Energy Relaxation in a 1-D Polariton Condensate

We study the kinetics of polariton condensation accounting for the condensation process as well as the energy relaxation of condensed polaritons due to their scattering with phonons and excitons. By assuming a Boltzmann kinetic description of the scattering process, we show that intra-condensate relaxation can be accounted for by an additional time-dependent term in the Gross-Pitaevskii equation. As an example, we apply the formalism to the experimental results recently obtained in polariton microwires [E. Wertz, et al., Nature Phys. 6, 860 (2010)]. In the presence of a local non-resonant optical pump, a dynamic balance between spatially dependent relaxation and particle loss develops and excites a series of modes, roughly equally spaced in energy. Upon comparison, excellent agreement is found with the experimental data.