Bifurcations and bistability in cavity assisted photoassociation of Bose-Einstein condensed molecules

TL;DR

This paper investigates how an optical cavity influences the formation of molecules from Bose-Einstein condensates, revealing bifurcations and bistability in the system's stationary states due to cavity-driven dynamics.

Contribution

It introduces a new dynamical degree of freedom in photoassociation processes and analyzes the resulting bifurcations and bistability in atom-molecule populations.

Findings

Bifurcation occurs at weak cavity driving, indicating a transition to nonlinear Rabi oscillations.

Bistability is observed in atom and molecule numbers under strong cavity driving.

Stationary solutions and their stability depend on experimentally controllable parameters.

Abstract

We study the photo-association of Bose-Einstein condensed atoms into molecules using an optical cavity field. The driven cavity field introduces a new dynamical degree of freedom into the photoassociation process, whose role in determining the stationary behavior has not previously been considered. The semiclassical stationary solutions for the atom and molecules as well as the intracavity field are found and their stability and scaling properties are determined in terms of experimentally controllable parameters including driving amplitude of the cavity and the nonlinear interactions between atoms and molecules. For weak cavity driving, we find a bifurcation in the atom and molecule number occurs that signals a transition from a stable steady state to nonlinear Rabi oscillations. For a strongly driven cavity, there exists bistability in the atom and molecule number.