Dynamics of long-range order in an exciton-polariton condensate

Long range spatial coherence lies at the heart of the remarkable quantum behaviour of matter manifested by superconductors and superfluids at the macroscopic scale. An intriguing question is how quickly the coherent field can be established when a normal incoherent gas is driven through the phase transition. Experimentally, such dynamics are not easily accessible in traditional superconductors and superflu-ids. Only recently the question of the formation of long range coherence in superfluids was addressed in experiments with ultracold atomic gases [1, 2], while the importance of this study was pointed out even before the realization of Bose Einstein condensation (BEC) [3, 4]. The demonstration of BEC in a solid state system was achieved a few years ago with exciton-polaritons [5]. Thanks to their half photonic nature, the coherence of the microcavity polaritons is directly accessible using optical techniques, which makes them ideal candidates to address the dynamics of long range order. In the present Letter, we report on time resolved measurements of the ground state population and first order spatial coherence in an exciton-polariton system. Long range spatial coherence is found to set in right at the onset of the condensate build up, on a picosecond time scale. However, in contrast to the condensate population, the coherence reaches its maximum value at later time, and stays much longer, up to a few hundreds of picoseconds. This behaviour can be qualitatively reproduced, using a stochastic classical field model describing interaction between the polariton condensate and the exciton reservoir within a disordered potential. A polariton is a quasi-particle that appears in the regime of strong coupling between a microcavity photon and a quantum well exciton. It inherits desirable properties for condensation from both components. Their excitonic content allows for the collisional relaxation, while the photonic component provides a light mass. The first experimental studies on their condensation have demonstrated the key features of exciton polariton BEC in the steady state: a massive occupation of a single quantum state and the appearance of long-range spatial coherence above a population threshold [5, 6, 7]. Further on many questions have been addressed concerning the properties of polariton BEC such as superfluity [8], the excitation spectrum [9, 10], the temporal coherence [11, 12] and the formation of quantized vortices [13]. In our study we take advantage of the half photonic nature of the exciton-polaritons as their properties are directly accessible through the near-and far-field photoluminescence [14]. …