The effect of atomic collisions on the quantum phase transition of a Bose-Einstein condensate inside an optical cavity

TL;DR

This study explores how atomic collisions influence the quantum phase transition in a Bose-Einstein condensate within an optical cavity, revealing control mechanisms via scattering interactions and mode excitations.

Contribution

It introduces a two-mode approximation considering atomic collisions and demonstrates control of the phase transition through s-wave scattering frequency.

Findings

Atomic collisions shift the quantum phase transition threshold.

Mode excitation occurs at the edges of the Brillouin zone.

Quantum fluctuations are affected by atom-atom interactions.

Abstract

In this paper, we investigate the effect of atomic collisions on the phase transition form the normal to the superradiant phase in a one-dimensional Bose-Einstein condensate (BEC) trapped inside an optical cavity. Specifically, we show that driving the atoms from the side of the cavity leads to the excitation of modes in the edges of the first Brillouin zone of every energy band, which results in the two-mode approximation of the BEC matter field in the limit of weak coupling regime. The nonlinear effect of atom-atom interaction shifts the threshold of the quantum phase transition of the BEC and also affect the power low behavior of quantum fluctuations in the total particle number. Besides, we show the possibility of controlling the quantum phase transition of the system through the s-wave scattering frequency when the the strength of the transverse pumping has been fixed.