 Okay, thank you very much for the organizers to give me the chance to entertain you about some experimental stuff here. It's not the first experimental talk, so you know what you're exposed to more or less. So what I will speak about is things we do in our lab in this when we basically use laser-cold atoms and we throw photons at this large crowd of cold atoms. And so we want to understand what's going on. And many different things go on. And just to show you a range of topics which can go on and this conference going from atomic scales as to physics scales, I give you some examples where we hope that we can bridge this gap. So clearly we will use atomic physics information. So this is a cloud of cold atoms we use. It's larger like my fingernail here, one centimeter typically. And we can study many things. I will discuss quite a lot today about what happens if you want to understand the undislocalization of light and how this might connect to long range interactions. But we also can look at what happens if you look at the motion of the atoms and this is a kind of movie what can happen if you throw photons in some regimes. And this is a cloud of cold atoms suspended in vacuum moving along, I will discuss shortly this. We also can study how photons jump around and this gives rise to levy statistics which is also connected to some astrophysical range and random lasing where we want to see if random lasing exists in astrophysics. So we do many things where we try to do experiments in the lab but more and more we try to see what type of systems or configuration can exist in astrophysics. But not all of them connected to long range physics. Okay, so the first thing I want to explain briefly here not the main part of my talk but because this is something we want to investigate in future in more detail is what happens on the motion of the position of the atoms if the photons bounce around in the cloud of cold atoms. So this by cloud of cold atoms. So consider that you are all atoms and I throw photons at you, what will happen? So one first thing which will happen is that this photon, one photon jumps from one atom and then it jumps to the other atom. But as the photon jumps from one atom to the other atom it will push away the other atom because that's radiation pressure. It's like if you have the light of the sun going on the tail of the comet it will push away the tail of the comet. This is the same thing which happens here. So if I have a photon jumping from one atom to the second atom it will push away this atom. And so it will push it away proportion to the intensity of the light arriving on the second atom. And the intensity arriving on the second atom is a power which is scattered by the first atom divided by the distance squared here. So this leads to a repulsive interaction between the atoms which skates like a Coulomb force. And so this is well known for more than 20 years now in our community. And one consequence of this is that if you have a few particles in the trap you have a small size of a millimeter size, let's say. And if you want to put more and more atoms in this trap because of this repulsion the traps get bigger and bigger and bigger. And so this you can easily see that this has been seen. And so this can be mapped on some extent to one component plasma situation. It has been considered detrimental and very bad for both agent condensation. So this is why many people in our community didn't like this type of physics but we take on this type of physics to study this long range mechanical forces. Something we found in our lab is that as we load more and more atoms in this cloud at some times this cloud becomes unstable and it oscillates, the size oscillates in time. And this is a situation which exists in astrophysics. There's some star Cepheids which oscillate in time. There's an instable balance between the gravitational pull to get a small cloud and the radiation pressure in the start which blows up the star. And we get similar things here and we get an oscillating behavior here. There's an instable regime we find in this cloud. And there's a very complex dynamics happening inside the cloud which has been simulated by Thomas Paul which maybe some of you know from other type of context working very much on Rydbeck atoms now but the tools they use can also be applied to this type of systems. So something we also stole from astrophysics just to see is always nice to go to conferences where you don't know most of the people. So you can steal ideas and you cite them but that's all you do. But you get new ideas and you can get nice papers in your community. So this is an idea I stole from astrophysics which is called photon bubbles. So close to some accreditation disk here what's happening in astrophysics is that there's a huge outflow of energy of light, let's say and this blows away the matter. And once the matter is away, this light can ballistically expand. There's no scattering any longer. So the light makes its way free and it can propagate and the matter is clumped in other regions. And this is what they call photon bubbles in astrophysics. And so we map this idea on what's happening in cold atoms. And there is the following that you have an equation of propagation here for the intensity of light. How is light propagating in the system? And here we use just a simple diffusion equation of light. And this diffusion equation of light depends on the density of the mean free path. So it depends on the matter. If there's no matter, there's no diffusion. If there's a lot of atoms, there will be a lot of diffusion. And so this is the equation for the light. And this is an equation as we just heard. Previously it's like a fluid equation for matter and the interaction here, this charge here is this effective cooler interaction which I just introduced previously. So we have an equation here for the position for the matter and here an equation for light. And if you couple these two equations, you can find the instability. And this instability leads to the same kind of region where light will be pushing away the atoms. And so this is what we call photon bubbles in cold atoms. And this is something which is used now to explain this type of movies here where this motion of atoms and light is coupled together. And this experiment is now also reproduced in Lisbon. And we explained this type of picture with photon bubbles physics. But I will not go into much detail of this work in progress. But so we can look at the basic ideas that we can look at what happens to the motion of the atoms with one of our squared forces, cooler like forces. And we can reproduce this in the lab. OK, but now I want to switch to something else. And this, not looking at the position and the velocities of the atoms, but looking at the internal degrees of freedom of the atoms. The forces on the atoms actually can be derived from, if I'm an atom, the force acting on me depends on some gradient of the Hamiltonian of the internal dynamics, which is, so I'm an atom. Laser comes on me. It will induce a dipole. And I will oscillate. And the magnetic field will push me. So the internal degrees of freedom of the atoms will be coupled to the atomic motion. And so now on, I will look at the atomic motion. I will just look at the internal degrees of freedom. How this electron on each atom will oscillate. And how this oscillation will be shared collectively in the large cloud of cold atoms. So one thing which can happen there is that you can find a different regime of how light can stay in the cloud. And that's our main goal. We want to look at something which is like a holy grail in the sub-community, which is under-stocalization of light. And so we want to throw a photon in the system. And we want to see how long does the photon stay in the system. And what are the mechanisms of a photon staying in the system? Once possibility is just radiation trapping, it's a random walk. And if the system of the size of the system is very large, it takes long for the photon to escape. But you don't need any interference effect to explain this. Other effects are based on interferences. One is under-stocalization. That's what we want to see. We didn't see it yet. No one has seen it yet. But that's what we want to see. And this would be the idea that if I have some modes of the system where these atoms here share the excitation, and there's an exponentially localized mode. And the other atoms in the other side of the room, they don't know that we share a mode here. And there's another way how to keep a photon in the system for a long time. And this is what I call dike-subradience, which is that the photon stays in the system. But we all oscillate together out of phase. And this keeps the photon in the system. But we all share this excitation. So there are different ways how to store a photon. And we want to understand how we go from one regime to the other. So first, look at the Anderson case. So random walk of photons. So the Anderson model, just to put it in the context of the last 50 years, was initially introduced for electrons. And so to explain the transition from a conductor to an insulator, electrons have a lot of applications in solid state devices. But they have interactions. And so this makes the situation much more complicated. So people were looking for non-interacting waves to study for this underslocalization. And so what we do is light, because light is a very nice non-interacting wave in principle. And people have used different type of scattering materials, semi-contact powders, white paint. And we add cold atoms as a scattering material. Also, in underslocalization, the holy grail is this three-dimensional phase transition, because there's a critical disorder. In one or two dimensions, most things our students have been observed. But in three dimensions, it's more difficult, because you need a critical disorder strength to localize. And so a lot of theory has been done in the last decades. But even up to now, there's no macroscopic exact theory of underslocalization. There's numerical simulations, but there's no analytical theory. The best we have is kind of self-consistent theory of localization. But this, for instance, gives a wrong critical exponent. So we know that this is not exact, but that's the best we have today. So there's no exact theory on this. And we are back to numerical simulations or experiments to study these effects. And so these are the two experiments which are the state-of-the-art nowadays. So that's the experiment way to look at the steady state signatures of underslocalization. And this is now considered to be masked by absorption. So this is no longer proof of underslocalization. And in a time-dependent experiment, there was inelastic scattering involved here. And so the authors of this paper now all agree that what they saw is no proof of underslocalization of light. So it has not been seen so far. So we can ask the question, does it exist? Maybe it does not exist. And I will show you some theory results of the last years which might claim that maybe it doesn't exist. So maybe you're looking for something which just doesn't exist. We don't know yet, we'll see. So what we did for many years ago now in our group in this is that we looked at something which is called weak localization, which is called the precursor of underslocalization. And the idea is that you throw photons at the cloud of cold atoms. They scatter. And then we look where they scatter using a camera here. And typically what happens, we see this enhanced back scattering peak, which means that photons they scatter, they do random walk. And they come back a little bit more in the backward direction than in the average all directions. So this means that the diffusion coefficients get reduced. And the idea is that if this reduction is so strong that the diffusion coefficient will be zero, that's what we call underslocalization. So this is why this enhanced coming back in the initial direction is a precursor of underslocalization. So this works in cold atoms. And so there's theory on this, but no exact theory but there's kind of a diagrammatic approach which works extremely well. There's a comparison between theory and experiment here. There's no free fitting parameter. And it works extremely well. So we have no reason to believe that this diagrammatic approach should not predict exactly underslocalization. So we were really confident that this works. And using this type of approach, it told us that we just need to increase the density of the atoms to go for underslocalization. So we just need to work a little bit in our parameter space to go for higher spatial densities. We were working the dilute limit and nowadays people have done this high densities but no one has seen underslocalization. So it's not so easy just increasing density as predicted by this initial diagrammatic approach was not so sufficient to make this jump to cross this magic line of underslocalization. Okay, so the question is what is going on? So we need to come back. So it doesn't work easily as we expected. So what can be going on? And so what I will show you now is that we're considering now a completely different situation, the same experimental but a different description, different interpretation. And we now consider light as a scattering wave with a one over R outgoing wave. And so this is a long range part here which will be important in what's going on. And maybe this is the key of the difference between underslocalization and Ticca Supradians what is going on in the experiment. Okay, so what we can do is we can come into the external field here and all these points are our atoms. And every atom here, I can describe it the evolution of this dipole so how this electron oscillates internally. It's driven by the external field. It has some free evolution here. And then, so this is what's happening the atom to independent. And then I have this extra term here which is describing the field scattered by the dipole M going to the dipole J. So this is the res scattered field which couples onto this dipole here. So this is like a self consistent equation here. And this term here is where all the complexity comes in. And here I have this one over R decrease. So this dipole is coupled with a one over R coupling term. This is where the long range comes in. And once I solve this equation numerically I can solve any observable like the field going out. I can compute what can I detect in the experiment. So that's easy step afterwards. But the complexity is coming in here. Okay, so what can I do? I can, for instance, compute where the light is going out in all directions. And I see many features here. I see like this much out of cold atoms light coming in, light coming out. So there's a very strong intensity around the fourth direction here which can be explained by a mean field. I don't know if it's called a real mean field but like what I would call a mean field description of a smooth density distribution of particles like a dielectric sea of glass. And this is just a lens. And so this will focus light in the fourth direction. That's what I see here. Then there's a pedestal background here which I can explain also without taking into account the interference effect. So that would like a random walk and diffusion equation would describe this pedestal here. And then I have this coherent back-scattering meat localization peak here which I described previously. So this simulation captures everything I already described to you. So this simulation is considered more or less exact to some limit for these experiments. Okay, so then we can look a little bit more detail what's happening in this type of equation. So we can, if you have an oscillator you can make different things. You can look at the Hamiltonian, you can look at the response function. So you can do this one. So let's look at the Hamiltonian here. We can have this, use an effective Hamiltonian which describes the evolution of each independent atom here which is the ground state excited state here. And this is the coupling term here which describes the coupling where the atom, the photon goes from one atom to the other. So it jumps from atom J to atom I. And this coupling term here is complicated. It has real and imaginary part. There's a phase evolution in there. And it has this long range. It also has short term, a short range here, one of our cube which is a big issue in our community. I will come slightly back to this but this is the complete description we need to take into account. And this looks like an Hamiltonian which is an open system because it has an I over here. And there's an I over here. It looks like an Anderson Hamiltonian because there's disorder here because the atoms are positioned at a random location. So this VIJ are random numbers here. So it looks a little bit like an Anderson Hamiltonian and it looks like a couple spins. It has long range coupling here. So it has all the ingredients. We like to compare what's happening in Anderson localization with long range effects. Okay, and so then we can look at the, if you have an Hamiltonian, you can look at the eigenvalues. So this is a spectrum of eigenvalues and it shows different things. This is the real part of the eigenvalue that's the imaginary part. So this corresponds to the lifetime of the mode and this of the frequency shift of the modes. And what we can see is that in the dense limit, if you take into account the near field effect or if you don't take into account just the far field here, if I add near field here, the distribution of these eigenvalues is completely different, which is not surprising. If atoms are very close together, the near field is important. And this can drastically affect the distribution of eigenvalues. And this will have a consequence that we'll show you later. Yeah, so here. So what we can do is we can use these eigenvalues here to make a statistical analysis of what's expected to happen. And so we can look, for instance, if I have all these modes, if these modes overlap or not. And there's a criterion which is called kind of overlap criterion or homeless criterion which tells you if this overlap is increasing if you increase the system size, you go to localization or you go to metallic regime or conductor regime. And so what has been shown by Sergei Skipetrov and what we also confirmed in our numerics is that if you take the real description with the near field terms, there's no phase transition for light. So this is like a no-go theory. There might be no localization of light in this type of systems, which is bad for us because that's what we were looking for for many years. So photons have polarization. They have near field coupling for dipole-dipole coupling. And maybe this near field coupling kills under-socalization. If you take it away in the model, there is a crossing here and the slope here goes from negative to positive. So in the Scala model, without polarization, without near field, there will be localization. And in the complete model which describes the real photons, there might be no localization. So this is quite recent and it might point to a situation where there's no under-socalization. So that's a very big issue for us. Now then, together with the people in St. Carlos, with Romain Bachelard and his colleagues, we looked at the 2D situation on this and we also confirmed that in the vectorial case, there's no localization. In the Scala case, there is localization. But what we found also is that time and space needs to be considered differently. You cannot just look at the time dependence or for something to infer what is spatial localization. For instance here, there's a lifetime of the modes of this eigenstate and the localization length, they're not correlated. So it's not because you have a long lifetime that you have a spatial localized mode or vice versa. So we need to discuss space and time localization differently which has not done in the literature before. Okay, so now the other thing is this long range dipole-dipole coupling. So for now we seem to say that under-socalization does not exist. So let's look for dicker sub-radius, the other way how to store photon system for many, many lifetimes. And so this is just a reminder for dicketed in the 50s here. He took a situation where you have N2 level systems and he treats the total Hilbert space here. And so they have, for instance here, one state where all the atoms are in the ground state. Here there's one state where all the atoms are in the excited state. In this here, there's one excitation, two excitation. So this is a full Hilbert space. And what he showed that if you start from the fully inverted system here, there's a cascade to the ground state here which is much faster if you have many dipole, many two level systems than if you have an individual single atoms. And this experiment, this has been seen the experiment in the 70s. So this is called super radians. So this cascade here grows very quickly because there's a stimulated emission process in this cascade. So this has been seen, this is working well. So what we focus on now is on the single excitation here. So we don't start from a fully inverted system. We just want to have one excitation in the system and see how this propagates and stays in the system. And so even in this case here, there's an n time enhancement for the decay rate of the symmetric states. So if you have a single excitation and if all this excitation were in phase, let's say, then this would decay n times faster than a single atom. And this, we have to pay a price for this. This means that all the other states here, they do not decay. And so they have a long lifetime. So this is what I call sub-radian state. And this fast decaying state is super-radian state. And so this has been done in the Dicke paper in the 50s. We extend this now to a regime where the size of the system is much larger than the wavelength. And so this scaling n is no longer scaling with the particle number, but it's scaling with the particle number divided by the number of optical modes available in the system. Which means if we have all a photon to get out of the room here, it depends on how many doors we have to get the photon out of the room. And how many doors there are, it depends on how many lambda squares I can fit on the surface on the roof. And so this number of optical modes here, and so we define a cooperativity parameter, which is the number of atoms divided by the number of optical modes which can go out of the system. And so this is the same as in cavity QD. It's number of particles which share the same mode. And this number here, I like it very much because this is also the unresistant optical thickness is something I can measure in the experiment. So this is a theory number, a criterion, which can be experimentally measured. So that's why I like this number very much. Okay, so sub-radient has been studied in the past for two particles. If you take two atoms close together, then the two dipoles can either oscillate in phase or out of phase. And there's been experiments in the 90s done by the group of crew where they could take two ions and put them very close together. And they saw a change in the lifetime and this dotted line here is the single atom lifetime and they saw a reduction of this lifetime if the atoms come close together. This means there were, it's one state which oscillate out of phase and that's what they saw. But this works if the atoms are very close together, it's not exploiting the long range nature of this interaction. So there's been one experiment where they claim some sub-radient and forward direction, but it was like a tensile excitation. So the laser comes here and in the forward direction, they saw a little slight change, but the main problem here is that photons can escape in the other directions and then they do not live in the system for a very long time. If you want to make a situation where the photons stay in the system for a long time, that needs to be no exit to at all, in no direction. So you need a three-dimensional spherical or cubic situation. So this sub-radient is difficult to observe. It does not require a large spatial density. It requires a large cooperativity parameter, but so you can have many, many atoms far away, but so the only parameter is the optical density. It's not the spatial density. So you can, if you want to have a large optical density, even if the atoms are far away, you just need more particles, but you can create a large system without having atoms very close together. So they don't feel the near field interactions, but you need the price you have to pay is you have to have more and more particles in your system. And so that's what we can do. So we need a large optical thickness and we exploit this one of our long-range coupling. That's what we exploit in our situation. And so we need some numerical simulation. So the idea is that you start with the ground state and then you come with a laser beam. You're excited mainly to the super-radian state and there's some coupling to this sub-radian metastable dark states here. And then you switch off the laser and then we want to see how the light comes out. And what we compute it here is that we expect a faster decay here and then some tail here, which would be the slow decay of the sub-radian states. And so we have to distinguish sub-radians from under-socalization and from random walk. And there's some scaling laws, how this time scale should scale. So sub-radians should scale like this cooperativity parameter which I just introduced. Relation trapping would scale like the optical thickness at the laser frequency square. And under-socalization maybe like the exponential. So that's what there's no precise here on this. But so this is what we expect for decay sub-radians in contrast to radiation trapping. And so we do the experiment. We come with laser beam here, switch everything off and look at the scattered light on the detector. So we are experts in this of creating large cloud of cold atoms. So for you this is not a big issue, but this is among the largest cloud of cold atoms you can see. So that's our expertise. We can go even more than this. We can go now up to 10 to 11 or 10 to 12 atoms trapped. So we can create very large cloud of cold atoms in the dilute limit where the near field coupling is not important. That's very important here. Okay and so this is the experiment. So when we switch off our laser most light goes out very quickly and then there are these tails here which really depend on the optic thickness. If I change this optic thickness here the photos stay in longer. If I change the detuning the slope does not change. So it does not depend on the detuning. And if I put all this data together I get a universal scaling which shows us lifetime here scales like the optical thickness. So it scales like the system size. So it's a global effect. It's not a local effect. It's not a dense defect. And so this is exactly what we expect from super radians and this is different from what you expect from radiation trapping. And this is probably the first observation of this dicker sub-radians in a large system in three dimensions without the canopy. Okay so that's okay. So now we have the dicker sub-range we have seen. We know that there must be super radiant peak as well because you're surprised to pay that if this leaves longer this is shorter. So we have done this. It's a little bit technically more difficult to switch off the laser quickly. But typically we can see a lifetime which is four or five times faster than the independent atom lifetime. And this decays faster than the single atom. So this we have seen and this will appear soon as well. There's some spin to this. It's very different from what you can do in the forward direction. In the forward direction you can describe all this with an index of refraction with a mean field. But we also look at a large angle and so at this large angle where we do the experiment there's no mean field approach to describe this fast decaying. So it's only the dicker super radiant mechanism which can explain this. Okay and then, so far this seems to say that okay under the organization we did no one saw in the experiment the theory says maybe it doesn't exist and we see sub-radians so that could be more or less the end of the story. But of course there's a lot of clever people around and they make proposals how to get around some no-go theories. And so one of this is what we do with Luca Gelardo. So there's a proposal how to solve this problem of under-slocalization with our system. So this is for the toy model and the toy model takes up the standard Anderson model on the lattice and adds opening here to the same channel here. So that's a toy model just to combine Anderson type of physics to a dicker type of super and sub-radians and to see how can you play with this two effects. And so what we saw is that in the Hilbert space you can separate two things. You separate the super radiant states and the sub-radian states. And if you look at the super radiant states you will not see any under-slocalization. I will not go into this about the super radiant state they are very strongly coupled to the outside field and they just leave very quickly. But the sub-radian state somehow they live in a closed system. So they don't know that there's an open system outside. They feel more this Hamiltonian closed system. And what we see is that there's a the sub-radian state they are still subject to the under-slocalization if you add additional diagonal disorder on this lattice system. So we see that here we can get under-slocalization under-slocalization of the sub-radian states. And the shape of the states has a what you call hybrid states. It has this under-slocalized peak and it has some plateau which is the residual of this the sub-radian extended state. So this has been seen now in the numerics in the kind of toy model and we have done this now in the more realistic model which is in progress here but we are confident that in the Hamiltonian we use where the initial prediction was that there's no under-slocalization using additional diagonal disorder we might be able to localize photons in this system. So that's very important because there seems to be a route around this no-go theorem for under-slocalization in code atoms. And so this is something we want to if this is really if you are confident enough on this theory that's what we're going to do in the experiment very soon. And so now I come to the conclusion. So we want to we're still optimistic that maybe there's a route for under-slocalization. Sergei Skifetrov has another proposal by adding a strong magnetic field to solve this type of problem and we'll see what type of route we will solve. There is still a problem that if the Hamiltonian approach says that there's under-slocalization the main problem is that we don't know how to see it from outside because we can go inside the cloud of code atoms. So there's still an important issue how to measure it. And there's some technical issues which you don't care about but for me it's very important. Probably we need to switch atoms from rubidium to eterbium which is a big issue for us but not relevant here. And then so then this is all about how the internal degrees of freedom can be sensitive to this long-range coupling or under-slocalization. And then there's the whole other regime where I look at the motion of the atoms which I shortly mentioned at the beginning of my talk, photon bubbles. So we look for the device screening. Can this repulsion between atoms make an arrangement of the atoms which is a little bit more subtle than just a homogeneous distribution. I would be very happy if I could find a way to change the sign of this Coulomb repulsion because right now I said that one atom pushes the other atom away but there are dipole forces in cold atoms which might make us attract so we can get a long-range attractive force in three dimensions that would be very nice. And then another question that's a question for this community. This past and slow relaxation super-subradians which scales like the system size which exploits this one of our connection. Maybe it's connected to this quasi-stationary state so we had some discussions with some people here. So maybe there's some connections. Maybe you could find some scaling laws, analytical scaling laws how this super-subradian scale should scale. And I want to finish but I want to first to mention all the people who work on this. As we heard before, experimental efforts implies a huge number of people which are not listed here. These are just the people who are right now in the lab but over the last 10 years might be 20 people have been working on this. Guillaume Laverie is the mastermind behind all this current backscattering weak localization experiment. William Guerin is the PI on this sub-radian state and Mathilde Fouchier just joined us on the random lasing part and these are students working on this project. And these are all the collaborators which are of course very important for us because first they give us new ideas. They say that we are maybe on the right track so we have Luca here, Romain is here, Julien is here, Marco Bruno is here. So many people you know here are very important for us because these give us new ideas and gives a solution to how to proceed in this fight. Our main thing is another organization of light just to mention this. And with this I thank you for your attention.