Dilute Fermi Gas in Quasi-One-Dimensional Traps: From Weakly Interacting Fermions via Hard Core Bosons to a Weakly Interacting Bose Gas

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 ($n{l}_{\perp }\ll 1$, 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 $a_F\sim \pm n{l}_{\perp }^2$. In conclusion, we discuss experimental implications of these results.

Figure 1

Phase diagram of quasi-1D Fermi gas.

Figure 2

Diagram for the Born scattering amplitude of two composite bosons.