Seminarium Fizyki Materii Skondensowanej

Classical-field calculations are a mainstay of simulations of the dynamics and stationary properties of ultracold atomic and polariton gases at nonzero temperature. They allow for temperatures too high to treat with other methods, strong fluctuations and defects, open systems, as well as the study of single experimental realisations and distribution functions. They do however omit any quantum fluctuations.We have derived an extended version of the stochastic GPE (SGPE) that preserves quantum fluctuations. So far, for the case of ultracold Bose gases. Thus, a very tractable, nonlinear description of the system has been obtained that also includes quantum fluctuations, depletion, shot noise, antibunching, and similar effects, and makes no assumptions of a condensate. In contrast to the usual ``truncated Wigner'' approach of adding virtual vacuum noise into the initial conditions, this method preserves quantum fluctuations even into the long-time stationary state.I will first describe the stochastic GPE model for an ultracold gas that allows for a stable but classical wave field description of the system with a set temperature, before presenting the newly derived extended version and briefly speculating about further generalisations.