We report new results of Bose-Einstein condensation of polaritons in specially designed microcavities with a very high quality factor, on the order of 10 6 , giving 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.

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) [1, 2], superfluidity [3], quantized vortices [4][5][6][7][8], and macroscopic quantum states [9, 10] have been realized at temperatures from tens of Kelvin up to room temperatures [11][12][13], and polaritonic devices such as spin switches [14] and optical transistors [15] 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 µm to the center of a lasergenerated 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.Much of the physics of polaritons is dominated by the fact that they have extremely light effective mass. When an exciton is mixed with a cavity photon to become an excitonpolariton, it has an effective mass about four orders of magnitude less than a vacuum electron, and about three orders of magnitude less than a typical semiconductor quantum well exciton. (The Supplementary Information gives a basic introduction to the properties of exciton-polaritons.) Therefore one can view the polaritons as excitons which are given much longer diffusion length, with propagation distance of polaritons up to millimeters [16,17]; this may have implications for solar cells, which depend crucially on the diffusive 2 migration of excitons [18]. Alternatively, exciton-polaritons can be viewed as photons with nonlinear interactions many orders of magnitude higher than in typical optical materials, due to their excitonic components [19]. The light effective mass of the polaritons (typically 10 −8 that of a hydrogen atom) allows for quantum phenomena to be realized at much higher temperatures than in cold atomic gases.Interactions among polaritons. The interaction of exciton-polaritons is presumed to come...

The experimental realization of Bose-Einstein condensation (BEC) with atoms and quasiparticles has triggered wide exploration of macroscopic quantum effects. Microcavity polaritons are of particular interest because quantum phenomena such as BEC and superfluidity can be observed at elevated temperatures. However, polariton lifetimes are typically too short to permit thermal equilibration. This has led to debate about whether polariton condensation is intrinsically a nonequilibrium effect. Here we report the first unambiguous observation of BEC of optically trapped polaritons in thermal equilibrium in a high-Q microcavity, evidenced by equilibrium Bose-Einstein distributions over broad ranges of polariton densities and bath temperatures. With thermal equilibrium established, we verify that polariton condensation is a phase transition with a well-defined density-temperature phase diagram. The measured phase boundary agrees well with the predictions of basic quantum gas theory. DOI: 10.1103/PhysRevLett.118.016602 The realization of exciton-polariton condensation in semiconductor microcavities from liquid-helium temperature [1,2] all the way up to room temperature [3][4][5] presents great opportunities both for fundamental studies of many-body physics and for all-optical devices on the technology side. Polaritons in a semiconductor microcavity are admixtures of the confined light modes of the cavity and excitonic transitions, typically those of excitons in semiconductor quantum wells placed at the antinodes of the cavity. Quantum effects such as condensation [1][2][3][4][5], superfluidity [6], and quantized vortices [7][8][9][10][11] have been reported. The dual light-matter nature permits flexible control of polaritons and their condensates, facilitating applications in quantum simulation. It is also straightforward to measure the spectral functions, Aðk; ωÞ, of polaritons, which can provide insights into the dynamics of many-body interactions in polariton systems. For cold atoms, the equilibrium occupation numbers can be measured [12], but the spectral function is not readily accessible. Observations of non-Hermitian physics [13] and phase frustration [14] have shown that polaritons are an important complement to atomic condensates.However, in most previous experiments, the lifetime of the polaritons in microcavities has been 30 ps or less [15] due to leakage of the microcavity. Thus, although there have been claims to partial thermalization of polaritons [16,17], no previous work has unambiguously shown a condensation in thermal equilibrium, leading to the common description of polariton condensates as "nonequilibrium condensates" [18][19][20]. The theory of nonequilibrium condensation is still an active field [21][22][23][24]. Although polariton experiments and theory have shown that a great number of canonical features of condensation persist in nonequilibrium, e.g., superfluid behavior [22,23], some aspects may not [25,26], and debates persist over whether polariton condensates can be called Bose-Einstein c...

Exciton-polaritons can be created in semiconductor microcavities. These quasiparticles act as weakly interacting bosons with very light mass, of the order of 10 −4 times the vacuum electron mass. Many experiments have shown effects which can be viewed as due to a Bose-Einstein condensate, or quasicondensate, of these particles. The lifetime of the particles in most of those experiments has been of the order of a few picoseconds, leading to significant nonequilibrium effects. By increasing the cavity quality, we have made new samples with longer polariton lifetimes. With a photon lifetime on the order of 100-200 ps, polaritons in these new structures can not only come closer to reaching true thermal equilibrium, a desired feature for many researchers working in this field, but they can also travel much longer distances. We observe the polaritons to ballistically travel on the order of one millimeter, and at higher densities we see transport of a coherent condensate, or quasicondensate, over comparable distances. In this paper we report a quantitative analysis of the flow of the polaritons both in a low-density, classical regime, and in the coherent regime at higher density. Our analysis gives us a measure of the intrinsic lifetime for photon decay from the microcavity and a measure of the strength of interactions of the polaritons.

This corrects the article DOI: 10.1103/PhysRevLett.118.016602.