 Thank you very much. Can you hear me? So it's always a great pleasure to be in Trieste. I'm very grateful for this invitation. So I'm going to be the first speaker on exit and polaritons. So I will give some short introduction on this subject which then will be addressed by several speakers in this meeting. So I will present a theoretical work. I'm a theorist. And this work has been done in collaboration with Aleksandr Sheremet from Russian Quantum Center in Moscow. Yura Ruboku is here from Yunam, Kurnavaka, Mexico and Ivan Shilik, who is now working in Iceland and Singapore. So this will be about some fundamental properties of exit and polaritons, superposition, light, metaclasm particles. And I will start from the overview of recent experiments which attracted a lot of attention to this field. And then I will try to analyze the intrinsic structure of this interesting quasi-particle, unusual quasi-particle exit and polariton and will try to link it with some philosophical questions of quantum mechanics. So the recent really avalanche of publications was devoted to the realization of this device which is called polariton laser. The concept was proposed by Imamoglu and Yamamoto in 1995. And it is quite simple. So imagine you have an optical cavity. So these are dielectric black mirrors that confine light within this green layer. And this green layer is a semiconductor where you can inject either optically or electronically through contacts. Electrons and holes. These electrons and holes can form excitons. Now what happens? That exciton, the dispersion of exciton is shown on this scheme by the horizontal line. And exciton has a parabolic dispersion but on this scale you would not see this parabola. It is like a straight line. So exciton can be coupled, even strongly coupled to light which means that it can emit photon but then photon comes back, absorbs and what exactly happens there is actually the subject of my talk. Just the consequence of this interaction which is not a subject of my talk but something you can find in textbooks now is the modification of dispersion of eigenmores of this system. So instead of the exciton dispersion which is this one and the photon dispersion which is parabolic because photon is confined in this direction. So the wave vector of light is fixed in this direction and you can only vary wave vector in plane. Now you obtain this parabolic dispersion with very light effectiveness. So as a result of the scalping you have two new dispersion branches which are called exciton polaritons. From the point of view of quantum mechanics these are superposition exciton photon states and what it means I am going to discuss today. So far just let us assume that it is so and let us inject this exciton polaritons in the system. Then due to the excitonic component they can interact with photons for example or between each other or with free carriers if there are any free carriers in this system and due to these interactions they can relax their energy down to the bottom of the low polariton branch. So this is the low polariton branch this is the upper polariton branch. As a result in the bottom of this low polariton branch you can form what is what can be called boson's time condensate of exciton polaritons. Here I must have mentioned that excitons are of course bosons because they are like cooper pairs they are composed by two fermions an electron is a fermion, a hole is a fermion so put two fermions together and you have a boson and photons are bosons of course. So this superposition quasi particle which is part exciton part photon is necessarily boson it follows bosonic statistics even though we are out of equilibrium usually there is pumping, there is decay in this system because light can go away tunneling through the mirror nevertheless one can hope to be able to create a macroscopically populated single quantum state somewhere here near the bottom of the low polariton branch. Now this state would of course also be characterized by some decay some radiative decay because light can go away from the structure by tunneling through these mirrors there is no ideal mirrors in the world and even if you have the best quality cavity your reflection coefficient is something like 99.9% that means that after just maybe 25 picoseconds your photon will go away from the cavity and then you can detect it you can see light going out from the cavity so the idea of imomoglu and imomotor was that this light which is emitted spontaneously there is no stimulated emission here it is spontaneous emission by the condensate but still this light will have all properties of laser light it will be monochromatic it will be characterized by a fixed wave vector which is perpendicular to the surface of the cavity and it is expected to be coherent because this light is generated by a coherent quantum state many body quantum states which is the condensate of exotin polarity so formally it will be laser but laser without stimulated emission of radiation the laser without inversion of population so kind of unusual laser, bosonic laser and after some discussion the term polaritone laser was accepted I believe by the major part of the community so now this device is referred to as polaritone laser so these polaritone lasers have been realized and the most famous paper is by the next speaker Peter Littlewood and co-authors where the boson-stank condensation of exotin polaritones was demonstrated at 5 Kelvin in cadmium telluride micro cavity but I should say that for polaritone laser you do not necessarily need strictly speaking boson-stank condensation because you do not care of thermodynamics you do not really need a thermal equilibrium in the system the only thing you need for the laser is to have this condensate so to put many identical exotin polaritones in the same quantum state what happens in other quantum states other their population is described by some equilibrium equilibrium distribution function or not is not so important so there were many papers where polaritone laser was reported not necessarily boson-stank condensation and there is still debate on what should be called boson-stank condensation what should be called polaritone laser so this is beyond the scope of my talk I just want to emphasize that now polaritone lasers are realized in many systems and they are realized also at room temperature in wideband gap semiconductors so there is an overwhelming I would say evidence that one can create condensates of this half light half matter quasi-particles called exotin polaritones now I come to actually to the topic of this artwork which is kind of rhetoric question what is an exotin polaritone so what are in detail how this superposition quasi-particles are organized what really happens inside the micro cavity and superposition means that you are for example half exotone half photon of course there are many superposition states in nature and it is not surprising to have a superposition state even circular polarized light can be considered a superposition of two linearly polarized lights but here the peculiarity is that it is a superposition of two quite different objects because one of them is a matter quasi-particle exotone which has an effective mass which has some dimension bore radius can interact with other particles etc can be decomposed after all it can be decomposed into an electron hole and another part of this state is a photon so what could be the microscopic image of this exotone polaritone so let us first of all consider not a micro cavity but just a crystal slab let us say this is some semiconductor crystal and we have a single photon source and we send a photon to this semiconductor slab so with some probability this photon can just go through and ignore I mean it can be absorbed but it can be not absorbed just propagates through and you will detect photon at the exit but of course there is a probability that it is absorbed and it creates an exotone so one image of exotone polaritone is a naive image I would say is the following that your photon enters to the crystal propagates for some time then at some stage it creates an exotone exotone is a very heavy compared to photon it almost does not move so it moves very very slowly then it recombines and creates another photon which keeps propagating and then creates again exotone et cetera et cetera so it is a chain of absorption and reemission acts it looks like an incoherent picture but why not? I mean there are situations and of course absorption and reemission are very well known phenomena and maybe observed in different systems so at least this scheme is not self-contradictive but the most generally accepted is a different scheme the most generally accepted is this one that you arrive and immediately inside this crystal you do not have a photon, you do not have exotone but you have this exotone polaritone so from the first works of the pioneers of this area Agranovic and Hofelt this is the generally accepted point of view and if we speak in terms of classical optics we describe this exotone polaritone by modifying the dielectric response function of this crystal so here light propagates according to its dispersion law in vacuum and here it propagates according to some different dispersion law which is obtained taken into account like metacoupling in a semiconductor so there is no exotone, no photons here but there is a new mode exotone polaritone which exists from this point to this point and then at the back edge it converts again to photon so it reminds this famous discussion of Bore and Einstein on the nature of wave function so I will come back to this thing again but let us remember these two images one is what I would call a statistical model where we have real exotones, real photons and real acts of absorption and emission maybe stochastic so we do not know where photon will convert to exotone and where exotone will convert to photon but we know that something happens here and we have exotones and photons and they really exist in the structure and the other image is that there is no exotones and photons there are completely new quasi particles which are the superposition particles exotone polaritones so no emission, no absorption acts just this conversion of photon to exotone polaritone and back on the surface now if we look at the microcavity structure then it becomes even more tricky because usually in this microcavity exotones can only be created in a quantum well so away from the quantum well you really cannot have any exotone you just have photon and then it is, well it looks like photon can go through the quantum well and be absorbed in a quantum well sorry, and how to do it, yeah and convert to this red tomato looking exotone and this is a stochastic process but on the other hand one can say that maybe this is the case in what is called weak coupling regime where people speak independently about exotone and photon but it would not apply to the strong coupling regime which is the most interesting for polaritone laser where due to the coupling between exotone and photon we have two new eigenstates which are the superposition states so maybe the answer is that in weak coupling we do really have exotones and photons but this cannot no more be applied to the strong coupling regime and sorry again for this let us go here and this is reminiscent to again the discussion of godfathers of quantum mechanics on the nature of wave function so suppose that we can capture this particle we can do the measurement and of course when we are doing the measurement we can see either photon for example like in a photo luminescence experiment or an exotone for example we can split an exotone into the couple and hole and it contributes to the electric current so when we do measurements necessarily we kill exotone polaritone we have either exotone or photon now the difference between two views I would say on this process is that what happens between acts of measurement either we have really exotones and photons we just do not know whether our polaritone is exotone or photon in this particular moment in this particular place in the space and this would be a materialistic point of view which was advocated by Schrodinger and Einstein or as more or less everybody believes in this community actually there is no exotone no photon until you do the measurement you cannot say what it is and so the matter does not exist if you do not observe it when you do measurement your wave function to either photonic or exotonic state and then you can speak about the outcome but between acts of measurements you are neither photon nor exotone so this is all philosophical and all very old so why I am coming back to this discussion because this discovery of bosonic condensates of exotone polaritones offers a new tool of studying this interesting problem so if we would have just one exotone polaritone in a given quantum state then any kind of measurement would not help us we can capture it as exotone we can capture it as photon but it would not give us any supplementary knowledge on what has been before but if we have a bosonic condensate this changes the situation so let us look at this scheme suppose that we have a condensate with six quasi-particles, six polaritones in the condensate so two possibilities are either some of them are exotones and some of them are photons for example exotones are white cats and photons are black cats this is one possibility and another possibility is that they are all identical and they are all exotone polaritones in this case when we do measurement the result would be different so let us see in the first case statistical interpretation of polaritone condensate we have a total number of polaritones at each particular moment of time which is equal to the number of exotones white cats plus number of photons black cats we do not know how many white cats how many black cats we have but this condition holds we can admit that they possibly convert to each other in the case of this exotone polaritone picture let's say Copenhagen school view we have this identical particles which are superpositions of exotones and photons and if we want to speak about exotone fraction and photon fraction which we can then detect then they are linked they are both proportional to the total number of exotone polaritone and the coefficients of proportionality are so-called Hopfield coefficients which were introduced by Hopfield in the beginning of 1960s they just tell us what is the weight of the exotonic component in this superposition state and what is the weight of the photonic component so these are some constants they do not look to it they are not stochastic these are just numbers and they satisfy this normalization condition so clearly these two situations are not equivalent and if we do this Gedanken experiment, thought experiment we will see some difference so the thought experiment is that we excite condensate in a micro cavity with a pulse of light so we create some exotone polaritones no matter what is the quantum state here but at least there are more than one in average and then we do two measurements we have here the photon counter which counts photons emitted by the system and we also apply electric field which destroys exotones so an exotone is decomposed into an electron whole pair and these electrons and holes give contribution to the photocurrent which is measured by a meter so we compare let us assume that we can do this experiment which is not trivial with a very good accuracy so we have some noise in this photocurrent some noise in this photoluminescence signal let us compare these two noises and see if there are any correlations between them now what I would expect if we are within the statistical model then of course I would expect some correlations because let us say the number of black cats is correlated with the number of white cats if I have more white cats I have less black cats and the other way around so signal of photoluminescence which is proportional to the number for example black cats is correlated with the signal of photocurrent which is proportional to the number of white cats on the other hand in case of this picture we would expect relatively no correlations because in each case we kill one cat and all cats are identical no matter we kill it converting it to photon or we kill it converting it to exciton we just kill it and it does not affect any how the statistics of the remaining state it depends on the detuning between your exciton and photon and the resonance so in this point you would have half exciton half photon state here half exciton half photon state there so here it is okay here it is written for the bulk crystal so if you go of course to this point you are entirely photonic but in a micro cavity the advantage is that you have confinement of light in this direction so you can have closed energy state in this system which is not at zero energy but which is at some finite energy so if you would move this parabola to this point so that you have the exact resonance you will be half exciton half photon then you can have any other proportionality depending on the detuning okay okay so let me let me go forward so these are all naive qualitative hand-waving arguments but let us try to calculate something quantitatively what we can calculate we can calculate some correlators suppose we can really do this exciton photon counting measurements then what can we measure we can measure the exciton photon correlator which is just the average product of exciton number to photon number divided by multiple by the product of averages we can do a simple G2 measurement for photons like in quantum optics this G2 second order coherence measurement we can do the same for excitons which would be very tricky from the experimental point of view and finally from these three correlators we can build a big correlator big exciton photon correlator G big which is squared exciton photon correlated normalized by exciton G2 and photon G2 so this quantity is interesting I introduced it on purpose because then it will give some some nice some nice it will be helpful for the following story so let us see what would be these correlators in the case of the Copenhagen let's say interpretation of exciton polaritons where we have polaritons not excitons not photons and in this case our exciton photon operators can be represented just as linear combinations of polariton operators for upper and lower polariton branches in this way so low is the annihilation operator of a polariton on the lower polariton branch upper you see you is the annihilation operator of a polariton on the upper polariton branch so this is a simplest linear linear combinations they allow us to express our correlators through polariton operators and we take advantage of the fact that our condensate sits on the lower polariton branch so the upper polariton branch is empty which is why the expectation value of this upper operator or the number of particles on the upper state is zero and this allows after a very simple algebra to reduce our exciton photon correlator to something very similar to just G2 in quantum physics so this combination and of course the answers would depend on the statistics of our polaritons in the condensate but this will be all textbook answers for the coherent state this correlator will be one for the thermal state it would be two for the number state it would be one minus one over the number of particles and so on so no surprises interestingly the big correlator this G big SC will be equal to one for any statistics so for all these states this big correlator is exactly one it is independent on the statistics this is a formal formal algebraic result so if it is one we can be sure that everything works correctly we have polaritons there is no any independent excitons and photons in the system and our vision of polaritonics as it was formulated by Hoplut and Agranovic 50 years ago is perfectly correct now of course the most interesting thing would be how to deviate from one how can I deviate from one so let us put ourselves in a different logic and let us allow for stochastic conversion of exciton to photon and photon to exciton so let us work in the exciton-photon basis and describe our system by some density matrix which has diagonal elements this p of an a and b which depends also on time an a is let us say number of excitons and b is number of photons so the other way around so the probability to have an a excitons and b photons in the system may be found from this master Boltzmann equation which can be derived from the general UV equation for the density matrix but it can be also written from the common sense so it allows for radiative decay where we destroy one photon in the system and it is characterized by some photonic lifetime tau photon there is also a possibility to destroy excitons for example by electric field which is characterized by time constant tau exciton and then we have to take into account this our stochastic conversion so we introduce a new parameter tau xc which is a rate of stochastic exciton to photon and photon to exciton conversion and accounting for the buzonic nature of our excitons and photons we can write the corresponding term into this master Boltzmann equation in this form so again it is a simple algebra and then we can work with this equation we can solve it assuming some initial state for example coherent initial state or number state or anything so let us see what it gives so here we have these probabilities probability to find an exciton and a excitons and b photons in our system as a function of time in the absence and in the presence of this stochastic conversion so in the absence means tau xc equal to infinity and ok we have some dynamics and clearly the dynamics of these probabilities changes in the presence of this stochastic conversion it changes in a very clear way actually the probabilities of all configurations corresponding to the same total number of polaritons total number of quasi-particles in the system become very close to each other and this is very natural if your excitons can randomly convert to photons and photons to excitons then eventually all configurations all possible configurations with a fixed total number of particles become will have the same probability so if you have 10 polaritons the probability to have 9 excitons and 1 photons and probability to have 1 excitons would be the same after all if these stochastic conversions are quick so this is what one would expect and let us see what it gives for our correlators so actually for our correlators it is dramatic because the correlators strongly change as a function of time for this stochastic conversion process so even this traditional G2 the photonic G2 which has been started actually in this condensate it strongly deviates from 1 we would expect G2 equal to 1 for the coherent state but here we see that because of this stochastic conversion it would go to something like 1.4 now the exciton photon correlator would go below 1 but more interestingly this big correlator which is always 1 for any statistics of polaritons within the polariton model let's say Copenhagen interpretation of polaritons it will go down to 1.4 so this is a huge difference factor of 4 so if it if we manage to do this experiment and we see that this huge G deviates from 1 goes below 1 then if it decays that something happens that there are these stochastic conversions whatever it means so the limiting case of very strong stochastic conversion so very short how we see maybe understood in terms of a classical model of two coupled oscillators so actually if we have two coupled oscillators with amplitudes a and b and we we impose a condition of energy conservation so that a squared plus b squared is some constant and then in case of fully random distribution of initial phases of these oscillators distribution function p of a and b which is simple delta function which reflects this normalization condition with normalization factor so then we can calculate all expectation values and we can calculate for example our xc correlator which is this quantity and we obtain two thirds which is exactly the limit we have here so this is not unexpected but still quite surprising if we think about it from the traditional point of view now if we look at the spectrum of emission of this condensate we can we can calculate two things we can calculate the energy of the condensate because our stochastic processes they do not conserve energy strictly speaking so the energy can be modified we can calculate the energy variance per particle and this gives the following thing if initially our condensate was in this lower at the lower polyethane branch in this point then due to stochastic conversions it would go up in energy and eventually it would arrive to the middle so this is like weak coupling regime in the weak coupling regime there is no polyethane branches we have just no solution so this is something which we would expect because naively in the weak coupling regime coupling of acetone to photon is so weak that well excitons live for some time without seeing photons photons live for some time without seeing excitons so this stochastic model of acetone to photon conversion would be would make sense and effectively this is what we see so introducing this let's say hidden parameter this tau xc we can describe transition from weak to strong coupling regime now yes now our point is that even in the strong coupling regime possibly these stochastic conversions do take place because we do not see from this reasoning that they immediately disappear that tau xc would go to infinity if we are apart from weak to strong coupling regime it is I would not expect it now of course this all needs to be experimentally verified so next thing we were thinking about was the experiment which would be easy to realize because okay one can count photons but one can hardly count excitons and this splitting of excitons to electron hole pairs and then detection of photons would imply very sophisticated measurements if you really want to have a accuracy on one single electron level so it is not impossible but very hard much easier would be to do a purely optical experiment so the next idea was to put the system in the regime of rhabiosilations in this regime with a short pulse of light you excite both polyethane branches together low and upper branch and then you observe bits between exciton state and photon state initially your system is in the fully photon state then on a frequency given by this splitting it converts to excitons then converts back to photons etc etc so this is a very well studied phenomenon experimentally observed even in 90s by many groups so in this regime what we propose to do we propose to fix at the upper branch and at the lower branch and at this particular selected frequencies put two photon counters and then measure correlations intensity-intensity correlations between upper and lower polyethane branches so this is a perfectly realistic experiment and quickly going through the theory which is similar to what I described earlier we come out with this for example for some given choice of parameters this results for the correlators between low and upper polyethane branches which are similar to what we observed for exciton photon correlators in particular this big correlator again composed from two color intensity-intensity correlator and single color correlators for upper and lower polyethane branches this one it strongly deviates from one it would be one within this Copenhagen model and then it would go to one quarter in the limit of strong stochastic conversions so this brings me to my conclusions so what I wanted to tell you is that stochastic exciton photon correlation processes conversion processes are described maybe described by what we call ambitiously hidden variable stochastic conversion time stochastic conversion time stochastic conversion time which so far was not studied neither experimentally nor theoretically to the best of my knowledge so in the limit of stochastic conversion time we have the traditional let's say quantum mechanical Copenhagen results for all correlators and no surprises but if this tau xc is less than infinity if it is finite then there are interesting things happen in particular if it is less than acted on photon lifetime but more than the inverse Rabi frequency we have very strong deviations of all correlators from the Copenhagen predictions and this big G correlator goes from one to one fourth which is a huge effect then if this tau xc becomes very small we have a transition to the weak coupling regime which is a well known effect and the final result corresponds well to the weak coupling picture so exciton photon conversion mixes actually two polariton branches and changes the energy of the condensate so in a sense it is not an energy concerning process and where the energy goes it depends on the micro model it can be discussed but we just suppose that this process exists but we do not explain where it comes from and finally in the regime of Rabi oscillations the upper low polariton correlator is expected to go below one due to stochastic process so this is something one should be able to check so maybe it goes below one maybe it sticks to one but this is an experiment which can be realized on existing samples within existing experimental facilities thank you very much thank you