Reply to Comment on "Superfluid stability in the BEC-BCS crossover" by Sheehy and Radzihovsky

TL;DR

This paper clarifies discrepancies in superfluid phase diagrams by arguing that positive susceptibility alone suffices to exclude unstable states, addressing prior conflicting claims.

Contribution

It demonstrates that positive susceptibility is enough to eliminate local maximum states in the free energy landscape, resolving previous disagreements.

Findings

Positive susceptibility rules out unstable states.

Clarification of phase diagram discrepancies.

Addresses prior conflicting claims.

Abstract

The reason behind the discrepancy between the phase diagrams of our earlier work [1] and the comment of Sheehy and Radzihovsky [2] is discussed. We show that, in contrast to what is claimed in [2], the requirement of positive susceptibility is sufficient to rule out states that are local maximum of the free energy (as a function of the order parameter $\Delta$