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Bound states in the continuum (BIC) are of special interest in photonics due to their theoretically infinite radiative lifetime. Here, we design a structure composed of a GaN layer with guided exciton-polaritons and a TiO$_2$ 1D photonic crystal slab. The photonic BIC hosted by the photonic crystal slab couples with the excitons of GaN to form a polaritonic BIC with a negative mass. This allows condensation to be reached with a low threshold in a structure suitable for electrical injection, paving the way for room-temperature polariton microdevices. We study in detail how the repulsive interaction between exciton-polaritons affects the condensate distribution in reciprocal space and, consequently, the condensate's overlap with the BIC resonance and, therefore, the condensate lifetime. We study an intrinsic contribution related to the formation of a bright soliton and the extrinsic contribution related to the interaction with an excitonic reservoir induced by spatially focused non-resonant pumping. We then study the peculiar dynamics of the condensation process in a BIC state for interacting particles using Boltzmann equations and hybrid Boltzmann-Gross Pitaevskii equations. We find optimal conditions allowing one to benefit from the long lifetime of the BIC for polariton condensation in a real structure.

One-dimensional Bose gases with contact repulsive interactions are characterized by the presence of infinite-lifetime quasiparticles whose momenta are called the `rapidities'. Here we develop a probe of the local rapidity distribution, based on the fact that rapidities are the asymptotic momenta of the particles after a long one-dimensional expansion. This is done by performing an expansion of a selected slice of the gas. We first apply this idea to a cloud in the quasi-condensate regime at equilibrium in a trap. We obtain an experimental picture of the position-dependent rapidity distribution which is in fair agreement with the theory prediction. The asymptotic regime is barely reached, but we show that finite expansion time can be taken into account using the Generalized Hydrodynamics theory. We then apply this local probe to an out-of-equilibrium situation where the local rapidity distribution is expected to be doubly peaked -- a hallmark of a non-thermal state -- even though the global rapidity distribution would possess no such distinctive feature. We observe the doubly-peaked local rapidity distribution.

The polarization discontinuity across interfaces in polar nitride-based heterostructures can lead to the formation of two-dimensional electron and hole gases. In the past, the observation of these electron and hole gases has been achieved through various experimental techniques, most often by electronic measurements but occasionally by optical means. However, the occurrence of a two-dimensional hole gas has never been demonstrated optically. The objective of this article is to demonstrate, thanks to the combination of various optical spectroscopy techniques coupled to numerical simulations, the presence of a two-dimensional hole gas in a GaN/AlGaN/GaN heterostructure. This is made possible thanks to a GaN/AlGaN/GaN heterostructure displaying a micrometer-thick AlGaN layer and a GaN cap thicker than in conventional GaN-based HEMTs structures. The band structure across the whole heterostructure was established by solving self-consistently the Schr\"odinger and Poisson equations and by taking into account the experimentally determined strain state of each layer. Continuous and quasi-continuos photoluminescence reveal the presence of a broad emission band at an energy around 50 meV below the exciton emission and whose energy blueshifts with increasing excitation power density, until it is completely quenched due to the complete screening of the internal electric field. Time-resolved measurements show that the emission arising from the two-dimensional hole gas can be assigned to the recombination of holes in the potential well with electrons located in the top GaN as well as electron from the bottom AlGaN, each of them displaying different decay times due to unequal electric fields. Besides the optical demonstration of a two-dimensional hole gas in a nitride-based heterostructure, our work highlights the optical recombination processes involved in the emission from such a hole gas.

So far, exciton-polariton (polariton) lasers were mostly single mode lasers based on microcavities. Despite the large repulsive polariton-polariton interaction, pulsed mode-locked polariton laser was never reported. Here, we use a $60 \ \mu m-$long GaN-based waveguide surrounded by distributed Bragg reflectors forming a multi-mode horizontal cavity. We demonstrate experimentally and theoretically a polariton mode-locked micro-laser operating in the blue-UV, at room temperature, with a 300$\ GHz$ repetition rate and 100$\ fs$-long pulses. The mode locking is demonstrated by the compensation (linearization) of the mode dispersion by the self-phase modulation induced by the polariton-polariton interaction. It is also supported by the observation in experiment and theory of the typical envelope frequency profile of a bright soliton., Comment: 16 pages, 12 figures

We consider the classical field integrable system whose evolution equation is the nonlinear Schr\"odinger equation with defocusing non-linearities, which is the classical limit of the quantum Lieb-Liniger model. We propose a simple derivation of the relation between two sets of conserved quantities: on the one hand the trace of the monodromy matrix, parameterized by the spectral parameter and introduced in the inverse-scattering framework, and on the other hand the rapidity distribution, a concept imported from the Lieb-Liniger model. To do so we use the definition of the rapidity distribution as the asymptotic momentum distribution after an expansion. More precisely we use thought experiments implementing an expansion and we present two different ways to derive our result, based on different thought experiments which lead to different calculations.

The stimulated emission of exciton-polaritons was proposed as a means of lowering the lasing threshold because it does not require the dissociation of excitons to obtain an electron-hole plasma, as in a classical semiconductor laser based on population inversion. In this work we propose a method to prove unambiguously the polaritonic nature of lasing by combining experimental measurements with a model accounting for the permittivity change as a function of the carrier density. To do so we use angle resolved photoluminescence to observe the lasing at cryogenic temperature from a polariton mode in a zinc oxide waveguide structure, and to monitor the continuous shift of the polaritonic dispersion towards a photonic dispersion as the optical intensity of the pump is increased (up to 20 times the one at threshold). This shift is reproduced thanks to a model taking into account the reduction of the oscillator strength and the renormalization of the bandgap due to the screening of the electrostatic interaction between electrons and holes. Furthermore, the measurement of the carriers lifetime at optical intensities in the order of those at which the polariton lasing occurs enables us to estimate the carrier density, confirming it is lower than the corresponding Mott density for zinc oxide reported in the literature.

We investigate the Lieb-Liniger gas initially prepared in an out-of-equilibrium state that is Gaussian in terms of the phonons. Because the phonons are not exact eigenstates of the Hamiltonian, the gas relaxes to a stationary state at very long times. Thanks to integrability, that stationary state needs not be a thermal state. We characterize the stationary state of the gas after relaxation and compute its phonon population distribution. Technically, this follows from the mapping between the exact eigenstates of the Lieb-Liniger Hamiltonian and those of a non-interacting Fermi gas -- a mapping provided by the Bethe equations -- , as well as on bosonization formulas valid in the low-energy sector of the Hilbert space. We apply our results to the case where the initial state is an excited coherent state for a single phonon mode, and we compare them to exact results obtained in the hard-core limit., Comment: Main text : 6 pages, 1 figures, Supplemental Material : 2 pages, 1 figure

We experimentally demonstrate the difference between a ridge polariton laser, and a conventional edge-emitting ridge laser operating under electron-hole population inversion. The horizontal laser cavities are 20 -- 60 $\mu$m long GaN etched ridge structures with vertical Bragg reflectors. We investigate the laser threshold under optical pumping and assess quantitatively the effect of a varying optically-pumped length. The laser effect is achieved for an exciton reservoir length of just 15% of the cavity length, which would not be possible in a conventional ridge laser, with an inversion-less polaritonic gain about 10 times larger than in equivalent GaN lasers. The modelling of the cavity free spectral range demonstrates the polaritonic nature of the modes.

We review the recent theoretical and experimental progress regarding the Generalized Hydrodynamics (GHD) behavior of the one-dimensional Bose gas with contact repulsive interactions, also known as the Lieb-Liniger gas. In the first section, we review the theory of the Lieb-Liniger gas, introducing the key notions of the rapidities and of the rapidity distribution. The latter characterizes the Lieb-Liniger gas after relaxation and is at the heart of GHD. We also present the asymptotic regimes of the Lieb-Liniger gas with their dedicated approximate descriptions. In the second section we enter the core of the subject and review the theoretical results on GHD in 1D Bose gases. The third and fourth sections are dedicated to experimental results obtained in cold atoms experiments: the experimental realization of the Lieb-Liniger model is presented in section 3, with a selection of key results for systems at equilibrium, and section 4 presents the experimental tests of the GHD theory. In section 5 we review the effects of atom losses, which, assuming slow loss processes, can be described within the GHD framework. We conclude with a few open questions., Comment: Review article, 75 pages

We investigate the effect of losses on an interacting quantum gas. We show that, for gases in dimension higher than one, assuming together a vanishing correlation time of the reservoir where dissipation occurs, and contact interactions leads to a divergence of the energy increase rate. This divergence is a combined effect of the contact interactions, which impart arbitrary large momenta to the atoms, and the infinite energy width of the reservoir associated to its vanishing correlation time. We show how the divergence is regularized when taking into account the finite energy width of the reservoir, and, for large energy width, we give an expression for the energy increase rate that involves the contact parameter. We then consider the specific case of a weakly interacting Bose Einstein condensate, that we describe using the Bogoliubov theory. Assuming slow losses so that the gas is at any time described by a thermal equilibrium, we compute the time evolution of the temperature of the gas. Using a Bogoliubov analysis, we also consider the case where the regularization of the divergence is due to the finite range of the interaction between atoms., Comment: 5 pages + appendices

In quantum gases with contact repulsion, the distribution of momenta of the atoms typically decays as $\sim 1/|p|^4$ at large momentum $p$. Tan's relation connects the amplitude of that $1/|p|^4$ tail to the adiabatic derivative of the energy with respect to the gas' coupling constant or scattering length. Here it is shown that the relation breaks down in the one-dimensional Bose gas with contact repulsion, for a peculiar class of stationary states. These states exist thanks to the infinite number of conserved quantities in the system, and they are characterized by a rapidity distribution which itself decreases as $1/|p|^4$. In the momentum distribution, that rapidity tail adds to the usual Tan contact term. Remarkably, atom losses, which are ubiquitous in experiments, do produce such peculiar states. The development of the tail of the rapidity distribution originates from the ghost singularity of the wavefunction immediately after each loss event. This phenomenon is discussed for arbitrary interaction strengths, and it is supported by exact calculations in the two asymptotic regimes of infinite and weak repulsion., Comment: v1: 6 pages. v2: accepted version. 6 pages+10 pages of Supplemental Material. Substantial revision, which includes a full derivation of Eq. (4), relating the tail of the momentum distribution to the one of the rapidity distribution

We theoretically investigate the effects of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of K-body losses (K = 1,2,3,...) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion -- where the gas behaves like an ideal Bose gas -- and hard-core repulsion -- where the gas is mapped to a non-interacting Fermi gas -- we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space., Comment: v1: 6 pages + 2 appendices, 4 figures. v2: 6.5 pages + 2 appendices, 4 figures. Minor improvements and references added, results unchanged. v3: typos corrected; published version

Multidimensional coherent spectroscopy directly unravels multiply excited states that overlap in a linear spectrum. We report multidimensional coherent optical photocurrent spectroscopy in a semiconductor polariton diode and explore the excitation ladder of cavity polaritons. We measure doubly and triply avoided crossings for pairs and triplets of exciton-polaritons, demonstrating the strong coupling between light and dressed doublet and triplet semiconductor excitations. These results demonstrate that multiply excited excitonic states strongly coupled to a microcavity can be described as two coupled quantum-anharmonic ladders.

We investigate the demonstration and quantification of the strong coupling between excitons and guided photons in a GaN slab waveguide. The dispersions of waveguide polaritons are measured from T=6~K to 300~K through gratings. They are carefully analyzed within four models based on different assumptions, in order to assess the strong coupling regime. We prove that the guided photons and excitons are strongly coupled at all investigated temperatures, with a small $(11 \%)$ dependence on the temperature. However the values of the Rabi splitting strongly vary among the four models: the "coupled oscillator" model over-estimates the coupling; the analytical "Elliott-Tanguy" model precisely describes the dielectric susceptibility of GaN near the excitonic transition, leading to a Rabi splitting equal to $82 \pm 10 \ meV$ for TE0 modes; the experimental ellipsometry-based model leads to smaller values of $55 \pm 6 \ meV.$ We evidence that for waveguides including active layers with large oscillator strengths, as required for room-temperature polaritonic devices, a strong bending of the modes dispersion is not necessarily the signature of the strong-coupling, which requires for its reliable assessment a precise analysis of the material dielectric susceptibility., Comment: 145 pages, 8 figures

We monitor the time evolution of the temperature of phononic collective modes in a one-dimensional quasicondensate submitted to losses. At long times the ratio between the temperature and the energy scale $mc^2$, where $m$ is the atomic mass and $c$ the sound velocity takes, within a precision of 20\%, an asymptotic value. This asymptotic value is observed while $mc^2$ decreases in time by a factor as large as 2.5. Moreover this ratio is shown to be independent on the loss rate and on the strength of interactions. These results confirm theoretical predictions and the measured stationary ratio is in quantitative agreement with the theoretical calculations., Comment: 9 pages, 3 figures

An ultra-low intensity and beatnote phase noise dual-frequency vertical-external-cavity surface-emitting laser is built at telecom wavelength. The pump laser is realized by polarization combining two single-mode fibered laser diodes in a single-mode fiber, leading to a 100 % in-phase correlation of the pump noises for the two modes. The relative intensity noise is lower than -140 dB/Hz, and the beatnote phase noise is suppressed by 30 dB, getting close to the spontaneous emission limit. The role of the imperfect cancellation of the thermal effect resulting from unbalanced pumping of the two modes in the residual phase noise is evidenced.

The emergence of a special type of fluid-like behavior at large scales in one-dimensional (1d) quantum integrable systems, theoretically predicted in 2016, is established experimentally, by monitoring the time evolution of the in situ density profile of a single 1d cloud of $^{87}{\rm Rb}$ atoms trapped on an atom chip after a quench of the longitudinal trapping potential. The theory can be viewed as a dynamical extension of the thermodynamics of Yang and Yang, and applies to the whole range of repulsion strength and temperature of the gas. The measurements, performed on weakly interacting atomic clouds that lie at the crossover between the quasicondensate and the ideal Bose gas regimes, are in very good agreement with the 2016 theory. This contrasts with the previously existing 'conventional' hydrodynamic approach---that relies on the assumption of local thermal equilibrium---, which is unable to reproduce the experimental data., Comment: v1: 6+11 pages, 4+4 figures. v2: published version, 6+11 pages, 4+6 figures

Planar microcavities filled with active materials containing excitonic resonances host radiative exciton-polariton (polariton) modes with in-plane wave vectors within the light cone. They also host at least one mode guided in the cavity plane by total internal reflection and which is not radiatively coupled to the vacuum modes except through defects or sample edges. We show that polariton lasing mediated by polariton stimulated scattering can occur concomitantly in both types of modes in a microcavity. By adjusting the detuning between the exciton and the radiative photon mode one can favor polariton lasing either in the radiative or in the guided modes. Our results suggest that the competition between these two types of polariton lasing modes may have played a role in many previous observations of polariton lasing and polariton Bose Einstein condensation.

We report the first demonstration of cooling by three-body losses in a Bose gas. We use a harmonically confined one-dimensional (1D) Bose gas in the quasi-condensate regime and, as the atom number decreases under the effect of three-body losses, the temperature $T$ drops up to a factor four. The ratio $k_B T/(m c^2)$ stays close to 0.64, where $m$ is the atomic mass and $c$ the sound speed in the trap center. The dimensionless 1D interaction parameter $\gamma$, evaluated at the trap center, spans more than two order of magnitudes over the different sets of data. We present a theoretical analysis for a homogeneous 1D gas in the quasi-condensate regime, which predicts that the ratio $k_B T/(mc^2)$ converges towards 0.6 under the effect of three-body losses. More sophisticated theoretical predictions that take into account the longitudinal harmonic confinement and transverse effects are in agreement within 30% with experimental data.

We present a general analysis of the cooling produced by losses on condensates or quasi-condensates. We study how the occupations of the collective phonon modes evolve in time, assuming that the loss process is slow enough so that each mode adiabatically follows the decrease of the mean density. The theory is valid for any loss process whose rate is proportional to the $j$th power of the density, but otherwise spatially uniform. We cover both homogeneous gases and systems confined in a smooth potential. For a low-dimensional gas, we can take into account the modified equation of state due to the broadening of the cloud width along the tightly confined directions, which occurs for large interactions. We find that at large times, the temperature decreases proportionally to the energy scale $mc^2$, where $m$ is the mass of the particles and $c$ the sound velocity. We compute the asymptotic ratio of these two quantities for different limiting cases: a homogeneous gas in any dimension and a one-dimensional gas in a harmonic trap.

We investigate the out-of-equilibrium dynamics following a sudden quench of the interaction strength, in a one-dimensional quasi-condensate trapped at the surface of an atom chip. Within a linearized approximation, the system is described by independent collective modes and the quench squeezes the phase space distribution of each mode, leading to a subsequent breathing of each quadrature. We show that the collective modes are resolved by the power spectrum of density ripples which appear after a short time of flight. This allows us to experimentally probe the expected breathing phenomenon. Our results are in good agreement with theoretical predictions which take the longitudinal harmonic confinement into account.

We demonstrate edge-emitting exciton-polariton (polariton) lasing from 5 to 300 K and amplification of non-radiative guided polariton modes within ZnO waveguides. The mode dispersion below and above the lasing threshold is directly measured using gratings present on top of the sample, fully demonstrating the polaritonic nature of the lasing modes. The threshold is found to be similar to that of radiative polarions in planar ZnO microcavities. These results open broad perspectives for guided polaritonics by allowing an easier and more straightforward implementation of polariton integrated circuits exploiting fast propagating polaritons.

We investigate the cooling produced by a loss process non selective in energy on a one-dimensional (1D) Bose gas with repulsive contact interactions in the quasi-condensate regime. By performing nonlinear classical field calculations for a homogeneous system, we show that the gas reaches a non-thermal state where different modes have acquired different temperatures. After losses have been turned off, this state is robust with respect to the nonlinear dynamics, described by the Gross-Pitaevskii equation. We argue that the integrability of the Gross-Pitaevskii equation is linked to the existence of such long-lived non-thermal states, and illustrate this by showing that such states are not supported within a non-integrable model of two coupled 1D gases of different masses. We go beyond a classical field analysis, taking into account the quantum noise introduced by the discreteness of losses, and show that the non-thermal state is still produced and its non-thermal character is even enhanced. Finally, we extend the discussion to gases trapped in a harmonic potential and present experimental observations of a long-lived non-thermal state within a trapped 1D quasi-condensate following an atom loss process.

The effect of atom losses on a homogeneous one-dimensional Bose gas lying within the quasi-condensate regime is investigated using a Monte Carlo wavefunction approach. The evolution of the system is calculated, conditioned by the loss sequence, namely the times of individual losses and the position of the removed atoms. We describe the gas within the linearized Bogoliubov approach. For each mode, we find that, for a given quantum trajectory, the state of the system converges towards a coherent state, i.e. the ground state, displaced in phase space. Provided losses are recorded with a temporal and spatially resolved detector, we show that quantum feedback can be implemented and cooling to the ground state of one or several modes can be realized.

We analyse the breathing-mode oscillations of a harmonically quenched Tonks-Giradeau (TG) gas using an exact finite-temperature dynamical theory. We predict a striking collective manifestation of impenetrability---a collective many-body bounce effect. The effect, while being invisible in the evolution of the in-situ density profile of the gas, can be revealed through a nontrivial periodic narrowing of its momentum distribution, taking place at twice the rate of the fundamental breathing-mode frequency. We identify physical regimes for observing the many-body bounce and construct the respective nonequilibrium phase diagram as a function of the quench strength and the initial temperature of the gas. We also develop a finite-temperature hydrodynamic theory of the TG gas, wherein the many-body bounce is explained by an increased thermodynamic pressure of the gas during the isentropic compression, which acts as a potential barrier at the inner turning points of the breathing cycle., Comment: 5 pages, 4 figures, and Supplemental Material. arXiv admin note: substantial text overlap with arXiv:1608.08720

Describing finite-temperature nonequilibrium dynamics of interacting many-particle systems is a notoriously challenging problem in quantum many-body physics. Here we provide an exact solution to this problem for a system of strongly interacting bosons in one dimension in the Tonks-Girardeau regime of infinitely strong repulsive interactions. Using the Fredholm determinant approach and the Bose-Fermi mapping we show how the problem can be reduced to a single-particle basis, wherein the finite-temperature effects enter the solution via an effective "dressing" of the single-particle wavefunctions by the Fermi-Dirac occupation factors. We demonstrate the utility of our approach and its computational efficiency in two nontrivial out-of-equilibrium scenarios: collective breathing mode oscillations in a harmonic trap and collisional dynamics in the Newton's cradle setting involving real-time evolution in a periodic Bragg potential., Comment: Final published version in PRA style; moved Supplemental Material into main text; 6 pages, 3 figures

We develop a finite-temperature hydrodynamic approach for a harmonically trapped one-dimensional quasicondensate and apply it to describe the phenomenon of frequency doubling in the breathing-mode oscillations of its momentum distribution. The doubling here refers to the oscillation frequency relative to the oscillations of the real-space density distribution, invoked by a sudden confinement quench. We find that the frequency doubling is governed by the quench strength and the initial temperature, rather than by the crossover from the ideal Bose gas to the quasicondensate regime. The hydrodynamic predictions are supported by the results of numerical simulations based on a finite-temperature c-field approach, and extend the utility of the hydrodynamic theory for low-dimensional quantum gases to the description of finite-temperature systems and their dynamics in momentum space., Comment: Final published version; 5 pages and 1 figure in the main text, plus Supplemental Material

GaN and ZnO microcavities have been grown on patterned silicon substrate. Thanks to a common platform these microcavities share similar photonic properties with large quality factors and low photonic disorder which gives the possibility to determine the optimal spot diameter and to realize a complete comparative phase diagram study. Both systems have been investigated under the same experimental condition. Experimental results are well reproduced by simulation using Boltzmann equations. Lower polariton lasing threshold has been measured at low temperature in the ZnO microcavity as expected due to a larger Rabi splitting. However the threshold is strongly impacted by LO phonons through phonon-assisted polariton relaxation. We observe and discuss this effect as a function of temperature and detuning. Finally the polariton lasing threshold at room temperature is quite similar in both microcavities. This study highlights polariton relaxation mechanism and their importance for threshold optimization.

The formation and propagation of a polariton condensate under tightly focused excitation is investigated in a ZnO microcavity both experimentally and theoretically. 2D near-field and far-field images of the condensate are measured under quasi-continuous non-resonant excitation. The corresponding spatial profiles are compared to a model based on the Gross-Pitaevskii equation under cylindrical geometry. This work allows to connect the experiments performed with a small excitation laser spot and the previous kinetic models of condensation in a 2D infinite microcavity, and to determine the relevant parameters of both the interaction and the relaxation between the reservoir and the condensate. Two main parameters are identified: the exciton-photon detuning through the polariton effective mass and the temperature, which determines the efficiency of the relaxation from the reservoir to the condensate., Comment: 13 pages, 3 tables and 9 figures

Analyzing the noise in the momentum profiles of single realizations of one-dimensional Bose gases, we present the experimental measurement of the full momentum-space density correlations $\langle \delta n_p \delta n_{p'}\rangle$, which are related to the two-body momentum correlation function. Our data span the weakly interacting region of the phase diagram, going from the the ideal Bose gas regime to the quasicondensate regime. We show experimentally that the bunching phenomenon, which manifests itself as super-Poissonian local fluctuations in momentum space, is present in all regimes. The quasicondensate regime is however characterized by the presence of negative correlations between different momenta, in contrast to Bogolyubov theory for Bose condensates, predicting positive correlations between opposite momenta. Our data are in good agreement with {\it ab-initio} calculations., Comment: 10 pages (including appendix)

The amplitude and phase noises of a dual-frequency vertical-external-cavity surface-emitting laser (DF-VECSEL) operating at telecom wavelength are theoretically and experimentally investigated in detail. In particular, the spectral behavior of the correlation between the intensity noises of the two modes of the DF-VECSEL is measured. Moreover, the correlation between the phase noise of the radio-frequency (RF) beatnote generated by optical mixing of the two laser modes with the intensity noises of the two modes is investigated. All these spectral behaviors of noise correlations are analyzed for two different values of the nonlinear coupling between the laser modes. We find that to describe the spectral behavior of noise correlations between the laser modes, it is of utmost importance to have a precise knowledge about the spectral behavior of the pump noise, which is the dominant source of noise in the frequency range of our interest (10 kHz to 35 MHz). Moreover, it is found that the noise correlation also depends on how the spatially separated laser modes of the DF-VECSEL intercept the noise from a multi-mode fiber-coupled laser diode used for pumping both the laser modes. To this aim, a specific experiment is reported, which aims at measuring the correlations between different spatial regions of the pump beam. The experimental results are in excellent agreement with a theoretical model based on modified rate equations.

A trapped atom interferometer involving state-selective adiabatic potentials with two microwave frequencies on a chip is proposed. We show that this configuration provides a way to achieve a high degree of symmetry between the two arms of the interferometer, which is necessary for coherent splitting and recombination of thermal (i.e. non-condensed) atoms. The resulting interferometer holds promise to achieve high contrast and long coherence time, while avoiding the mean-field interaction issues of interferometers based on trapped Bose-Einstein condenstates.

We report on the quantum confinement of zero-dimensional polaritons in perovskite-based microcavity at room temperature. Photoluminescence of discrete polaritonic states are observed for polariton localized in symmetric sphere-like defects which are spontaneously nucleated on the top dielectric Bragg mirror. The linewidth of these confined states are found much sharper (almost one order of magnitude) than that of photonic modes in the perovskite planar microcavity. Our results show the possibility to study organic-inorganic cavity polariton in confined microstructure and suggest a fabrication method to realize integrated polaritonic devices operating at room temperature.

A new platform for fabricating polariton lasers operating at room temperature is introduced: nitride-based distributed Bragg reflectors epitaxially grown on patterned silicon substrates. The patterning allows for an enhanced strain relaxation thereby enabling to stack a large number of crack-free AlN/AlGaN pairs and achieve cavity quality factors of several thousands with a large spatial homogeneity. GaN and ZnO active regions are epitaxially grown thereon and the cavities are completed with top dielectric Bragg reflectors. The two structures display strong-coupling and polariton lasing at room temperature and constitute an intermediate step in the way towards integrated polariton devices.

We measure the position- and momentum- space breathing dynamics of trapped one-dimensional Bose gases. The profile in real space reveals sinusoidal width oscillations whose frequency varies continuously through the quasicondensate to ideal Bose gas crossover. A comparison with theoretical models taking into account the effect of finite temperature is provided. In momentum space, we report the first observation of a frequency doubling in the quasicondensate regime, corresponding to a self-reflection mechanism. The disappearance of this mechanism through the quasicondensation crossover is mapped out.

A laser threshold is determined by the gain condition, which has been progressively reduced by the use of heterostructures and of quantum confinement. The polariton laser is the ultimate step of this evolution: coherent emission is obtained from the spontaneous decay of an exciton-polariton condensate, without the achievement of any gain condition. ZnO, with its unique excitonic properties, is the best choice for a blue/UV-emitting polariton laser device. We report on the fabrication of a new family of fully hybrid microcavities that combine the best-quality ZnO material available (bulk substrate) and two dielectric distributed Bragg reflectors, demonstrating large quality factors (>2500) and Rabi splittings (~200 meV). Low threshold polariton lasing is achieved between 4 and 300 K and for excitonic fractions ranging between 12% and 96 %. A phase diagram highlighting the role of LO phonon-assisted relaxation in this polar semiconductor is established, and a remarkable switching between polariton modes is demonstrated.

We analyze the two-body momentum correlation function for a uniform weakly interacting one-dimensional Bose gas. We show that the strong positive correlation between opposite momenta, expected in a Bose-Einstein condensate with a true long-range order, almost vanishes in a phase-fluctuating quasicondensate where the long-range order is destroyed. Using the Luttinger liquid approach, we derive an analytic expression for the momentum correlation function in the quasicondensate regime, showing (i) the reduction and broadening of the opposite-momentum correlations (compared to the singular behavior in a true condensate) and (ii) an emergence of anticorrelations at small momenta. We also numerically investigate the momentum correlations in the crossover between the quasicondensate and the ideal Bose-gas regimes using a classical field approach and show how the anticorrelations gradually disappear in the ideal-gas limit., Comment: Final published version

We investigate the momentum distribution of weakly interacting 1D Bose gases at thermal equilibrium both experimentally and theoretically. Momentum distribution of single 1D Bose gases is measured using a focusing technique, whose resolution we improve via a guiding scheme. The momentum distribution compares very well with quantum Monte Carlo calculations for the Lieb-Liniger model at finite temperature, allowing for an accurate thermometry of the gas that agrees with (and improves upon) the thermometry based on in situ density fluctuation measurements. The quasi-condensation crossover is investigated via two different experimental parameter sets, corresponding to the two different sides of the crossover. Classical field theory is expected to correctly describe the quasi-condensation crossover of weakly interacting gases. We derive the condition of validity of the classical field theory, and find that, in typical experiments, interactions are too strong for this theory to be accurate. This is confirmed by a comparison between the classical field predictions and the numerically exact quantum Monte Carlo calculations., Comment: 8 pages

Polariton relaxation mechanisms are analysed experimentally and theoretically in a ZnO-based polariton laser. A minimum lasing threshold is obtained when the energy difference between the exciton reservoir and the bottom of the lower polariton branch is resonant with the LO phonon energy. Tuning off this resonance increases the threshold, and exciton-exciton scattering processes become involved in the polariton relaxation. These observations are qualitatively reproduced by simulations based on the numerical solution of the semi-classical Boltzmann equations.

The lasing operation of a ZnO planar microcavity under optical pumping is demonstrated from T=80 K to 300 K. At the laser threshold, the cavity switches from the strong coupling to the weak coupling regime. A gain-related transition, which appears while still observing polariton branches and, thus, with stable excitons, is observed below 240K. This shows that exciton scattering processes, typical of II-VI semiconductors, are involved in the gain process.

In order to achieve polariton lasing at room temperature, a new fabrication methodology for planar microcavities is proposed: a ZnO-based microcavity in which the active region is epitaxially grown on an AlGaN/AlN/Si substrate and in which two dielectric mirrors are used. This approach allows as to simultaneously obtain a high-quality active layer together with a high photonic confinement as demonstrated through macro-, and micro-photoluminescence ({\mu}-PL) and reflectivity experiments. A quality factor of 675 and a maximum PL emission at k=0 are evidenced thanks to {\mu}-PL, revealing an efficient polaritonic relaxation even at low excitation power., Comment: 12 pages, 3 figures

We report on local measurements of atom number fluctuations in slices of a single 1D Bose gas with repulsive interactions. For weakly interacting gases, the fluctuations are super-Poissonian at intermediate atomic densities and become sub-Poissonian at high densities once the gas enters into the quantum quasi-condensate regime. At stronger interactions, when approaching the fermionization regime, we no longer observe super-Poissonian statistics; the fluctuations go from Poissonian to sub-Poissonian as the density is increased, as those in a Fermi gas.

By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasi-condensate regime throughout the dimensional crossover from a purely 1D to an almost 3D gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasi-condensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas.

We perform measurements of the third moment of atom number fluctuations in small slices of a very elongated weakly interacting degenerate Bose gas. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasi-condensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three body correlations in the system.

We have studied the thermal properties of atom chips consisting o high thermal conductivity Aluminum Nitride (AlN) substrates on which gold microwires are directly deposited. We have measured the heating of wires of several widths and with different thermal couplings to the copper mount holding the chip. The results are in good agreement with a theoretical model where the copper mount is treated as a heat sink and the thermal interface resistance between the wire and the substrate is vanishing. We give analytical formulas describing the different transient heating regimes and the steady state. We identify criteria to optimize the design of a chip as well as the maximal currents $I_c$ that can be fed in the wires. For a 600 $\mu$m thick-chip glued on a copper block with Epotek H77, we find $I_c=16$ A for a 3 $\mu$m high, 200 $\mu$m wide-wire.

The strong coupling regime in a ZnO microcavity is investigated through room temperature photoluminescence and reflectivity experiments. The simultaneous strong coupling of excitons to the cavity mode and the first Bragg mode is demonstrated at room temperature. The polariton relaxation is followed as a function of the excitation density. A relaxation bottleneck is evidenced in the Bragg-mode polariton branch. It is partly broken under strong excitation density, so that the emission from this branch dominates the one from cavity-mode polaritons.

In this review article, we describe the studies of 1D gases realised on atom-chip experiments.