A phase transition from a classical thermal mixed state to a quantum-mechanical pure state of exciton polaritons is observed in a GaAs multiple quantum-well microcavity from the decrease of the second-order coherence function. Supporting evidence is obtained from the observation of a nonlinear threshold behavior in the pump-intensity dependence of the emission, a polariton-like dispersion relation above threshold, and a decrease of the relaxation time into the lower polariton state. The condensation of microcavity exciton polaritons is confirmed.

Topology describes properties that remain unaffected by smooth distortions. Its main hallmark is the emergence of edge states localized at the boundary between regions characterized by distinct topological invariants. This feature offers new opportunities for robust trapping of light in nanoand micro-meter scale systems subject to fabrication imperfections and to environmentally induced deformations. Here we show lasing in such topological edge states of a one-dimensional lattice of polariton micropillars that implements an orbital version of the Su-Schrieffer-Heeger Hamiltonian. We further demonstrate that lasing in these states persists under local deformations of the lattice. These results open the way to the implementation of chiral lasers in systems with broken time-reversal symmetry and, when combined with polariton interactions, to the study of nonlinear topological photonics.Topological phase transitions in condensed matter have been extensively studied over the last decade. A key manifestation of these transitions is the emergence, at the frontier between materials exhibiting distinct topological phases, of localized states that are unaffected by disorder. One example of this topological protection is provided by chiral edge states at the surface of topological insulators that allow unidirectional transport immune to backscattering 1 .Initially proposed by Haldane and Raghu 2 , the idea of extending these topological arguments to the realm of photonics has recently triggered considerable efforts to engineer optical devices that are unaffected by local perturbations and fabrication defects 3 . For example, topological properties have been used to create polarizationdependent unidirectional waveguides 4 , optical delay lines with enhanced transport properties 5 , backscatteringimmune chiral edge states 6-9 , and protected bound states in parity-time-symmetric crystals 10,11 .The emergence of edge states at the boundary between materials with distinct topological invariants provides an efficient way to create localized photonic modes whose existence is protected by topology 9 . Lasing in these kind of modes would then be robust against fabrication defects, local deformations caused by temperature or other unstable ambient conditions, and long term degradation, all of which would eventually result in the modification of the local optical potential 12 . The main difficulty that has prevented the observation of lasing in topological modes is the need to implement topological lattices in media exhibiting optical gain. In this sense, microcavity polaritons, mixed quasiparticules formed from the strong coupling between cavity photons and quantum well excitons 13 , provide a unique platform: they allow for low-threshold lasing 14,15 , even at room temperature 16,17 , and the engineering of topological properties in lattices of resonators 18,19 .In this work we report lasing in topological edge states of a 1D lattice of coupled semiconductor micropillars. The lattice implements an orbital version of the Su-Schrieff...

A source of triggered entangled photon pairs is a key component in quantum information science; it is needed to implement functions such as linear quantum computation, entanglement swapping and quantum teleportation. Generation of polarization entangled photon pairs can be obtained through parametric conversion in nonlinear optical media or by making use of the radiative decay of two electron-hole pairs trapped in a semiconductor quantum dot. Today, these sources operate at a very low rate, below 0.01 photon pairs per excitation pulse, which strongly limits their applications. For systems based on parametric conversion, this low rate is intrinsically due to the Poissonian statistics of the source. Conversely, a quantum dot can emit a single pair of entangled photons with a probability near unity but suffers from a naturally very low extraction efficiency. Here we show that this drawback can be overcome by coupling an optical cavity in the form of a 'photonic molecule' to a single quantum dot. Two coupled identical pillars-the photonic molecule-were etched in a semiconductor planar microcavity, using an optical lithography method that ensures a deterministic coupling to the biexciton and exciton energy states of a pre-selected quantum dot. The Purcell effect ensures that most entangled photon pairs are emitted into two cavity modes, while improving the indistinguishability of the two optical recombination paths. A polarization entangled photon pair rate of 0.12 per excitation pulse (with a concurrence of 0.34) is collected in the first lens. Our results open the way towards the fabrication of solid state triggered sources of entangled photon pairs, with an overall (creation and collection) efficiency of 80%.

Cavity exciton-polaritons 1,2 (polaritons) are bosonic quasiparticles offering a unique solid-state system for investigating interacting condensates 3-10 . Up to now, disorder-induced localization and short lifetimes 4,6,11 have prevented the establishment of long-range off-diagonal order 12 needed for any quantum manipulation of the condensate wavefunction. In this work, using a wire microcavity with polariton lifetimes much longer than in previous samples, we show that polariton condensates can propagate over macroscopic distances outside the excitation area, while preserving their spontaneous spatial coherence. An extended condensate wavefunction builds up with a degree of spatial coherence larger than 50% over distances 50 times the polariton de Broglie wavelength. The expansion of the condensate is shown to be governed by the repulsive potential induced by photogenerated excitons within the excitation area. The control of this local potential offers a new and versatile method to manipulate extended polariton condensates. As an illustration, we demonstrate synchronization of extended condensates by controlled tunnel coupling 13,14 and localization of condensates in a trap with optically controlled dimensions.Modern semiconductor technology allows the realization of nanostructures where both electronic and photonic states undergo quantum confinement. In particular in semiconductor microcavities, excitons confined in quantum wells and photons confined in a Fabry-Perot resonator can enter the light-matter strong coupling regime. This gives rise to the formation of cavity polaritons, mixed exciton-photon states that obey bosonic statistics 2 . The polariton dispersion presents a sharp energy minimum close to the states with zero in-plane wave vector (k = 0) with an effective mass m * three orders of magnitude smaller than that of the bare quantum well exciton. Recently, polariton Bose-Einstein condensation 3-10 (BEC) and related effects such as vortices 15,16 or superfluid 17-19 behaviour have been reported at unprecedented high temperatures. As a result of their finite lifetime, cavity polaritons are a model system to investigate dynamical BEC (refs 20,21), also referred to as a polariton laser effect, with a technological control of the resonator geometry and the polariton lifetime. In previously reported polariton laser systems, the cavity lifetime and the photonic disorder prevented the build-up of extended condensates needed for the realization of polariton circuits 22,23 . The measured coherence length ranged at best from 10 to 20 µm (refs 4,6,11,24), a few times the polariton thermal de Broglie wavelength.Here, we report on the spontaneous formation of extended polariton condensates with a spatial coherence extending over 50 times the thermal de Broglie wavelength. These condensates, made of a quantum degenerated light-matter state, are strongly out of equilibrium, thus deeply differing from atomic BEC. Spatial control of such extended condensates is demonstrated, opening the way to a new range of physic...

We report on the observation of the strong-coupling regime between the excitonic transition of a single GaAs quantum dot and a discrete optical mode of a microdisk microcavity. Photoluminescence is performed at various temperatures to tune the quantum dot exciton with respect to the optical mode. At resonance, we observe a clear anticrossing behavior, signature of the strong-coupling regime. The vacuum Rabi splitting amounts to 400 microeV and is twice as large as the individual linewidths.

Below a critical temperature, a sufficiently high density of bosons undergoes Bose-Einstein condensation (BEC). Under this condition, the particles collapse into a macroscopic condensate with a common phase, showing collective quantum behaviour like superfluidity, quantised vortices, interferences, etc. Up to recently, BEC was only observed for diluted atomic gases at μK temperatures. Following the recent observations of non-equilibrium BEC in semiconductor microcavities at temperatures of ~10 K, using momentum-1 and real-space 2 trapping, the quest is now towards the observation of the superfluid motion of a polariton BEC. For the same reasons that polaritons benefit from unusually favourable features for condensation, such as very high critical temperatures, it is expected that their superfluid properties would likewise manifest with altogether different magnitudes, such as very high critical velocities. Since they have shown many deviations in their Bose-condensed phase from the cold atoms paradigm, it is not clear a priori to which extent their superfluid properties would coincide or depart from those observed with atoms, among which quantised vortices 6 , frictionless motion 7 , linear dispersion for the elementary excitations 8 , or more recently Čerenkov emission of a condensate flowing at supersonic velocities 9 , are among the clearest signatures of quantum fluid propagation.Microcavity polaritons are two-dimensional bosons of mixed electronic and photonic nature, formed by the strong coupling of excitons-confined in semiconductor quantum wells-with photons trapped in a micron scale resonant cavity. First observed in 1992 10 , these particles have been profusely studied in the last fifteen years due to their unique features. Thanks to their photon fraction, polaritons can easily be excited by an external laser source and detected by light emission in the direction perpendicular to the cavity plane. However, as opposed to photons, they experience strong interparticle interactions owing to their partially electronic fraction. Due to the deep polariton dispersion, the effective mass of these particles is 10 4 -10 5 smaller than the free electron mass, resulting in a very low density of states. This allows for a high state 3 occupancy even at relatively low excitation intensities. However, polaritons live only a few 10 -12 s in a cavity before escaping and therefore thermal equilibrium is never achieved. In this respect, a macroscopically degenerate state of polaritons departs strongly from an atomic Bose-condensed phase. The experimental observations of spectral and momentum narrowing, spatial coherence and long range order-which have been used as evidence for polariton Bose-Einstein condensation-are also present in a pure photonic laser 11 . The recent observation of long range spatial coherence 12 , vortices 4 and the loss of coherence with increasing density in the condensed phase 13,14 , are in accordance with macroscopic phenomena proper of interacting, coherent bosons 15 . But a direct manifestation ...

Two-dimensional lattices of coupled micropillars etched in a planar semiconductor microcavity offer a workbench to engineer the band structure of polaritons. We report experimental studies of honeycomb lattices where the polariton low-energy dispersion is analogous to that of electrons in graphene. Using energy-resolved photoluminescence, we directly observe Dirac cones, around which the dynamics of polaritons is described by the Dirac equation for massless particles. At higher energies, we observe p orbital bands, one of them with the nondispersive character of a flatband. The realization of this structure which holds massless, massive, and infinitely massive particles opens the route towards studies of the interplay of dispersion, interactions, and frustration in a novel and controlled environment.

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