BCS-BEC crossover of collective excitations in two-band superfluids

TL;DR

This paper investigates the evolution of collective excitations in two-band superfluids across the BCS-BEC crossover using a functional integral approach, providing analytical and numerical insights into mode behaviors.

Contribution

It offers a comprehensive analysis of collective modes in two-band superfluids across all coupling regimes, extending Leggett's results and including numerical studies of mode evolution.

Findings

Analytical results in weak and strong coupling regimes.

Numerical analysis of out-of-phase and in-phase modes.

Potential experimental observability in atomic gases.

Abstract

We use the functional integral approach to study low energy collective excitations in a continuum model of neutral two-band superfluids at T=0 for all couplings with a separable pairing interaction. In the long wavelength and low frequency limit, we recover Leggett's analytical results in weak coupling (BCS) for s-wave pairing, and further obtain analytical results in strong coupling (BEC) for both two and three dimensional systems. We also analyse numerically the behavior of the out-of-phase {\it exciton} (finite frequency) mode and the in-phase {\it phonon} (Goldstone) mode from weak to strong coupling limits, including the crossover region. In principle, the evolution of Goldstone and finite frequency modes from weak to strong coupling may be accessible experimentally in the superfluid phase of neutral Fermi atomic gases, and could serve as a test of the validity of the theoretical analysis and approximations proposed here.