Phase transitions to quantum condensed phases--such as Bose-Einstein condensation (BEC), superfluidity, and superconductivity--have long fascinated scientists, as they bring pure quantum effects to a macroscopic scale. BEC has, for example, famously been demonstrated in dilute atom gas of rubidium atoms at temperatures below 200 nanokelvin. Much effort has been devoted to finding a solid-state system in which BEC can take place. Promising candidate systems are semiconductor microcavities, in which photons are confined and strongly coupled to electronic excitations, leading to the creation of exciton polaritons. These bosonic quasi-particles are 10(9) times lighter than rubidium atoms, thus theoretically permitting BEC to occur at standard cryogenic temperatures. Here we detail a comprehensive set of experiments giving compelling evidence for BEC of polaritons. Above a critical density, we observe massive occupation of the ground state developing from a polariton gas at thermal equilibrium at 19 K, an increase of temporal coherence, and the build-up of long-range spatial coherence and linear polarization, all of which indicate the spontaneous onset of a macroscopic quantum phase.

One of the most striking quantum effects in an interacting Bose gas at low temperature is superfluidity. First observed in liquid 4 He, this phenomenon has been intensively studied in a variety of systems for its remarkable features such as the persistence of superflows and the proliferation of quantized vortices 1 . The achievement of Bose-Einstein condensation in dilute atomic gases 2 provided the opportunity to observe and study superfluidity in an extremely clean and well-controlled environment. In the solid state, Bose-Einstein condensation of exciton polaritons has been reported recently 3-6 . Polaritons are strongly interacting light-matter quasiparticles that occur naturally in semiconductor microcavities in the strong-coupling regime and constitute an interesting example of composite bosons. Here, we report the observation of spontaneous formation of pinned quantized vortices in the Bose-condensed phase of a polariton fluid. Theoretical insight into the possible origin of such vortices is presented in terms of a generalized Gross-Pitaevskii equation. Whereas the observation of quantized vortices is, in itself, not sufficient for establishing the superfluid nature of the non-equilibrium polariton condensate, it suggests parallels between our system and conventional superfluids.Vortices in superfluids carry quantized phase winding and circulation of the superfluid particles around their core. By definition, vortices are characterized by (1) a rotation of the phase around the vortex by an integer multiple of 2π, commonly known as the topological charge of the vortex and (2) the vanishing of the superfluid population at their core. Owing to their major importance for the understanding of superfluidity, they have been intensively studied theoretically 7 and experimentally 8-10 in disorder-free, stirred three-dimensional Bose-Einstein condensates (BECs) of dilute atomic gases and in quasi-two-dimensional BECs where they spontaneously emerge from thermal fluctuations 11,12 and are strictly related to the Berezinskii-Kosterlitz-Thouless phase transition [13][14][15] . Here, we observed the spontaneous appearance of pinned singly quantized vortices as an intrinsic feature of non-equilibrium polariton BECs in the presence of disorder. The same planar CdTe microcavity sample was used as in our previous studies 3, 16,17 . The polariton condensate was created by means of non-resonant continuous-wave optical excitation, the intensity of which is used to drive the polaritons throughout the phase transition, as demonstrated by the condensate emission energy being located close to the bottom of the polariton dispersion. The condensate steady state is determined by a dynamical balance between the incoming and the outgoing flow of polaritons: in contrast to atomic BECs, the polariton condensate is in an intrinsically non-equilibrium condition. From this point of view, it is therefore closer to a laser, but fundamental differences are still to be noted with respect to a standard photon laser: the bosonic particles under in...

Cavity polaritons, the elementary optical excitations of semiconductor microcavities, may be understood as a superposition of excitons and cavity photons. Owing to their composite nature, these bosonic particles have a distinct optical response, at the same time very fast and highly nonlinear. Very efficient light amplification due to polariton-polariton parametric scattering has recently been reported in semiconductor microcavities at liquid-helium temperatures. Here we demonstrate polariton parametric amplification up to 120 K in GaAlAs-based microcavities and up to 220 K in CdTe-based microcavities. We show that the cut-off temperature for the amplification is ultimately determined by the binding energy of the exciton. A 5-micrometer-thick planar microcavity can amplify a weak light pulse more than 5,000 times. The effective gain coefficient of an equivalent homogeneous medium would be 107 cm-1. The subpicosecond duration and high efficiency of the amplification could be exploited for high-repetition all-optical microscopic switches and amplifiers. 105 polaritons occupy the same quantum state during the amplification, realizing a dynamical condensate of strongly interacting bosons which can be studied at high temperature.

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Singly quantized vortices have already been observed in many systems, including the superfluid helium, Bose-Einstein condensates of dilute atomic gases, and condensates of exciton-polaritons in the solid state. Two-dimensional superfluids carrying spin are expected to demonstrate a different type of elementary excitations referred to as half-quantum vortices, characterized by a p rotation of the phase and a p rotation of the polarization vector when circumventing the vortex core. We detect half-quantum vortices in an exciton-polariton condensate by means of polarization-resolved interferometry, real-space spectroscopy, and phase imaging. Half-quantum vortices coexist with single-quantum vortices in our sample.

We report on the observation of spontaneous coherent oscillations in a microcavity polariton bosonic Josephson junction. Condensation of exciton polaritons here takes place under incoherent excitation in a double potential well naturally formed in the disorder. Coherent oscillations set on at an excitation power well above the condensation threshold. The time resolved population and phase dynamics reveal the analogy with the ac Josephson effect. A theoretical two-mode model describes the observed effects, explaining how the different realizations of the pulsed experiment can be in phase.

The fundamental mechanisms which control the phase coherence of the polariton Bose-Einstein condensate (BEC) are determined. It is shown that the combination of number fluctuations and interactions leads to decoherence with a characteristic Gaussian decay of the first-order correlation function. This line shape, and the long decay times ( approximately 150 ps) of both first- and second-order correlation functions, are explained quantitatively by a quantum-optical model which takes into account interactions, fluctuations, and gain and loss in the system. Interaction limited coherence times of this type have been predicted for atomic BECs, but are yet to be observed experimentally.

We measure the polariton distribution function and the condensation threshold versus the photon-exciton detuning and the lattice temperature in a CdTe microcavity under nonresonant pumping. The results are reproduced by simulations using semiclassical Boltzmann equations. At negative detuning we find a kinetic condensation regime: the distribution is not thermal and the threshold is governed by the relaxation kinetics. At positive detuning, the distribution becomes thermal and the threshold is governed by the thermodynamic parameters of the system. Both regimes are a manifestation of polariton lasing, whereas only the latter is related to Bose-Einstein condensation defined as an equilibrium phase transition.