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(). In the dilute limit (nl()<<1, where n is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length aF. When l()/aF goes from -∞ to +∞, 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 aF∼±nl()2. In conclusion, we discuss experimental implications of these results