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Bose-Fermi systems such as mixtures of electrons with excitons or exciton-polaritons are extensively discussed as candidates to host a variety of intriguing phenomena, including polaron formation, drag effects, supersolidity, and superconductivity. In this work, assuming the strong-coupling regime between the semiconductor excitons and cavity photons, we develop the many-body theory approach addressing the interplay of different types of interaction among various species in such a mixture, wherein we take into account dynamical density responses of both the Bose-condensed exciton-polaritons and the two-dimensional electron gas inside an optical microcavity. As was anticipated previously, at high enough polariton densities the lower hybrid mode of the system's excitation spectrum acquires a roton minimum, making the system prone to superconducting pairing in the vicinity of the roton instability. We analyze the possibility of polariton-BEC-mediated superconductivity in the electron gas taking into account full momentum and frequency dependence of the gap, as well as in the Eliashberg approach where the momentum dependence is neglected, and in the Bardeen-Cooper-Schrieffer approach that discards the frequency dependence and dynamical effects. Considering the interaction screening in Thomas-Fermi and in random-phase approximations, we estimate the critical temperatures of superconductivity to be not larger than 0.1 K in the vicinity of instability. As possible realizations of the coupled polariton-electron system, semiconductor quantum wells and two-dimensional transition metal dichalcogenides are considered., Comment: 19 pages, 8 figures

We develop the many-body theory of dipolar exciton-polaritons in an optical microcavity in crossed transverse electric and in-plane magnetic fields. Even for relatively weak fields, we reveal the existence of two minima in the bare lower-polariton dispersion, which give rise to the tuneable transition between the polariton Bose-Einstein condensate and that of excitons, produced by the competition between these minima. We predict that such dipolar condensate exhibits a roton-maxon character of the excitation spectrum, never before observed for polaritons. We show that upon the transition between the two condensation regimes, the weak correlations in the polariton gas give way to the intermediate interparticle correlations characteristic for excitons, and that the transition is accompanied by a sharp quenching of photoluminescence as the lifetime is increased by several orders of magnitude. While in the polariton regime, the luminescence peak corresponding to the condensate is shifted to a non-zero angle. The angular dependence of the two-photon decay time in the Hanbury Brown and Twiss experiment is calculated and used as a tool to evidence the formation of the macroscopically-coherent state. Our proposal opens opportunities towards manipulating the superfluid properties and extended-range dipole-dipole correlations of exciton-polariton condensates., Comment: 16 pages, 6 figures

Geometrical aspects underlying the cosmos and its laws have been put in emphasis since Einstein. Later on, the Berry curvature provided a powerful unifying tool among several branches of science and topology. Topological defects or quantum vortices have been under the spotlight, as quanta of rotation in condensates, superfluids, and optics. Here, we use microcavity polaritons to imprint a dynamical pseudospin texture, whose reshaping involves both the ultrafast spiraling of the vortex cores and the associated Berry curvature itself. The pseudospin topology is a double conformal mapping of the whole Bloch sphere of states, whose projection density is represented by the curvature. Any evolution of the states on the sphere is imaged to the real space plane mediated by this link. We show that polaritons represent a tailored system to study the Berry concepts and invoke a new role of the curvature in describing the vortex cores' velocity directly in real space., Comment: 11 pages, 4 figures, 2 videos

We propose a way to increase the lifetime of two-dimensional direct excitons and show the possibility to observe their macroscopically coherent state at high temperatures. For a single GaAs quantum well embedded in photonic layered heterostructures with subwavelength period, we predict the exciton radiative decay to be strongly suppressed. Quantum hydrodynamic approach is used to study the Berezinskii-Kosterlitz-Thouless crossover in a finite exciton system with intermediate densities. Below the estimated critical temperatures, drastic growth of the correlation length is shown to be accompanied by a manyfold increase of the photoluminescence intensity., Comment: 6 pages of the main text, and 5 pages of the Supplemental Material; 7 figures