Oscillatory pairing amplitude and magnetic compressible-incompressible transitions in imbalanced fermionic superfluids in optical lattices of elongated tubes

TL;DR

This paper investigates oscillatory pairing and phase transitions in imbalanced fermionic superfluids confined in optical lattice tubes, revealing FFLO-like phases and magnetization transitions relevant for cold atom experiments.

Contribution

It demonstrates the existence of oscillatory pairing gaps and magnetization transitions in elongated tube geometries, providing a phase diagram and experimental signatures for FFLO states.

Findings

Oscillatory pairing gap along and across tubes.

Magnetization undergoes incompressible-compressible transition.

Parity of tube-filling imbalance is protected by pairing oscillations.

Abstract

We study two-species fermion gases with attractive interaction in two-dimensional optical lattices producing an array of elongated tube confinements. Focusing on the interplay of Cooper pairing, spin imbalance (or magnetization) and intertube tunneling, we find the pairing gap can exhibit oscillatory behavior both along and across the tubes, reminiscent of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We obtain a Bose-Hubbard-like phase diagram that shows that the magnetization of the system undergoes an incompressible-compressible transition as a function of magnetic field and intertube tunneling strength. We find the parity of tube-filling imbalance in incompressible states is protected by that of the oscillatory pairing gap. Finally, we discuss signatures of this transition and thus (indirectly) of the FFLO pairing in cold atom experiments.