Superfluidity of identical fermions in an optical lattice: atoms and polar molecules

TL;DR

This paper explores the conditions under which $p$-wave superfluidity can emerge in 2D optical lattices for both atoms and polar molecules, highlighting the role of lattice depth and long-range interactions in stabilizing topological superfluids.

Contribution

It demonstrates that while atomic $p$-wave superfluidity is suppressed in deep lattices, polar molecules with dipole-dipole interactions can form stable topological $p_x+ip_y$ superfluids in 2D lattices.

Findings

Atomic superfluidity is suppressed in deep lattices due to reduced scattering amplitude.

Moderate lattice depths can support atomic $p$-wave superfluids with sizable transition temperatures.

Dipolar polar molecules can form stable topological $p_x+ip_y$ superfluids in 2D lattices due to long-range interactions.

Abstract

In this work, we discuss the emergence of $p$-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms, the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the $p$-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic $p$-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological $p_x+ip_y$ superfluid of identical microwave-dressed polar molecules.