Fabrice P. Laussy

Polariton laser and polariton superfluidity in microcavities

Abstract Excitons coupled to light in microcavities form exciton–polaritons (polaritons) having very light effective masses. These 2-dimensional quasiparticles exhibit local condensation or Kosterlitz–Thouless phase transition towards superfluidity, allowing for polariton lasing at temperatures that could be higher than 300xa0K. Polariton lasers are devices producing monochromatic and coherent light spontaneously emitted by Bose-condensed exciton–polaritons. They do not require inversion of population and, theoretically, have no threshold. We show great advantages of cavity polaritons with respect to excitons to achieve bosonic phase transition. We review experimental and theoretical activity that has been developed in this research field since the discovery of strong exciton-light coupling in microcavities 10 years ago. We present basic thermodynamic properties of polariton systems modeled as a weakly interacting Bose gas at equilibrium. We present an analysis of the relaxation kinetics of cavity polaritons in the framework of a semiclassical Boltzmann equation. The main obstacle that prevents polariton condensation is their finite lifetime: polaritons disappear before they have time to condense. We discuss the ways to improve their relaxation kinetics in real structures.

Polariton laser: thermodynamics and quantum kinetic theory

Cavity exciton–polaritons are considered to be two-dimensional weakly interacting true bosons. We analyse their thermodynamic properties and show that they can exhibit local condensation or Kosterlitz–Thouless phase transition towards superfluidity, so that polariton lasing can be achieved. The dynamical evolution of the condensate in a non-resonantly pumped cavity is described by a quantum kinetic formalism. The distribution function of polaritons is described by a semi-classical Boltzmann equation. A master equation for the ground-state density matrix is derived in the framework of the Born–Markov approximation. The dynamics of the ground-state population and its coherence are deduced.

Effects of Bose-Einstein condensation of exciton polaritons in microcavities on the polarization of emitted light

It is shown theoretically that Bose condensation of spin-degenerated exciton-polaritons results in spontaneous buildup of the linear polarization in emission spectra of semiconductor microcavities. The linear polarization degree is a good order parameter for the polariton Bose condensation. If spin-degeneracy is lifted, an elliptically polarized light is emitted by the polariton condensate. The main axis of the ellipse rotates in time due to self-induced Larmor precession of the polariton condensate pseudospin. The polarization decay time is governed by the dephasing induced by the polariton-polariton interaction and strongly depends on the statistics of the condensed state.

Real-space collapse of a polariton condensate

Microcavity polaritons are two-dimensional bosonic fluids with strong nonlinearities, composed of coupled photonic and electronic excitations. In their condensed form, they display quantum hydrodynamic features similar to atomic Bose–Einstein condensates, such as long-range coherence, superfluidity and quantized vorticity. Here we report the unique phenomenology that is observed when a pulse of light impacts the polariton vacuum: the fluid which is suddenly created does not splash but instead coheres into a very bright spot. The real-space collapse into a sharp peak is at odd with the repulsive interactions of polaritons and their positive mass, suggesting that an unconventional mechanism is at play. Our modelling devises a possible explanation in the self-trapping due to a local heating of the crystal lattice, that can be described as a collective polaron formed by a polariton condensate. These observations hint at the polariton fluid dynamics in conditions of extreme intensities and ultrafast times.

9 – Luminescence spectra of quantum dots in microcavities

: nThe physics of strong light-matter coupling of a quantum dot in a microcavity is described at its most fundamental level, that of the Jaynes–Cummings Hamiltonian. Dissipation, dephasing and incoherent excitation are included in the Lindblad form to account for the most important experimental degrees of freedom. We focus on the photoluminescence emission and elucidate the complexity that can arise from the delicate interplay of pumping and decay. A unified picture is presented of several regimes of excitation describing spontaneous emission, quantum nonlinearities and lasing. The theoretical findings are fully supported by experimental observations when systems with sufficiently high figures of merit are within reach.

Statistics of excitons in quantum dots and their effect on the optical emission spectra of microcavities

F. P. Laussy, ∗ M. M. Glazov, A. V. Kavokin, D. M. Whittaker, and G. Malpuech University of Sheffield, Department of Physics and Astronomy, Sheffield, S3 7RH, United Kingdom A. F. Ioffe Physico-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia University of Southampton, Physics and Astronomy School, Southampton, SO17 1BJ, United Kingdom LASMEA, Université Blaise Pascal, 24, av. des Landais, 63 177 Aubière, France

Coherence dynamics in microcavities and polariton lasers

We study theoretically the second-order coherence g(2)(0) of light emitted by polariton lasers, i.e., devices based on stimulated relaxation and condensation of exciton–polaritons in microcavities. We solve kinetic equations for the polaritons in different approximations and show that (i) the coherence introduced into the polariton condensate by an external source can be conserved by the system over a macroscopically long time, and (ii) if the total number of polaritons is fixed by the excitation conditions, the correlations between the populations of the ground and excited polariton states can also result in the spontaneous buildup of second-order coherence in the polariton condensate. Both results are obtained neglecting polariton–polariton interactions in the condensate.

The colored Hanbury Brown-Twiss effect

The Hanbury Brown–Twiss effect is one of the celebrated phenomenologies of modern physics that accommodates equally well classical (interferences of waves) and quantum (correlations between indistinguishable particles) interpretations. The effect was discovered in the late thirties with a basic observation of Hanbury Brown that radio-pulses from two distinct antennas generate signals on the oscilloscope that wiggle similarly to the naked eye. When Hanbury Brown and his mathematician colleague Twiss took the obvious step to propose bringing the effect in the optical range, they met with considerable opposition as single-photon interferences were deemed impossible. The Hanbury Brown–Twiss effect is nowadays universally accepted and, being so fundamental, embodies many subtleties of our understanding of the wave/particle dual nature of light. Thanks to a novel experimental technique, we report here a generalized version of the Hanbury Brown–Twiss effect to include the frequency of the detected light, or, from the particle point of view, the energy of the detected photons. Our source of light is a polariton condensate, that allows high-resolution filtering of a spectrally broad source with a high degree of coherence. In addition to the known tendencies of indistinguishable photons to arrive together on the detector, we find that photons of different colors present the opposite characteristic of avoiding each others. We postulate that fermions can be similarly brought to exhibit positive (boson-like) correlations by frequency filtering.

Multiplets in the optical emission spectra of large quantum dots in microcavities

We show theoretically that the emission spectrum of a single large quantum dot strongly coupled to a single photon mode in a microcavity can be qualitatively different from the spectrum obtained with an atom in a cavity. Instead of the well-known Mollow triplet we predict appearance of multiplets with the number of peaks a function of the quantum dot size and pumping intensity. The mutiplets can appear if the quantum dot is larger than the exciton Bohr radius, so that excitons are confined as whole particles in the dot. In this case, the Pauli principle is relaxed and one can accommodate more than one exciton (but still a finite number) in a given quantum state.

Dephasing of strong coupling in the non‐linear regime

We study the effect of pure dephasing on the strong‐coupling of a two‐level system (typically, a quantum dot) with the single mode of a microcavity. Whereas dephasing merely broadens the line in the linear regime, it results in a new spectral shape when transitions between higher manifolds of the Jaynes‐Cummings ladder are involved, namely, a triplet, that we show does not imply weak‐coupling. Higher excitation brings the system into lasing. Description of this intermediate triplet allows to demonstrate quantum nonlinearities even in noisy systems and to measure the magnitude of dephasing.