Collective modes in asymmetric ultracold Fermi systems

TL;DR

This paper derives the effective theory for collective excitations in asymmetric ultracold Fermi gases, revealing how the Higgs and Goldstone modes behave with varying chemical potential mismatch, and predicting observable effects in superfluid vortices.

Contribution

It provides a detailed low-energy effective action for collective modes in asymmetric fermionic superfluids, including novel insights into Higgs mode behavior and vortex properties.

Findings

Higgs mode mass decreases with increasing chemical potential mismatch.

Energy cost for condensate fluctuations varies between gapped and gapless phases.

Vortex core radius may sharply increase in the gapless superfluid phase.

Abstract

We derive the low energy effective action for the collective modes in systems of fermions interacting via a short-range s-wave attraction, featuring unequal chemical potentials for the two fermionic species (asymmetric systems). As a consequence of the attractive interaction, fermions form a condensate that spontaneously breaks the U(1) symmetry associated with total number conservation. Therefore at sufficiently small temperatures and asymmetries, the system is a superfluid. We reproduce previous results for the stability conditions of the system as a function of the four-fermion coupling and asymmetry. We obtain these results analyzing the coefficients of the low energy effective Lagrangian of the modes describing fluctuations in the magnitude (Higgs mode) and in the phase (Goldstone mode) of the difermion condensate. We find that for certain values of parameters, the mass of the Higgs mode decreases with increasing mismatch between the chemical potentials of the two populations, if we keep the scattering length and the gap parameter constant. Furthermore, we find that the energy cost for creating a position dependent fluctuation of the condensate is constant in the gapped region and increases in the gapless region. These two features may lead to experimentally detectable effects. As an example, we argue that if the superfluid is put in rotation, the square of the radius of the outer core of a vortex should sharply increase on increasing the asymmetry, when we pass through the relevant region in the gapless superfluid phase. Finally, by gauging the global U(1) symmetry, we relate the coefficients of the effective Lagrangian of the Goldstone mode with the screening masses of the gauge field.