Induced interactions in a superfluid Bose-Fermi mixture

TL;DR

This paper investigates how a superfluid Fermi gas influences a Bose-Einstein condensate through induced interactions, revealing strong momentum and frequency dependence, divergence at sound modes, and damping effects, which can be used to probe Fermi superfluid properties.

Contribution

The study introduces a combined quasiparticle RPA and Beliaev approach to analyze induced interactions in a Bose-Fermi mixture across the BCS-BEC crossover, highlighting novel spectral features.

Findings

Induced interactions vary strongly with momentum and frequency.

Divergence occurs at the Fermi superfluid's sound mode, causing avoided crossings.

Quasiparticle excitations lead to damping of BEC excitations.

Abstract

We analyse a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC cross-over. Using a quasiparticle random phase approximation combined with Beliaev theory to describe the Fermi superfluid and the BEC respectively, we show that the single particle and collective excitations of the Fermi gas give rise to an induced interaction between the bosons, which varies strongly with momentum and frequency. It diverges at the sound mode of the Fermi superfluid, resulting in a sharp avoided crossing feature and a corresponding sign change of the interaction energy shift in the excitation spectrum of the BEC. In addition, the excitation of quasiparticles in the Fermi superfluid leads to damping of the excitations in the BEC. Besides studying induced interactions themselves, these prominent effects can be used to systematically probe the strongly interacting Fermi gas.