Quantum Dynamics of Polariton Condensates

Abstract

We illustrate the rich and fundamental physics that is accessible with the semiconductor implementation of the quantum superposition of light and matter: exciton–polaritons. The short lifetime of polaritons makes them an out-of-equilibrium system. Their dynamic is an important ingredient in their behaviour and properties. Their peculiar dispersion also allows a rich engineering of various processes, tuning the system from light- to matter-like. Finally, the exciton–exciton interaction turns them into a non-linear system. The interplay of all these factors makes polaritons one of today’s most versatile and fruitful research arena, both theoretically and experimentally. In this chapter we give a rather general picture of these specificities that we isolate in various dimensionalities (0, 1, and 2D). One of the most intensively researched area in the semiconductor implementation of the polariton physics is related to Bose–Einstein condensation. We solve exactly a configuration of relaxation from the Rayleigh circle into the ground state in the framework of quantum Boltzmann master equations and show how coherence builds up spontaneously in the system, by copying in a single quantum state statistical features characteristic of the macroscopic system. In this way, we extend to higher order correlations the historical reasoning of Einstein, who predicted the phenomenon by arguments on the mean populations. We show how lifetime and pumping allow a simpler treatment by reducing the required number of states, for which we present a full quantum treatment. We contrast this condensate build-up with the 0D case where the reduced complexity allows an exact numerical treatment. The coherence build-up in this cavity QED limit manifests as lasing with a sharp line in the cavity mode that produces a variation of the Mollow triplet in the exciton emission, as the cavity effectively replaces the laser in the conventional resonance fluorescence scenario. We show how lasing also arises in this case as a condensation of polaritons, and can be substituted in the case of vanishing intensities by a coherent field formed when strong coupling is optimum. This zero-dimensional limit also provides an exact picture of the transition from the quantum to the classical regime, a universal process of unsuspected complexity. Finally, we illustrate the recent development of polariton quantum hydrodynamics with propagation of coherent wave packets. The short lifetime allows a continuous observation of this dynamics in real space, a picture completed with the observation of their emission spectra in energy–momentum space. The peculiar polariton dispersion is the source of interesting behaviours even when described by the most fundamental and simplest equation of quantum physics: the Schrodinger equation.