Density and Spin Linear Response of Atomic Fermi Superfluids with Population Imbalance in BCS-BEC Crossover

TL;DR

This paper develops a theoretical framework for analyzing the density and spin linear responses of population-imbalanced Fermi superfluids across the BCS-BEC crossover, emphasizing the importance of order parameter fluctuations and symmetry constraints.

Contribution

It introduces a comprehensive linear response theory that accounts for order parameter fluctuations and applies it to the entire BCS-BEC crossover with population imbalance.

Findings

Spin responses differ significantly with population imbalance.

Susceptibilities diverge near instability, indicating phase separation.

Collective modes influence responses even without broken symmetry.

Abstract

We present a theoretical study of the density and spin (representing the two components) linear response of Fermi superfluids with tunable attractive interactions and population imbalance. In both linear response theories, we find that the fluctuations of the order parameter must be treated on equal footing with the gauge transformations associated with the symmetries of the Hamiltonian so that important constraints including various sum rules can be satisfied. Both theories can be applied to the whole BCS-Bose-Einstein condensation crossover. The spin linear responses are qualitatively different with and without population imbalance because collective-mode effects from the fluctuations of the order parameter survive in the presence of population imbalance, even though the associated symmetry is not broken by the order parameter. Since a polarized superfluid becomes unstable at low temperatures in the weak and intermediate coupling regimes, we found that the density and spin susceptibilities diverge as the system approaches the unstable regime, but the emergence of phase separation preempts the divergence.