Two-component Bose gases with one-body and two-body couplings

TL;DR

This paper develops a mean-field framework to analyze how one-body and two-body couplings influence correlations and excitations in two-component Bose gases, revealing how these couplings control phase fluctuations.

Contribution

It provides a comprehensive mean-field theory for coupled Bose gases with position-dependent interactions and trapping, including formulas for correlations and excitation spectra.

Findings

One-body coupling sets the relative phase between components.

Repulsive two-body coupling suppresses phase fluctuations.

Attractive two-body coupling enhances phase fluctuations.

Abstract

We study the competition between one-body and two-body couplings in weakly-interacting two-component Bose gases, in particular as regards field correlations. We derive the meanfield theory for both ground state and low-energy pair excitations in the general case where both one-body and two-body couplings are position-dependent and the fluid is subjected to a state-dependent trapping potential. General formulas for phase and density correlations are also derived. Focusing on the case of homogeneous systems, we discuss the pair-excitation spectrum and the corresponding excitation modes, and use them to calculate correlation functions, including both quantum and thermal fluctuation terms. We show that the relative phase of the two components is imposed by that of the one-body coupling, while its fluctuations are determined by the modulus of the one-body coupling and by the two-body coupling. One-body coupling and repulsive two-body coupling cooperate to suppress relative-phase fluctuations, while attractive two-body coupling tends to enhance them. Further applications of the formalism presented here and extensions of our work are also discussed.