Dilute Fermi gas in quasi-one-dimensional traps: From weakly interacting fermions via hard core bosons to weakly interacting Bose gas

TL;DR

This paper explores the equilibrium states of a quasi-one-dimensional two-component Fermi gas, revealing a transition from weakly interacting fermions to bosonic regimes, with exact solutions across different interaction strengths.

Contribution

It provides an exact solution for a 2-component Fermi gas in a quasi-1D trap across all interaction regimes, detailing the crossover from fermionic to bosonic behavior.

Findings

Identifies three regimes: weakly interacting Fermi gas, hard core Bose gas, weakly interacting Bose gas.

Determines the crossover points at $a_{F} o eq ext{pm} nl_{ot}^2$.

Discusses experimental implications of the regime transitions.

Abstract

We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size $l_{\perp}$. In the dilute limit ($nl_{\perp}\ll 1$, where $n$ is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length $a_{F}$. When $l_{\perp}/a_{F}$ goes from $-\infty$ to $+\infty$, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas and weakly coupled Bose gas. The regimes are separated by two crossovers at $a_{F}\sim \pm nl_{\perp}^{2}$. In conclusion we discuss experimental implications of these results.