Bistable behavior of a two-mode Bose-Einstein condensate in an optical cavity

TL;DR

This paper investigates the bistable behavior of a two-mode Bose-Einstein condensate in an optical cavity, revealing conditions under which the system exhibits two stable states based on laser pump intensity and coupling strength.

Contribution

It develops an effective nonlinear optical model for the system considering beyond Rotating Wave Approximation and analyzes bistability through analytical and numerical methods.

Findings

Bistability occurs under specific laser pump and coupling conditions.

Stationary solutions show two stable states for cavity field and magnetization.

The model extends understanding of nonlinear dynamics in cavity-condensate systems.

Abstract

We consider a two-component Bose-Einstein condensate in a one-dimensional optical cavity. Specifically, the condensate atoms are taken to be in two degenerate modes due to their internal hyperfine spin degrees of freedom and they are coupled to the cavity field and an external transverse laser field in a Raman scheme. A parallel laser is also exciting the cavity mode. When the pump laser is far detuned from its resonance atomic transition frequency, an effective nonlinear optical model of the cavity-condensate system is developed under Discrete Mode Approximation (DMA), while matter-field coupling has been considered beyond the Rotating Wave Approximation. By analytical and numerical solutions of the nonlinear dynamical equations, we examine the mean cavity field and population difference (magnetization) of the condensate modes. The stationary solutions of both the mean cavity field and normalized magnetization demonstrate bistable behavior under certain conditions for the laser pump intensity and matter-field coupling strength.