Chaotic dynamics of Bose-Einstein condensates in optical cavities

Abstract

Summary form only given. We perform a theoretical and numerical analysis of a system comprising a Bose-Einstein condensate (BEC) interacting with a laser beam in an optical cavity. Recent studies have modelled this system with two motional modes coupled with a light mode and have shown nonlinear behaviour, e.g. bistability [1,2]. Our approach tackles the full Gross-Pitaevskii equation coupled to the cavity field as well as expansions in a number of motional modes.We consider a fixed value of the cavity-pump detuning and increase the pump intensity to cross the region of bistability (see Fig. 1 left panel). The system then displays a variety of behaviours, including regular oscillations, chaotic dynamics, and quasi-periodic behaviour, as displayed in the right panel of Fig. 1. In Fig. 1 we have used a coupled-equation system comprising the Schrödinger wave equation and a cavity-field evolution [3], where we have adiabatically eliminated the latter leading to a conservative dynamics. The chaotic dynamics here is not induced by the detector noise and is an intrinsic property of the light-BEC interaction.Our second model considers a multiple-modes expansion. By using just three modes, the chaotic dynamics observed in the full simulation is recovered. The bifurcation structure, typical of conservative dynamics in the vicinity of a separatrix, is identified through the use of projections and power spectra. Our results suggest that chaotic oscillations in this system are deterministic in nature and arise purely from nonlinear effects. In more general terms, the model is a novel example of quantum matter exhibiting chaotic behaviour and invites further research.