Polariton Bose-Einstein condensate from a bound state in the continuum.

Bound states in the continuum (BICs)1-3 are peculiar topological states that, when realized in a planar photonic crystal lattice, are symmetry-protected from radiating in the far field despite lying within the light cone4. These BICs possess an invariant topological charge given by the winding number of the polarization vectors5, similar to vortices in quantum fluids such as superfluid helium and atomic Bose-Einstein condensates. In spite of several reports of optical BICs in patterned dielectric slabs with evidence of lasing, their potential as topologically protected states with theoretically infinite lifetime has not yet been fully exploited. Here we show non-equilibrium Bose-Einstein condensation of polaritons-hybrid light-matter excitations-occurring in a BIC thanks to its peculiar non-radiative nature, which favours polariton accumulation. The combination of the ultralong BIC lifetime and the tight confinement of the waveguide geometry enables the achievement of an extremely low threshold density for condensation, which is reached not in the dispersion minimum but at a saddle point in reciprocal space. By bridging bosonic condensation and symmetry-protected radiation eigenmodes, we reveal ways of imparting topological properties onto macroscopic quantum states with unexplored dispersion features. Such an observation may open a route towards energy-efficient polariton condensation in cost-effective integrated devices, ultimately suited for the development of hybrid light-matter optical circuits.

Measurement of the quantum geometric tensor and of the anomalous Hall drift.

Topological physics relies on the structure of the eigenstates of the Hamiltonians. The geometry of the eigenstates is encoded in the quantum geometric tensor1-comprising the Berry curvature2 (crucial for topological matter)3 and the quantum metric4, which defines the distance between the eigenstates. Knowledge of the quantum metric is essential for understanding many phenomena, such as superfluidity in flat bands5, orbital magnetic susceptibility6,7, the exciton Lamb shift8 and the non-adiabatic anomalous Hall effect6,9. However, the quantum geometry of energy bands has not been measured. Here we report the direct measurement of both the Berry curvature and the quantum metric in a two-dimensional continuous medium-a high-finesse planar microcavity10-together with the related anomalous Hall drift. The microcavity hosts strongly coupled exciton-photon modes (exciton polaritons) that are subject to photonic spin-orbit coupling11 from which Dirac cones emerge12, and to exciton Zeeman splitting, breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured using polarization-resolved photoluminescence. The associated quantum geometry of the bands is extracted, enabling prediction of the anomalous Hall drift, which we measure independently using high-resolution spatially resolved epifluorescence. Our results unveil the intrinsic chirality of photonic modes, the cornerstone of topological photonics13-15. These results also experimentally validate the semiclassical description of wavepacket motion in geometrically non-trivial bands9,16. The use of exciton polaritons (interacting photons) opens up possibilities for future studies of quantum fluid physics in topological systems.

Polariton Condensation in Gap-Confined States of Photonic Crystal Waveguides.

The development of patterned multiquantum well heterostructures in GaAs/AlGaAs waveguides has recently made it possible to achieve exciton-polariton condensation in a topologically protected bound state in the continuum (BIC). Polariton condensation was shown to occur above a saddle point of the two-dimensional polariton dispersion in a one-dimensional photonic crystal waveguide. A rigorous analysis of the condensation phenomenon in these systems, as well as the role of the BIC, is still missing. In the present Letter, we theoretically and experimentally fill this gap by showing that polariton confinement resulting from the negative effective mass and the photonic energy gap in the dispersion play a key role in enhancing the relaxation toward the condensed state. In fact, our results show that low-threshold polariton condensation is achieved within the effective trap created by the exciting laser spot, regardless of whether the resulting confined mode is long-lived (polariton BIC) or short-lived (lossy mode). In both cases, the spatial quantization of the polariton condensate and the threshold differences associated to the corresponding state lifetime are measured and characterized. For a given negative mass, a slightly lower condensation threshold from the polariton BIC mode is found and associated to its reduced radiative losses, as compared to the lossy one.

Enhancement of Parametric Effects in Polariton Waveguides Induced by Dipolar Interactions.

Exciton-polaritons are hybrid light-matter excitations arising from the nonperturbative coupling of a photonic mode and an excitonic resonance. Behaving as interacting photons, they show optical third-order nonlinearities providing effects such as optical parametric oscillation or amplification. It has been suggested that polariton-polariton interactions can be greatly enhanced by inducing aligned electric dipoles in their excitonic part. However, direct evidence of a true particle-particle interaction, such as superfluidity or parametric scattering, is still missing. In this Letter, we demonstrate that dipolar interactions can be used to enhance parametric effects such as self-phase modulation in waveguide polaritons. By quantifying these optical nonlinearities, we provide a reliable experimental measurement of the direct dipolar enhancement of polariton-polariton interactions.

Exciting Polaritons with Quantum Light.

We discuss the excitation of polaritons-strongly coupled states of light and matter-by quantum light, instead of the usual laser or thermal excitation. As one illustration of the new horizons thus opened, we introduce "Mollow spectroscopy"-a theoretical concept for a spectroscopic technique that consists of scanning the output of resonance fluorescence onto an optical target-from which weak nonlinearities can be read with high precision even in strongly dissipative environments.

Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons.

We report an experimental study of superfluid hydrodynamic effects in a one-dimensional polariton fluid flowing along a laterally patterned semiconductor microcavity and hitting a micron-sized engineered defect. At high excitation power, superfluid propagation effects are observed in the polariton dynamics; in particular, a sharp acoustic horizon is formed at the defect position, separating regions of sub- and supersonic flow. Our experimental findings are quantitatively reproduced by theoretical calculations based on a generalized Gross-Pitaevskii equation. Promising perspectives to observe Hawking radiation via photon correlation measurements are illustrated.

Collective fluid dynamics of a polariton condensate in a semiconductor microcavity.

Semiconductor microcavities offer unique systems in which to investigate the physics of weakly interacting bosons. Their elementary excitations, polaritons-mixtures of excitons and photons-can accumulate in macroscopically degenerate states to form various types of condensate in a wide range of experimental configurations, under either incoherent or coherent excitation. Condensates of polaritons have been put forward as candidates for superfluidity, and the formation of vortices as well as elementary excitations with linear dispersion are actively sought as evidence to support this. Here, using a coherent excitation triggered by a short optical pulse, we have created and set in motion a macroscopically degenerate state of polaritons that can be made to collide with a variety of defects present in the microcavity. Our experiments show striking manifestations of a coherent light-matter packet, travelling at high speed (of the order of one per cent of the speed of light) and displaying collective dynamics consistent with superfluidity, although one of a highly unusual character as it involves an out-of-equilibrium dissipative system. Our main results are the observation of a linear polariton dispersion accompanied by diffusionless motion; flow without resistance when crossing an obstacle; suppression of Rayleigh scattering; and splitting into two fluids when the size of the obstacle is comparable to the size of the wave packet. This work opens the way to the investigation of new phenomenology of out-of-equilibrium condensates.

Ultrafast Control and Rabi Oscillations of Polaritons.

We report the experimental observation and control of space and time-resolved light-matter Rabi oscillations in a microcavity. Our setup precision and the system coherence are so high that coherent control can be implemented with amplification or switching off of the oscillations and even erasing of the polariton density by optical pulses. The data are reproduced by a quantum optical model with excellent accuracy, providing new insights on the key components that rule the polariton dynamics.

Build up of off-diagonal long-range order in microcavity exciton-polaritons across the parametric threshold.

We report an experimental study of the spontaneous spatial and temporal coherence of polariton condensates generated in the optical parametric oscillator configuration, below and at the parametric threshold, and as a function of condensate area. Above the threshold we obtain very long coherence times (up to 3 ns) and a spatial coherence extending over the entire condensate (40 µm). The very long coherence time and its dependence on condensate area and pump power reflect the suppression of polariton-polariton interactions by an effect equivalent to motional narrowing.

Frictionless flow in a binary polariton superfluid.

We study the properties of a binary microcavity polariton superfluid coherently injected by two lasers at different momenta and energies. The crossover from the supersonic to the subsonic regime, where motion is frictionless, is described by evaluating the linear response of the system to a weak defect potential. We show that the coupling between the two components requires that either both components flow without friction or both scatter against the defect, though scattering can be small when the two fluids are weakly coupled. By analyzing the drag force exerted on a defect, we give a recipe to experimentally address the crossover from the supersonic to the subsonic regime.

Propagation and amplification dynamics of 1D polariton condensates.

The dynamics of propagating polariton condensates in one-dimensional microcavities is investigated through time resolved experiments. We find a strong increase in the condensate intensity when it travels through the nonresonantly excited area. This amplification is shown to come from bosonic stimulated relaxation of reservoir excitons into the polariton condensate, allowing for the repopulation of the condensate through nonresonant pumping. Thus, we experimentally demonstrate a polariton amplifier with a large band width, opening the way towards the transport of polaritons with high densities over macroscopic distances.

Control and ultrafast dynamics of a two-fluid polariton switch.

We investigate the cross interactions in a two-component polariton quantum fluid coherently driven by two independent pumping lasers tuned at different energies and momenta. We show that both the hysteresis cycles and the on-off threshold of one polariton signal can be entirely controlled by a second polariton fluid. Furthermore, we study the ultrafast switching dynamics of a driven polariton state, demonstrating the ability to control the polariton population with an external laser pulse, in less than a few picoseconds.

Onset and dynamics of vortex-antivortex pairs in polariton optical parametric oscillator superfluids.

We study, both theoretically and experimentally, the occurrence of topological defects in polariton superfluids in the optical parametric oscillator (OPO) regime. We explain in terms of local supercurrents the deterministic behavior of both the onset and dynamics of vortex-antivortex pairs generated by perturbing the system with a pulsed probe. Using a generalized Gross-Pitaevskii equation, including photonic disorder, pumping and decay, we elucidate the reason why topological defects form in couples and can be detected by direct visualizations in multishot OPO experiments.

Motion of spin polariton bullets in semiconductor microcavities.

The dynamics of optical switching in semiconductor microcavities in the strong coupling regime is studied by using time- and spatially resolved spectroscopy. The switching is triggered by polarized short pulses which create spin bullets of high polariton density. The spin packets travel with speeds of the order of 10(6) m/s due to the ballistic propagation and drift of exciton polaritons from high to low density areas. The speed is controlled by the angle of incidence of the excitation beams, which changes the polariton group velocity.

Effect of pure dephasing on the Jaynes-Cummings nonlinearities.

We study the effect of pure dephasing on a two-level system in strong coupling in the nonlinear regime with the single mode of a cavity. The photoluminescence spectrum of the cavity has a robust tendency to display triplet structures, instead of the expected Jaynes-Cummings pairs of doublets at the incommensurate frequencies +/- (square root n +/- square root (n-1)) for integer n. We discuss recent experimental works that may already manifest signatures of single photon nonlinearities.

Propagating wave packets and quantized currents in coherently driven polariton superfluids.

We study the properties of propagating polariton wave packets and their connection to the stability of doubly charged vortices. Wave-packet propagation and related photoluminescence spectra exhibit a rich behavior dependent on the excitation regime. We show that, because of the nonquadratic polariton dispersion, doubly charged vortices are stable only when initiated in wave packets propagating at small velocities. Vortices propagating at larger velocities, or those imprinted directly into the polariton optical parametric oscillator signal and idler, are unstable to splitting.

Effect of interactions on vortices in a nonequilibrium polariton condensate.

We demonstrate the creation of vortices in a macroscopically occupied polariton state formed in a semiconductor microcavity. A weak external laser beam carrying orbital angular momentum (OAM) is used to imprint a vortex on the condensate arising from the polariton optical parametric oscillator (OPO). The vortex core radius is found to decrease with increasing pump power, and is determined by polariton-polariton interactions. As a result of OAM conservation in the parametric scattering process, the excitation consists of a vortex in the signal and a corresponding antivortex in the idler of the OPO. The experimental results are in good agreement with a theoretical model of a vortex in the polariton OPO.

Polariton condensates put in motion.

We present several examples of the interesting phenomenology shown by a moving polariton condensate in semiconductor microcavities. The superfluid behavior is probed by colliding the polariton condensate against physical obstacles in the form of natural defects of the sample, demonstrating a clear suppression of scattering when the speed of the flow lies below the critical velocity. At higher velocities Cerenkov-like shock waves around the defect and disruption of the condensate are also observed.

Observation of charge transport by negatively charged excitons.

We report transport of electron-hole complexes in semiconductor quantum wells under applied electric fields. Negatively charged excitons (X-), created by laser excitation of a high electron mobility transistor, are observed to drift upon applying a voltage between the source and drain. In contrast, neutral excitons do not drift under similar conditions. The X- mobility is found to be as high as 6.5 x 10(4) cm2 V-1 s-1. The results demonstrate that X- exists as a free particle in the best-quality samples and suggest that light emission from opto-electronic devices can be manipulated through exciton drift under applied electric fields.