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We report the canonical properties of Bose-Einstein condensation of polaritons, seen previously in many low-temperature experiments, at room temperature in a GaAs/AlGaAs structure. These effects include a nonlinear energy shift of the polaritons, showing that they are not non-interacting photons, and dramatic line narrowing due to coherence, giving coherent emission with spectral width of 0.24 meV at room temperature with no external stabilization. This opens up the possibility of room temperature nonlinear optical devices based on polariton condensation.

We present a careful calibration of the exciton fraction of polaritons in high-$Q$ ($\sim 300,000$), long-lifetime ($\sim 300$ ps), GaAs/AlGaAs microcavities.This is a crucial parameter for many-body theories which include the polariton-polariton interactions.It is much harder to establish this number in high-$Q$ structures compared to low-$Q$ structures, because the upper polariton is nearly invisible in high-$Q$ cavities.We present a combination of photoluminescence, photoluminescence excitation, and reflectivity measurements to highly constrain the fit model, and compare the results of this model to the results from low-$Q$ structures.We present a fitted curve of exciton fraction as a function of the lower polariton energy for multiple samples which have been used in prior experiments., Comment: 16 pages, 11 figures

We have created a spatially homogeneous polariton condensate in thermal equilibrium, up to very high condensate fraction. Under these conditions, we have measured the coherence as a function of momentum, and determined the total coherent fraction of this boson system from very low density up to density well above the condensation transition. These measurements reveal a consistent power law for the coherent fraction as a function of the total density over nearly three orders of its magnitude. The same power law is seen in numerical simulations solving the two-dimensional Gross-Pitaevskii equation for the equilibrium coherence. This power law has not been predicted by prior analytical theories.

Phase fluctuations determine the low-energy properties of quantum condensates. However, at the condensation threshold, both density and phase fluctuations are relevant. While strong emphasis has been given to the investigation of phase fluctuations, which dominate the physics of the quantum system away from the critical point -- number fluctuations have been much less explored, even in thermal equilibrium. In this work, we report experimental observation and theoretical description of fluctuations in a circularly-confined non-equilibrium Bose-Einstein condensate of polaritons near the condensation threshold. We observe critical fluctuations, which combine the number fluctuations of a single-mode condensate state and competition between different states. The latter are analogous to mode hopping in photon lasers. Our theoretical analysis indicates that this phenomenon is of a quantum character, while classical noise of the pump is not sufficient to explain the experiments. The manifestation of a critical quantum state competition unlocks new possibilities for the study of condensate formation while linking to practical realizations in photonic lasers.

Equilibrium Bose-Einstein condensation of exciton-polaritons, demonstrated with a long-lifetime microcavity [Phys. Rev. Lett. 118, 016602 (2017)], has proven that driven-dissipative systems can undergo thermodynamic phase transitions in the limit where the quasiparticle lifetime exceeds the thermalization time. Here, we identify the role of dimensionality and polariton interactions in determining the degree of thermalization in optically generated traps. To distinguish the effect of trapping from interactions and lifetimes, we measured the polariton distribution under four nonresonant Gaussian pumps in a square geometry and compared it with polariton distributions measured with each pump individually. We found that significant redistribution of polaritons arises by trapping and modification of the density of states. Surprisingly efficient polariton-polariton scattering below the condensation threshold is evidenced by the depletion of the inflection-point polaritons. Our work provides a deeper understanding of polariton distributions and their interactions under various geometries of optically generated potentials.

It is now routine to make Bose-Einstein condensates of polaritons with long enough lifetime and low enough disorder to travel ballistically for hundreds of microns in quasi-one-dimensional (1D) wires. We present observations of a polariton condensate injected at one point in a quasi-1D ring, with a well-defined initial velocity and direction. A clear precession of the circular polarization is seen, which arises from an effective spin-orbit coupling term in the Hamiltonian. Our theoretical model accurately predicts the experimentally observed behavior, and shows that "zitterbewegung" behavior plays a role in the motion of the polaritons., Comment: accepted by Phys. Rev. B

The Higgs amplitude mode is a collective excitation studied and observed in a broad class of matter, including superconductors, charge density waves, antiferromagnets, 3He p-wave superfluid, and ultracold atomic condensates. In all the observations reported thus far, the amplitude mode was excited by perturbing the condensate out of equilibrium. Studying an exciton-polariton condensate, here we report the first observation of this mode purely driven by intrinsic quantum fluctuations without such perturbations. By using an ultrahigh quality microcavity and a Raman spectrometer to maximally reject photoluminescence from the condensate, we observe weak but distinct photoluminescence at energies below the condensate emission. We identify this as the so-called ghost branches of the amplitude mode arising from quantum depletion of the condensate into this mode. These energies, as well as the overall structure of the photoluminescence spectra, are in good agreement with our theoretical analysis.

The interaction between aligned dipoles is long-ranged and highly anisotropic: it changes from repulsive to attractive depending on the relative positions of the dipoles. We report on the observation of the attractive component of the dipolar coupling between excitonic dipoles in stacked semiconductor bilayers. We show that the presence of a dipolar exciton fluid in one bilayer modifies the spatial distribution and increases the binding energy of excitonic dipoles in a vertically remote layer. The binding energy changes are explained by a many-body polaron model describing the deformation of the exciton cloud due to its interaction with a remote dipolar exciton. The results open the way for the observation of theoretically predicted new and exotic collective phases, the realization of interacting dipolar lattices in semiconductor systems as well as for engineering and sensing their collective excitations., Comment: 11 Pages, 9 Figures

We measure the spin-resolved transport of dipolar excitons in a biased GaAs double quantum well structure. From these measurements we extract both spin lifetime and mobility of the excitons. We find that below a temperature of $4.8$K, there is a sharp increase in the spin lifetime of the excitons, together with a sharp reduction in their mobility. Below a critical power the spin lifetime increases with increasing mobility and density, while above the critical power the opposite trend is observed. We interpret this transition as an evidence of the interplay between two different spin dephasing mechanisms: at low mobility the dephasing is dominated by the hyperfine interaction with the lattice nuclei spins, while at higher mobility the spin-orbit interaction dominates, and a Dyakonov-Perel spin relaxation takes over. The excitation power and temperature regime where the hyperfine interaction induced spin dephasing is observed correlates with the regime where a dark dipolar quantum liquid was reported recently on a similar sample.

Spatially indirect excitons in semiconducting double quantum wells have been shown to exhibit rich collective many-body behavior that result from the nature of the extended dipole-dipole interactions between particles. For many spectroscopic studies of the emission from a system of such indirect excitons, it is crucial to separate the single particle properties of the excitons from the many-body effects arising from their mutual interactions. In particular, knowledge of the relation between the emission energy of indirect excitons and their radiative lifetime could be highly beneficial for control, manipulation, and analysis of such systems. Here we study a simple analytic approximate relation between the radiative lifetime of indirect excitons and their emission energy. We show, both numerically and experimentally, the validity and the limits of this approximate relation. This relation between the emission energy and the lifetime of indirect excitons can be used to tune and determine their lifetime and their resulting dynamics without the need of directly measuring it, and as a tool for design of indirect exciton based devices., Comment: * Added references. * Corrected the Al content mentioned as the sample's and used in Sec. II

We demonstrate condensation of microcavity polaritons with a very sharp threshold occuring at two orders of magnitude lower pump intensity than previous demonstrations of condensation. The long cavity-lifetime and trapping and pumping geometries are crucial to the realization of this low threshold. Polariton condensation, or "polariton lasing" has long been proposed as a promising source of coherent light at lower threshold than traditional lasing, and these results suggest methods to bring this threshold even lower., Comment: 4 pages, one figure, one table

Exciton-polaritons in semiconductor microcavities have been used to demonstrate quantum effects such as Bose-Einstein condensation, superfluity, and quantized vortices. However, in these experiments, the polaritons have not reached thermal equilibrium when they undergo the transition to a coherent state. This has prevented the verification of one of the canonical predictions for condensation, namely the phase diagram. In this work, we have created a polariton gas in a semiconductor microcavity in which the quasiparticles have a lifetime much longer than their thermalization time. This allows them to reach thermal equilibrium in a laser-generated confining trap. Their energy distributions are well fit by equilibrium Bose-Einstein distributions over a broad range of densities and temperatures from very low densities all the way up to the threshold for Bose-Einstein condensation. The good fits of the Bose-Einstein distribution over a broad range of density and temperature imply that the particles obey the predicted power law for the phase boundary of Bose-Einstein condensation.

Exciton-polaritons in a microcavity are composite two-dimensional bosonic quasiparticles, arising from the strong coupling between confined light modes in a resonant planar optical cavity and excitonic transitions, typically using excitons in semiconductor quantum wells (QWs) placed at the antinodes of the same cavity. Quantum phenomena such as Bose-Einstein condensation (BEC), quantized vortices, and macroscopic quantum states have been reported at temperatures from tens of Kelvin up to room temperatures, and polaritonic devices such as spin switches \cite{Amo2010} and optical transistors have also been reported. Many of these effects of exciton-polaritons depend crucially on the polariton-polariton interaction strength. Despite the importance of this parameter, it has been difficult to make an accurate experimental measurement, mostly because of the difficulty of determining the absolute densities of polaritons and bare excitons. Here we report the direct measurement of the polariton-polariton interaction strength in a very high-Q microcavity structure. By allowing polaritons to propagate over 40 $\mu$m to the center of a laser-generated annular trap, we are able to separate the polariton-polariton interactions from polariton-exciton interactions. The interaction strength is deduced from the energy renormalization of the polariton dispersion as the polariton density is increased, using the polariton condensation as a benchmark for the density. We find that the interaction strength is about two orders of magnitude larger than previous theoretical estimates, putting polaritons squarely into the strongly-interacting regime. When there is a condensate, we see a sharp transition to a different dependence of the renormalization on the density, which is evidence of many-body effects., Comment: 27 pages, 14 figures

The possible phases and the nano-scale particle correlations of two-dimensional interacting dipolar particles is a long-sought problem in many-body physics. Here we observe a spontaneous condensation of trapped two-dimensional dipolar excitons with internal spin degrees of freedom from an interacting gas into a high density, closely packed liquid state made mostly of dark dipoles. Another phase transition, into a bright, highly repulsive plasma is observed at even higher excitation powers. The dark liquid state is formed below a critical temperature $T_c \approx 4.8K$, and it is manifested by a clear spontaneous spatial condensation to a smaller and denser cloud, suggesting an attractive part to the interaction which goes beyond the purely repulsive dipole-dipole forces. Contributions from quantum mechanical fluctuations are expected to be significant in this strongly correlated, long living dark liquid. This is a new example of a two-dimensional atomic-like interacting dipolar quantum liquid, but where the coupling of light to its internal spin degrees of freedom plays a crucial role in the dynamical formation and the nature of resulting ground state., Comment: Supplementary information follows the references section

In this paper we show experimental evidence of a few correlation regimes of a cold dipolar exciton fluid, created optically in a semiconductor bilayer heterostructure. In the higher temperature regime, the average interaction energy between the particles shows a surprising temperature dependence which is an evidence for correlations beyond the mean field model. At a lower temperature, there is a sharp increase in the interaction energy of optically active excitons, accompanied by a strong reduction in their apparent population. This is an evidence for a sharp macroscopic transition to a dark state as was suggested theoretically.

We report new results of Bose-Einstein condensation of polaritons in specially designed microcavities with very high quality factor, on the order of $10^6$, giving the polariton lifetimes of the order of 100 ps. When the polaritons are created with an incoherent pump, a dissipationless, coherent flow of the polaritons occurs over hundreds of microns, which increases as density increases. At high density, this flow is suddenly stopped, and the gas becomes trapped in a local potential minimum, with strong coherence., Comment: 4 figures. Physical Review X (2013)