Ultracold Bose Mixtures with Spin-Dependent Fermion-Mediated Interactions

TL;DR

This paper develops a theoretical framework for binary Bose-Einstein condensates coupled to polarized fermions, revealing how spin-dependent fermion-mediated interactions influence quasiparticle spectra, phase stability, and quantum fluctuations.

Contribution

It introduces a functional integral approach to analyze spin-dependent fermion-mediated interactions in binary Bose-Einstein condensates, highlighting their effects on excitations and phase behavior.

Findings

Density quasiparticle branch is modified by interactions.

Stable miscible phases can be achieved by tuning parameters.

Spin density fluctuations are unaffected by fermion-mediated interactions.

Abstract

We develop a functional integral formulation for binary Bose-Einstein condensates coupled to polarized fermions. We find that spin-dependent fermion-mediated interactions have dramatic effects on the properties of the binary condensates. The quasiparticle spectrum features two branches. The upper branch, which is of density nature, gets modified by the induced interactions, while the lower branch, which is of spin nature, is left intact. The ground-state phase diagram consists of stable region of miscible phases and unstable region toward phase separation. In the stable region, it is further classified by the damping of excitations of the upper branch. We show that it is possible to find region of well-defined, long-lived quasiparticle excitations by tuning relevant parameters, such as boson-fermion mass ratio, boson-fermion number density ratio, and interspecies interactions between bosons as well. We explore the effects of quantum fluctuation due to the effective potential on the binary condensates. It turns out that both the density structure factor and spin density structure factor fulfill the Feynman relation, except that the latter is immune to the fermion-mediated interactions.