Dimensional Crossover in a Spin-imbalanced Fermi gas

TL;DR

This paper investigates the dimensional crossover in a spin-imbalanced Fermi gas, analyzing how the system transitions from 1D to 3D behavior with changing interactions and density, and maps it to an effective 1D model.

Contribution

It provides a mean-field phase diagram for the 1D-3D crossover in a trapped Fermi gas, highlighting the conditions for different dimensional behaviors and the density dependence of the effective scattering length.

Findings

Weak interactions show 1D-like behavior with multiple channels opening.

Strong interactions lead to 3D-like behavior across densities.

Effective 1D scattering length depends significantly on density.

Abstract

We model the one-dimension (1D) to three-dimension (3D) crossover in a cylindrically trapped Fermi gas with attractive interactions and spin-imbalance. We calculate the mean-field phase diagram, and study the relative stability of exotic superfluid phases as a function of interaction strength and temperature. For weak interactions and low density, we find 1D-like behavior, which repeats as a function of the chemical potential as new channels open. For strong interactions, mixing of single-particle levels gives 3D-like behavior at all densities. Furthermore, we map the system to an effective 1D model, finding significant density dependence of the effective 1D scattering length.