FFLO state in 1, 2, and 3 dimensional optical lattices combined with a non-uniform background potential

TL;DR

This paper explores the phase diagram of imbalanced Fermi gases in 1-3D optical lattices, revealing how Van Hove singularities influence the FFLO state and identifying observable signatures in noise correlations.

Contribution

It provides a comprehensive analysis of phase structures in optical lattices, including the effects of Van Hove singularities and harmonic confinement, with detailed predictions for experimental signatures.

Findings

Van Hove singularities significantly affect the FFLO state in different dimensions.

Distinct shell structures like normal-FFLO-BCS are predicted in trapped gases.

Clear noise correlation signatures of FFLO are identified in 1D systems.

Abstract

We study the phase diagram of an imbalanced two-component Fermi gas in optical lattices of 1-3 dimensions, considering the possibilities of the FFLO, Sarma/breached pair, BCS and normal states as well as phase separation, at finite and zero temperatures. In particular, phase diagrams with respect to average chemical potential and the chemical potential difference of the two components are considered, because this gives the essential information about the shell structures of phases that will occur in presence of an additional (harmonic) confinement. These phase diagrams in 1, 2 and 3 dimensions show in a striking way the effect of Van Hove singularities on the FFLO state. Although we focus on population imbalanced gases, the results are relevant also for the (effective) mass imbalanced case. We demonstrate by LDA calculations that various shell structures such as normal-FFLO-BCS-FFLO-normal, or FFLO-normal, are possible in presence of a background harmonic trap. The phases are reflected in noise correlations: especially in 1D the unpaired atoms leave a clear signature of the FFLO state as a zero-correlation area (``breach'') within the Fermi sea. This strong signature occurs both for a 1D lattice as well as for a 1D continuum. We also discuss the effect of Hartree energies and the Gorkov correction on the phase diagrams.