Nonlinear mixing of quasiparticles in an inhomogeneous Bose condensate

We use a one-dimensional time-dependent nonlinear Schrödinger equation (NLSE) to study the temporal evolution of excited-state populations of an inhomogeneous Bose condensate. We show how one can decompose an arbitrary single-particle wave function into a condensate and a collection of quasiparticles and we use this method to analyze simulations in which the initial wave function contains a finite amount of excitation in a single mode. The nonlinear mixing of the quasiparticles is dominated by processes that approximately conserve energy and we see the reversible transfer of excitation between energetically matched modes. We show analytically how the time scale for nonlinear mixing depends on the amount of initial excitation and the size of the nonlinearity. We propose that, by averaging over the phase of the excitations, the NLSE can be used as a simple tool for the simulation of incoherent excitations. This will allow the techniques presented here to be used to explore finite-temperature mixing effects.