Abstract

We consider a simple growth model for a one-component trapped Bose-Einstein condensate - the Gross-Pitaevskii (GP) equation modified by a linear uniform gain term g. Our motivation is to provide a physical understanding of the behaviour of condensates observed in simulations of quantum evaporative cooling[1]. In particular, we are interested in departures from thermal equilibrium that may result in non-equilibrium quantum noise effects, relevant to atom-laser applications. We investigate asymptotic solutions to the GP equation with gain for long times - i.e., steadily growing solutions, valid some time after initial nucleation of the condensate, yet before any gain saturation has occurred. Following the construction successfully used recently in optical fiber environments [2] - we suppose that the amplitude has a self-similar behavior at large time. The phase has a uniform chirp giving a radially dependent outward momentum. In addition, we allow for center-of-mass oscillation of the growing condensate.

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