Spectroscopy of the soliton lattice formation in quasi-one-dimensional fermionic superfluids with population imbalance

TL;DR

This paper investigates the formation of a soliton lattice in quasi-one-dimensional fermionic superfluids with population imbalance, revealing inhomogeneous order parameters and quasiparticle bands, and proposes experimental detection methods.

Contribution

It provides an exact mean-field analysis of soliton lattice formation in imbalanced superfluids and suggests experimental techniques for identifying this state.

Findings

Soliton lattice forms when the effective magnetic field exceeds a critical value.

The soliton lattice creates a band of quasiparticle states inside the energy gap.

Experimental detection methods like Bragg scattering and RF spectroscopy are effective.

Abstract

Motivated by recent experiments in low-dimensional trapped fermionic superfluids, we study a quasi-one-dimensional (quasi-1D) superfluid with a population imbalance between two hyperfine states using an exact mean-field solution for the order parameter. When an effective "magnetic field" exceeds a critical value, the superfluid order parameter develops spatial inhomogeneity in the form of a soliton lattice. The soliton lattice generates a band of quasiparticle states inside the energy gap, which originate from the Andreev bound states localized at the solitons. Emergence of the soliton lattice is accompanied by formation of a spin-density wave, with the majority fermions residing at the points in space where the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) order parameter vanishes. We discuss possibilities for experimental detection of the quasi-1D FFLO state using elastic and inelastic optical Bragg scattering and radio-frequency spectroscopy. We show that these measurements can provide necessary information for unambiguous identification of the spatially-inhomogeneous quasi-1D FFLO state and the soliton lattice formation.