Nonlinear effects of atomic collisions on the optomechanical properties of a Bose-Einstein condensate in an optical cavity

TL;DR

This paper theoretically examines how atomic collisions influence the optomechanical behavior of a Bose-Einstein condensate in an optical cavity, revealing shifts in mode energies, reduced photon numbers, and decreased entanglement.

Contribution

It introduces a discrete-mode approximation considering interband transitions and analyzes the nonlinear effects of atomic collisions on cavity and condensate dynamics.

Findings

Atomic collisions shift excited mode energies.

Collisions reduce cavity photon number.

Collisions decrease atom-photon entanglement.

Abstract

In this paper, we have investigated theoretically the influence of atomic collisions on the behaviour of a one-dimensional Bose-Einstein condensate inside a driven optical cavity. We develop the discrete-mode approximation for the condensate taking into account the interband transitions due to the s-wave scattering interaction. We show that in the Bogoliubov approximation the atom-atom interaction shifts the energies of the excited modes and also plays the role of an optical parametric amplifier for the Bogoliubov side mode which can affect its normal-mode splitting behaviour. On the other hand due to the atomic collisions the resonance frequency of the cavity is shifted which leads to the decrease of the number of cavity photons and the depletion of the Bogoliubov mode. Besides, it reduces the effective atom-photon coupling parameter which consequently leads to the decrease of the entanglement between the Bogoliubov mode and the optical field.