A Unified Josephson Dynamics Perspective for Single-Cavity BECs: From Self-Trapping to Dynamical Phase Transitions

Abstract

We investigate a two-component Bose-Einstein condensate (BEC) strongly coupled to a single optical cavity, effectively described by a mean-field Dicke model supplemented with interatomic nonlinearities. Here, we propose a unified theoretical framework demonstrating that macroscopic quantum self-trapping (MQST) natively emerges between two internal atomic energy levels within a single cavity. By deriving the dimensionless semiclassical Josephson equations (SJE) governing this purely internal-state architecture, we analytically determine the critical nonlinear threshold and intrinsic phase shift mechanism for the phase transition. Based on this framework, we present two approaches for manipulating quantum phase transitions: dynamic in-situ tuning via photon pumping and inducing non-equilibrium dynamical phase transitions (DPT) via real-time parameter quenches. Furthermore, we rigorously prove that the effective charging energy driving this system scales exactly as one-quarter of the effective spin-dependent interaction energy -- the precise parameter governing recent spin-orbit coupled (SOC) BEC experiments. Incorporating realistic ${}^{87}$Rb atomic parameters, we substantiate that these single-cavity MQST and transition dynamics are highly feasible for observation under current state-of-the-art cold-atom technologies.

v2: Corrected typographical errors in the designation of the hyperfine states; numerical results and main physical conclusions remain entirely unchanged. Improved formatting and added references to match journal submission version