Phase structure of mass- and spin-imbalanced unitary Fermi gases

TL;DR

This paper investigates the phase diagram of mass- and spin-imbalanced unitary Fermi gases, using renormalization group methods to identify critical points and potential inhomogeneous phases, revealing a relation with two-body binding energies.

Contribution

It introduces a renormalization group approach to analyze fluctuation effects and estimates the emergence of inhomogeneous phases in imbalanced Fermi gases.

Findings

Critical temperature matches Monte Carlo results in the unpolarized limit.

Inhomogeneous phases likely exist for mass ratios above three.

Inhomogeneous phase extent grows with increasing mass imbalance.

Abstract

We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techniques. We thus obtain estimates for critical values of the temperature, mass and spin imbalance, above which the system is in the normal phase. In the unpolarized, equal-mass limit, our result for the critical temperature is in accordance with state-of-the-art Monte Carlo calculations. In addition, we estimate the location of regions in the phase diagram where inhomogeneous phases are likely to exist. We show that an intriguing relation exists between the general structure of the many-body phase diagram and the binding energies of the underlying two-body bound-state problem, which further supports our findings. Our results suggest that inhomogeneous condensates form for mass ratios of the spin-down and spin-up fermions greater than three. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.