Bose-Einstein Condensates in a Cavity-mediated Triple-well

TL;DR

This paper explores how a high finesse optical cavity influences the energy structure and dynamics of Bose-Einstein condensates in a triple-well potential, revealing bistability, loop structures, and chaos in tunneling behavior.

Contribution

It introduces the effects of cavity-mediated nonlinearity on BEC energy levels and tunneling dynamics, including bistability, loop structures, and chaos, expanding understanding of cavity-BEC interactions.

Findings

Bistability appears in energy levels and intra-cavity photon number.

Loop structures emerge in energy levels with increased pump-cavity detuning.

Transition from oscillation to localization can be controlled and is associated with chaos.

Abstract

We investigate the energy structures and the dynamics of a Bose-Einstein condensates (BEC) in a triple-well potential coupled a high finesse optical cavity within a mean field approach. Due to the intrinsic atom-cavity field nonlinearity, several interesting phenomena arise which are the focuses of this work. For the energy structure, the bistability appears in the energy levels due to this atoms-cavity field nonlinearity, and the same phenomena can be found in the intra-cavity photons number. With an increase of the pump-cavity detunings, the higher and lower energy levels show a loop structure due to this cavity-mediated effects. In the dynamical process, an extensive numerical simulation of localization of the BECs for atoms initially trapped in one-, two-, and three-wells are performed for the symmetric and asymmetric cases in detail. It is shown that the the transition from oscillation to the localization can be modified by the cavity-mediated potential, which will enlarge the regions of oscillation. With the increasing of the atomic interaction, the oscillation is blocked and the localization emerges. The condensates atoms can be trapped either in one-, two-, or in three wells eventually where they are initially uploaded for certain parameters. In particular, we find that the transition from the oscillation to the localization is accompanied with some irregular regime where tunneling dynamics is dominated by chaos for this cavity-mediated system.