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

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 mean-field 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.