Self-organized Limit Cycles in Red-detuned Atom-cavity Systems

TL;DR

This paper explores the complex dynamical behaviors, including limit cycles and chaos, in a driven Bose-Einstein condensate coupled to a cavity field, revealing new phenomena arising from atom-light interactions and dissipation.

Contribution

It presents the first detailed dynamical phase diagram of a red-detuned atom-cavity system, identifying novel limit cycles and the effects of quantum fluctuations and atomic interactions.

Findings

Identification of dynamical instabilities as limit cycles and chaos.

Discovery of merging limit cycles related by Z2 symmetry.

Observation of a new limit cycle formed by atomic excitations.

Abstract

Recent experimental advances in the field of cold-atom cavity QED provide a powerful tool for exploring non-equilibrium correlated quantum phenomena beyond conventional condensed-matter scenarios. We present the dynamical phase diagram of a driven Bose-Einstein condensate coupled with the light field of a cavity, with a transverse driving field red-detuned from atomic resonance. We identify regions in parameter space showing dynamical instabilities in the form of limit cycles, which evolve into chaotic behavior in the strong driving limit. Such limit cycles originate from the interplay between cavity dissipation and atom-induced resonance frequency shift, which modifies the phase of cavity mode and gives excessive negative feedback on the atomic density modulation, leading to instabilities of the superradiant scattering. We find interesting merging of the limit cycles related by a $Z_2$ symmetry, and identify a new type of limit cycle formed by purely atomic excitations. The effects of quantum fluctuations and atomic interactions are also investigated.