Coexisiting Polariton Condensates and Their Temporal Coherence in Semiconductor Microcavities

In this chapter, we study macroscopically occupied condensates, which can be observed in semiconductor microcavities under conditions of resonant or non-resonant excitation. In the case of resonant excitation, polariton condensates form due to optical parametric oscillation (OPO) and are strongly non-equilibrium states. In case of non-resonantly incoherently pumped system, the distribution of the higher energy polaritons shows some thermalisation, but the resultant polariton condensates are also far from thermodynamic equilibrium due to finite polariton lifetime. In this chapter, we show that both systems have very similar properties. We reveal the effects of polariton–polariton interactions and non-equilibrium character on the condensate properties. Above threshold condensation into several polariton levels with different energies and k-vectors is observed, which arises from the non-equilibrium character of the polariton system. The specific k-vectors at which condensation is triggered are determined by the local disorder potential landscape. We also investigate the coherence of a single condensed mode by measuring the first (g (1))- and second (g (2))-order correlation functions. We find that the decay times of these functions are
, much longer than the 1.5 ps polariton lifetime. Even though the polariton condensate is a non-equilibrium system, the strong slowing down of the decay allows coherence decay processes characteristic of an equilibrium, interacting BEC to be observed. The signature of the interactions is a Gaussian form for the g (1)-function and a saturation of coherence time with increasing number of particles in the condensate, as observed experimentally and confirmed theoretically. Although predicted, these effects have not been observed for atom BECs.