Bosonic binary mixtures with Josephson-type interactions

TL;DR

This paper investigates bosonic binary mixtures with Josephson interactions, revealing how phase locking and condensate fractions depend on system parameters, with implications for experimental control of quantum states.

Contribution

It introduces a mean-field and Gaussian fluctuation analysis of a bosonic mixture model with Josephson interactions, highlighting phase locking and parameter-dependent condensate behavior.

Findings

Both species condense below a critical temperature.

Relative phases are locked by the laser phase.

Condensate fractions depend on the ratio of Rabi frequency to detuning.

Abstract

Motivated by experiments in bosonic mixtures composed of a single element in two different hyperfine states, we study bosonic binary mixtures in the presence of Josephson interactions between species. We focus on a particular model with $O(2)$ isospin symmetry, lifted by an imbalanced population parametrized by a Rabi frequency, $\Omega _{R}$, and a detuning, $\nu $, which couples the phases of both species. We have studied the model at mean-field approximation plus Gaussian fluctuations. We have found that both species simultaneously condensate below a critical temperature $T_{c}$ and the relative phases are locked by the applied laser phase, $\alpha$. Moreover, the condensate fractions are strongly dependent on the ratio $\Omega _{R}/|\nu |$ that is not affected by thermal fluctuations.