NONLINEAR MIXING OF QUASI-PARTICLES IN AN INHOMOGENEOUS BOSE CONDENSATE

We use a one-dimensional time-dependent nonlinear Schrodinger equation (NLSE) to study the temporal evolution of excited-state populations o f an inhomogeneous Bose condensate. We shaw how one can decompose an a rbitrary single-particle wave function into a condensate and a collect ion of quasiparticles and we use this method to analyze simulations in which the initial wave function contains a finite amount of excitatio n in a single mode. The nonlinear mixing of the quasiparticles is domi nated by processes that approximately conserve energy and we see the r eversible transfer of excitation between energetically matched modes. We show analytically how the time scale for nonlinear mixing depends o n the amount of initial excitation and the size of the nonlinearity. W e propose that, by averaging over the phase of the excitations, the NL SE can be used as a simple tool for the simulation of incoherent excit ations. This will allow the techniques presented here to be used to ex plore finite-temperature mixing effects.