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

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 ($n{l}_{\perp }\ll 1$, 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.

RevTex4, 4 pages, 2 eps figures; revised version with new references and extended discussion of the physics of qusi-1D "BCS-BEC" crossover

References in corpus (9)

• Observation of resonance condensation of fermionic atom pairs
• Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance
• Observation of Bose-Einstein Condensation of Molecules
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Exciting Collective Oscillations in a Trapped 1D Gas
• Momentum spectroscopy of 1D phase fluctuations in Bose-Einstein condensates
• Measurement of the Spatial Correlation Function of Phase Fluctuating Bose-Einstein Condensates
• Quasi-one-dimensional Bose gases with large scattering length
• Pseudopotential model of ultracold atomic collisions in quasi-one- and two-dimensional traps

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