Fluctuations and steady-state of a Bose-Einstein condensate interacting with a bath of thermal atoms

Summary form only given.We use quantum kinetic theory to calculate the steady-state and the fluctuations of a trapped Bose-Einstein condensate at finite temperature. We divide the system into two parts. The first part consists of the condensate particles. They are described quantum mechanically using the number-conserving Bogoliubov method that allows us to characterize the condensate by the number of condensed particles. The second part are the noncondensed particles. They are treated as a classical gas in thermal equilibrium. Using quantum kinetic theory we find a master equation for the reduced density operator of the Bose-Einstein condensate. We calculate the steady-state of the system and investigate the effect of one-, two- and three-particle losses on the condensate. Using linearized Ito equations we find expressions for the intensity fluctuations and the amplitude fluctuations in the condensate. The effect of the trap losses on the particle statistics is also studied. We then assume that the condensate particles are coherently pumped into an untrapped internal energy level and fall down in gravity. For this situation we derive the relation between the statistics of the trapped condensate particles and the statistics of the particles arriving at an atom detector positioned below the condensate.