Cavity-mediated oscillating and trapping dynamics in a two-component condensate

TL;DR

This paper investigates how a cavity can influence the dynamics of a two-component condensate, revealing mechanisms for oscillation, trapping, and stability control through cavity-mediated effects.

Contribution

It introduces a model where cavity-mediated interactions induce novel oscillating and trapping behaviors in a two-component condensate beyond steady-state assumptions.

Findings

Cavity can induce gauge potentials leading to Josephson dynamics.

Cavity parameters control transition between oscillating and trapped states.

Stability of fixed points can be tuned via cavity and driving field parameters.

Abstract

Cold atoms in cavity provides a new platform for exploring exotic many-body phases. Here we explore the dynamics of a two-component condensate coupled to a finesse cavity, in which the Raman coupling is mediated by pumping laser and cavity mode. In this model, the energy scale of cavity mode is several order of magnitude bigger than that in the condensate, thus the small fluctuations in the cavity field may have important consequence in the dynamics of condensate. Beyond the steady-state approximaton, we show the cavity can play two different roles to this dynamics. In the first case, it imprints a gauge potential to the dynamics of condensate, giving rise to zero and $\pi$ Josephson dynamics. Nevertheless, in the other case, it plays the role of non-reciprocial transportation between the two hyperfine states, in which the stability of the fixed points are tuned from elliptic to stable spiral for one of the trapped phase and unstable spiral for the other trapped phase, thus the oscillating dynamics will finally ceased. The transition between these dynamics can be controlled by the parameters of the cavity field and the driving field. Our results demonstrate an novel way to engineer the dynamics of condensate by tuning the stability of the fixed points.