Effective interactions in a quantum Bose-Bose mixture

TL;DR

This paper extends the Beliaev diagrammatic theory to binary Bose mixtures, deriving coupled Green's functions and excitation spectra, revealing renormalization effects and providing a foundation for studying emergent phases in quantum degenerate gases.

Contribution

It introduces a generalized theoretical framework for binary Bose mixtures, including coupled Dyson equations and analytical Green's functions, accounting for renormalization and superfluid drag effects.

Findings

Two excitation branches with parabolic form in spin-independent limit

Renormalization of magnon mass and spin-wave velocity due to entrainment

Drag effects influence magnon dispersion in 2D systems

Abstract

We generalize the Beliaev diagrammatic theory of an interacting spinless Bose-Einstein condensate to the case of a binary mixture. We derive a set of coupled Dyson equations and find analytically the Green's functions of the system. The elementary excitation spectrum consists of two branches, one of which takes the characteristic parabolic form in the limit of a spin-independent interaction. We observe renormalization of the magnon mass and the spin-wave velocity due to the Andreev-Bashkin entrainment effect. For a 3D weakly-interacting gas the spectrum can be obtained by applying the Bogoliubov transformation to the second-quantized Hamiltonian in which the microscopic two-body potentials in each channel are replaced by the corresponding off-shell scattering amplitudes. The superfluid drag density can be calculated by considering a mixture of phonons and magnons interacting via the effective potentials. We show that this problem is identical to the second-order perturbative treatment of a Bose polaron. In 2D the drag contributes to the magnon dispersion already in the first approximation. Our consideration provides a basis for systematic study of emergent phases in quantum degenerate Bose-Bose mixtures.