispersion. We have our medium particles which are fermions again with some dispersion and some chemical potential. And what I want to emphasize is that actually we find it convenient in the single impurity problem to work in a case where we have, you know, a canonical ensemble for our single impurity so we have fixed number of particles whereas we're using a grand canonical ensemble for the medium particles. So this turns out to be kind of interesting. A convenient way of describing it. Now all of this here you can just think of that as some kind of interaction term between the fermions and the impurities. Here I've chosen to use a two channel model because that's necessary to describe some of the experiments but that's sort of a detail. But essentially what we can think of is the system here is described by a scattering amplitude which has a scattering length and potentially also an effective range. Okay, and now in order to do time dynamics and potentially take into account temperature what we do is we introduce some variational operators for the system here. And these variational operators here they consist of terms where I have, you know, higher and higher order particle hole excitations of the medium. So what we can think of this here as this here is a bearing impurity with some weight here and this here is a term where my impurity has excited a particle hole pair here and it's taking some recoil here and again I have some weight here which is some weight function in my variational approach. And now in order to do dynamics what I can do is I can introduce an error operator which is the difference between essentially this here is a Heisenberg equation of motion that I have on the right-hand side. Of course that would usually be equal to zero but in fact once I have made a truncation of my Hilbert space this here is done zero. So this is actually some finite operator and now I can define an error quantity here which is a trace over this error operator kind of squared. And I can now minimize this error quantity here with respect to my weight functions. And what I want to emphasize is that this here gives you a very nice kind of variational approach for dynamics in the system. It works at finite temperature in particular because I have taken kind of operators for the impurities I can now apply it to any arbitrary state of the Fermi gas. So I can have any kind of superposition of states. And this you can prove because of this structure here that this approach is exact at short times or also in the high temperature limit where you get kind of cluster expansions. Okay. So now first let me talk about temperature evolution how we can describe that of this system here. So like I said the injection and ejection spectroscopy is related by this free energy here. And it turns out that this free energy is in turn related to what we call the contact which is a quantity that quantifies the strength of the correlations between impurity and medium particles. How often we see the impurity close to a medium particle. And now we can use this variational theory using our realization that this contact actually gives us this relation between the injection and ejection spectroscopy and what we find here is the contact as a function of temperature at uniterity. And this is for lithium atoms and a lithium firmacy. And here this here is maybe let's just forget about this maybe I just want to talk about this picture here. So this is equal masses. What we see here is that our calculated contact has this non-monotonic dependence as a function of temperature and that actually matches the experiment extremely well at least with an error bias. Now the reason the origin for this non-monotonic behavior here is actually kind of it's non-trivial but you can kind of understand it if you think about the phase diagram of the system. Like I said I have my attractive branch here I have a repulsive branch here but actually what I didn't mention before is that there is this other branch here which is where the impurity binds the particle from the firmacy and forms a molecule. And eventually this molecule actually becomes a ground state here. So at uniterity this molecule here sits as an excited state but it has a larger slope than the ground state here. So if you look at the changes function of one on A here this here has a larger slope than this. And so once you go to finite temperature actually the reason why you're increasing the contact initially is that you're seeing the effect of these excited states here. And then eventually at last temperature your contact has to go to zero because you're going to have an ideal gas limit. Are there any questions about any of this? Yes? What's the difference between this theory and just doing that putting in thermal functions in the oh like some... Oh yeah, you can do this in terms of ladder diagrams as well. I think what people haven't realized is that the contact can be written as an integral over the ejection spectral function where you introduce now the self-energy in terms of ladder diagrams for instance and you can calculate it also like that. Yeah. We found numerically actually it was easier to do it in a discrete formulation and that's because of the large exponential tails in the problem. And the red point here we get in the marking point? Yes, yes. Yeah. So that fits quite nicely here. So that's an experiment from a few years ago. What we can also do is actually we can look at this here not only at uniterity but we can look at the temperature evolution as a function of interaction scale. So what we're doing here is well here's a plot of the free energy and here's a plot of the contact and what you see here is the free energy if I plot it like this here and I measured it with respect to the kind of bare two-body binding energy. Here I see that I have this crossing here which is this transition to this molecular state that I was talking about before. Now if I look at finite temperature so this is point one here these red dots here and point two here is the blue dots here. I see that now I get something that's very smooth across this. You can think of this as a single particle phase transition where it binds the particle. And actually this you know it's difficult to see anything interesting happen in the free energy here at finite temperature. What you can see is actually in the contact if I instead plot the contact which as I said was related to derivative of the free energy then I find that here in this regime where I'm kind of in the regime where I have deep bound pairs as a function of temperature the contact is going this way here so I have 0.1 0.2 Tf temperature on the other hand over here the temperature is initially the contact is going up with temperature initially so that means that I'll have some non-monotonic behavior in this vicinity of this single particle phase transition here like for instance here I see I go from 0 to 0.1 to 0.2 here so this non-monotonic behavior of the contact is actually related to this underlying phase transition single impurity phase transition now the question is can you see this in experiment and at least so far the answer is no so this here is an experiment from Joao Saki a couple of years ago and if you plot the contact here on a large scale here you see that actually this matches the theory quite well if you zoom in if you subtract the part that's just coming from two-body binding unity then you see that actually we really need to get the error bars down to really see if there's anything interesting happening here so now yes I have time so now let me switch to really focusing on this repulsive polar and branch so I want to focus on that both in the context of cold atomic gases and so by this repulsive branch I really mean this branch here which in principle decay down to either this molecular branch or to this attractive polar branch here so it's a stable state it's quite difficult to describe theoretically and you know so it's a challenge to us theorists and I guess also to experiment and it's been observed both in 3D and 2D in various experiments and one fundamental question that people have been asking about is actually what is the nature of the broadening of this repulsive polar on here is it that it decays into these lower energy states like this here is that what really describes or determines the cost of particle lifetime or is it something else and so we went about this by investigating Rabi oscillation data first of all from the experiment that I was talking about before by which is in a 3D lithium gas but also in a 2D uterpium gas and so we did this variational time dependent method and what you see here is that we can describe the Rabi oscillations extremely well in the weakly interacting limit also as we get to stronger interactions we describe both the damping and the frequency of these systems here now in the extremely strongly interacting limit where the repulsive branch is just a big broad block then it becomes quite difficult but still we get something that actually does not compare too badly with the experiment in 2D we see something very similar where we can describe extremely well the Rabi oscillations both the frequency and the damping of the Rabi oscillations so that gives us confidence that we are actually understanding the underlying physical processes even though we are only including this one particle whole excitation of the medium so now from this we can extract the damping of these Rabi oscillations both in 2D and in 3D and we do this in different ways so the experiment of these black dots here and what we see is that this experiment here matches extremely well with the same extraction of the Rabi damping from our theory lines which are these blue kind of symbols here and this is a case both in 2D and in 3D although in 3D close to uniterity we start to see some deviation and more over this actually also matches the width of the quasi particle peak calculated within this single particle whole pair ansatz that I was talking about so all of these kind of methods they agree quite well with each other but what's important to emphasize here is that this theory that we've developed here it does not contain the decay channel from this repulsive branch to the attractive branch so we are only describing the impurity that's getting dressed by the medium but we cannot describe the process where it essentially decays to the lower branch because that requires additional particle whole pairs so if you thought that the decay rate to the attractive branch is the primary kind of damping mechanism then you would have thought that we shouldn't be able to describe the experiment but actually we describe it quite well so our explanation for this and I know Geo violently disagrees for this is that this here is an effect of what we call many body defacing so essentially it's because you have interactions between the impurity and the medium and these interactions push the impurity energy up into the two body scattering continuum and now this essentially leads to a broadening of this line here so it's because you have a discrete line coupled to a continuum and we can calculate this broadening here which scales like the scattering to the fourth power and we can compare this with the decay rate of so-called three body recombination processes which are known to scale like the scattering length to the sixth power so we see that at least at relatively weak interactions and up to about k of a equal to one we actually describe this process here dominates over this process here and and so this really shows that at least the weak interactions collisional relaxation is not the dominant decay channel I thought I had another slide on this did you want to stop me here or yes of course ok ok so let me describe now some more recent experiments from solid state where actually we see the opposite behavior which is kind of interesting ok so let me first describe what I'm showing here so here once again we have an impurity problem in this case here it's exotones which is immersed in a firmacy of electrons so in this case here is molybdenum diseline and in this system here the sample is gated so we can control the experimental group of LA and B they can control the doping in the system here so they can either go to positive electron doping here or negative electron doping here so we're focusing on this positive on the electron doping rather than hold doping and once again so this here is reflecting spectra and it's actually very difficult to see on this color on this projector here but you see again you see this here we just have the bare exotone branch and now as we go to this electron doping we see first that there's a repulsive polon branch here and then as we increase the doping we see more and more evidence of an attractive polon here and now in this context here what we should think of this doping here as doing is changing the fermi energy here so now the energy diagram looks sort of flipped on its head now we have energy as a function of fermi energy and we keep the interactions fixed so in cold atoms we always vary in the interaction strength here we are instead varying the doping level and now again we get this repulsive polon and it can potentially decay to that attractive polon can you yes what does the picture reflect and how do I get these lines maybe it's also the projector so there's a white block here but it's weaker than this here but it's very difficult to see now we get so where you put the attractive polon lines the dashed lines and outlines where the ridge of that block goes exactly and then there's some black there yes so there again you see it's kind of following it right here but it actually very quickly disappears so the repulsive polon like I said it becomes very broad and essentially the peak disappears already here and this is the axes are how is this done experimentally so this reflects the spectrum so you take your 2D material you gate it to have a fixed doping in the system and then you shine a laser on it and you look at essentially what gets transmitted, what gets reflected so what is the fraction of the light that gets reflected from the sample and this gives you an indication of what is the absorption of the sample so if we have a cut along the horizontal axis you will see at least 2 peaks one for attractive one for responsive a cut here would show this peak here and a much broader peak here but that's when the main x-ton peak go away then these two show that so the main x-ton peak is just in the absence of doping here and so that's very broad very bright and now here you really get this transfer spectral weight from the repulsive to the attractive polon but this is really just to characterize to see that these polon branches are there this is not the main experimental result so maybe let me go to the main experimental result so what they are actually doing in this experiment here is this 4-way mixing type experiment so they do this 2-dimensional coherent type of spectroscopy where they essentially what they have is they have 3 different pulses here will you know they think momentum and frequencies and now they can measure you know you can think of this here as a 4-way but they measure a particular combination of these of these pulses so if this here has momentum k1 k2 k3 then they can for instance measure at the position of the momentum minus k1 plus k2 plus k3 and so this gives you know one counter-rotating term in your frequency and two rotating terms in the frequencies so essentially this allows you to pick out specific channels that are contributing to a signal so you have if you have 3 pulses and they both have co-rotating and counter-rotating part you have 8 different possibilities so you can pick out just one of them in the experiment the nice thing about this here is it gives you access to these now 2-dimensional spectra and these are really this is really beyond linear response so on these spectra here what you do is you Fourier transform the time between the first 2 pulses and the time between the third pulse and the measurement and this kind of analysis you can think of this axis here as the absorption energy which is this corresponding to this time here this time is kept fixed and this time here is Fourier transform to the emission energy so and then you can do this at different voltages so you can do it for instance with a 0 volt where you're here and in the deep we see that we are absorbing and emitting at the exciton peak but now you can start increasing the doping in the system and you see these other peaks kind of appearing so for instance at 0.7 volts here you should see this repulsive polarization peak here and indeed what you see if you analyze the peak shape here you see that it's shifted from this exciton bare exciton peak here so this is a repulsive polarization and indeed you also see very weak you see this attractive polarization peak here and now you can increase the doping here now as you increase the doping this repulsive polarization completely disappears and indeed this peak here is gone and now we only have the attractive polarization and if you increase the doping even more than this attractive polarization here becomes very broad and difficult to characterize so what this gives us access to is first of all the energies of these systems here but it also gives us access to actually the lifetime broadening of this because the lifetime broadening is related to now the width of the signal along this diagonal here and so if you now what you can do is you can take your signal here and you can fit the shape of a signal for instance this is a diagonal cut through the repulsive polarization peak and what you can find then is the peak position and the width and so this gives us access to the repulsive polarization energy and lifetime broadening and you can do of course the same attractive polarization and the results kind of in bare parameters are these ones here so what you see is that the repulsive polarization here here we just have like a baseline here that's when it's just purely exotonic but now as we hit a certain voltage we start to dope the system and indeed we see that the repulsive polarization width grows very very rapidly and that attractive polarization width stays fairly constant until something happens that we honestly still don't quite understand but we have some ideas but essentially so this shows again that attractive polarization is the ground state in the system and so we would expect that it does not broaden with doping and indeed we see that it stays fairly constant here likewise the energy is we see that attractive polarization actually if you analyze this data here you see that it has this it goes relatively linearly which is the line that we had on the previous on the reflectance data and we also have this attractive polarization here now there are many reasons why the attractive polarization can start to kind of move up because you can get effects like band gap renormalization in these systems here but the difference of of polar and physics is not to look at the energies themselves but the difference between the energies and if you now plot that as a function of doping then you find that it actually grows like is essentially three half times a year somehow we didn't write that here and that's what the theory predicts so we find an extremely good agreement here and that's we don't have any fitting parameters in the theory here we just do this kind of variational theory and it just comes out to fit there are no fitting parameters that are specifically related to this we just take the fermionity the masses these kind of things put them in and out comes this line we can also look at the oscillator strength which is the residue in the system and we find that the repulsive polar on residue and attractive polar on residues is essentially like you know in the theory so essentially this peak here the weight is transferred from the repulsive branch to the attractive branch here as we increase the only place where we don't find good agreement with the theory is for the width which is kind of a mystery because I was just arguing that we find excellent agreement for the repulsive polar on width in the case of cold atoms that purple line here is our theory so this was kind of a mystery because like I said we had excellent agreement for the repulsive polar in the cold atomic gas so what's going on? so that's our new and improved theory that I'll discuss now so in the cold atomic gas one of the reasons why we had this 8 to the 6th behavior of the three-body recombination dual levels was because it necessarily involves two identical fermions and so this means that this process is suppressed but in the semiconductor case actually what we do is or what the experimentalists do is that they excite the exciton in one so-called valley in momentum space and these electron hole excitations address this exciton here primarily in the opposite valley and this sort of process here is suppressed because these are more identical fermions but now we can still have three-body recombination where essentially this process here you go from the repulsive branch by exciting a particle whole pair in this valley here and going down to the attractive polar and branch so we can estimate the rate at which this happens using just a simple kind of Fermi's golden rule calculation and actually the final result here that we find fits within a factor of 2 so it has a factor of 2 too much but I mean this is just a Fermi's golden rule back at the envelope calculation so we think that this is actually this is evidence this is actually physics related to the two valleys so in other words because we have dressing now we have the possibility of exciting particle whole pairs here actually this changes this power of the repulsive attractive polar and decay from this power here which would be if I did three-body recombination involving this valley here to this power here and this theory fits quite well so I don't know if I have more time actually because I also wanted to talk about interactions if I so let me just spend a little bit of time talking about another experiment by Jeff Davis at Swinburne so this kind of I want to change gears a little bit and talk about interactions between attractive polarance so this material here is tungsten disulfide and it's quite an interesting material because it has a very intriguing band structure so let me just explain so all the all the bright excitons in this system here they involve this upper band here, upper conduction band so I have you know bright excitons here, bright excitons here etc so I have two different bright excitons they involve the upper conduction band now when I start to dope the system I will dope the system in the lower conduction bands here or here so that's this block here or this block here now because of this fine structure of the band structure I actually I have different possible triumphs in the system I have four different band states so I can form a band state like this here which is a singlet so called singlet trion it involves the spin up exciton which is this red guy here and a spin down electron from this pharmacy likewise I can form the opposite singlet trion but I can also form this triplet trion here which involves three electrons three particles two electrons from the same spin and it has a slightly smaller binding energy here so this is kind of interesting I have four different three body band states and so I should have also related several different attracted polarons in the system so in this experiment likewise they do this 2D spectroscopy so we have the absorption here we have the emission here we have a repulsive polaron here we have an attractive polaron here and indeed if you look at this attractive polaron peak here you see that it has quite a lot of structure there are all these different blocks here so we want to try and analyze what's happening here okay and it turns out that these different blocks they're actually related to interactions between polarons and the interactions work as follows so what they can do is this experiment here was all by using linearly polarized light but now you can do circularly polarized so you can probe either this exciton here or this exciton here so now so here if you're excited to excitons of the same spin here it turns out okay I should make one point first in these multidimensional spectroscopies you only see a signal if you have interactions between the different particles you can show that if you don't have interactions there's no signal so that's one of the really nice things about these multidimensional spectroscopies is that actually there's always evidence of some kind of interactions in the system and here what we see is that in the two excitons of the same spin I only see a signal on the diagonal here okay and that's a sign that I only have interactions between these kind of three-body bound states involving a spin-off exciton and a spin-down electron two identical three-body states all equivalently between the trials and the reason why there's only one block here is that we have inhomogeneous broadening that emerges in two peaks and this is quite well carried out in the simulation likewise if we now do the experiment where we do opposite spins in the system so we really do a spin-resolved measurement then we see interactions between these guys here so now we excite for instance a spin-down exciton and a spin-off exciton and we see that they only interact if the polarance that we formed and the attractive polarance that we formed they share the same electron here and we don't have anything here and indeed we don't have anything on the diagonal here and once again this is carried out by the simulation so let me just explain briefly what the theory does here what we are assuming is that let me first look at this situation here so if I have two excitons here that are addressed two different attractive polarance and they are addressed by two different pharmacies so this is addressed by electrons in the say spin-off pharmacy and this one is addressed by electrons in the spin-down pharmacy I don't have any interference between them they are not interacting and so I don't see a signal related to this but now if these two excitons they try to address themselves by the same electrons then this electron here can only interact with one of them and they are able to interact with the other so it's a sort of phase-based filling effect that leads to interactions between these guys and so we see that we really see that in the simulations and in the experiment now in the experiment we also see these two additional blocks here and they are actually related to an attractive bipolar state um okay so so this phase-based filling argument is essentially that some operators cannot exist more than once okay let me just maybe skip this so okay so I'll just mention that we also saw these two additional peaks here they are actually related to extremely tightly bound states between two polarance so it's two excitons sharing one electron in a bound state like a three-body bound state and we can see that this is the case because of some pathway analysis maybe I don't want to go into it okay so let me just conclude here so I've discussed how you can probe the physics of the Fermi-Polaron using for instance RS spectroscopy or dynamical methods like Rabia's relations we learned something about the nature of the polaron from this I've talked about how this temperature dependence can signal the underlying signal impurity transition which is kind of interesting and has not really been done in an experiment yet at least not close to the transition and I've talked about how this repulsive branch in the concept of cold atoms is dominated by this phase in the case of the 2D semiconductor it's dominated instead by this second value and then finally I've mentioned some very recent results on polaron interactions so I think I should also go to this slide here so this involved collaboration with a lot of experiments both at LEMS Francesco and Matteo at LMU Nelson and Simon and at the recent semiconductor experiments carried out by Lane B and her group and by Jeff Davis and also this has involved a lot of people at Monash the student Hayden a few postdocs Weisscher and Jörgy and also is involved in another another faculty Mitri and Fimkin and of course so let me thank you all for your attention