We discuss the transition from a fully decoherent to a (quasi-)condensate regime in a harmonically trapped weakly interacting 1D Bose gas. By using analytic approaches and verifying them against exact numerical solutions, we find a characteristic crossover temperature and crossover atom number that depend on the interaction strength and the trap frequency. We then identify the conditions for observing either an interaction-induced crossover scenario or else a finite-size Bose-Einstein condensation phenomenon characteristic of an \\textit{ideal} trapped 1D gas.We discuss the transition from a fully decoherent to a (quasi-)condensate regime in a harmonically trapped weakly interacting 1D Bose gas. By using analytic approaches and verifying them against exact numerical solutions, we find a characteristic crossover temperature and crossover atom number that depend on the interaction strength and the trap frequency. We then identify the conditions for observing either an interaction-induced crossover scenario or else a finite-size Bose-Einstein condensation phenomenon characteristic of an \\textit{ideal} trapped 1D gas.

Nov 24, 20061 citation

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

I. V. Tokatly

We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size ${l}_{\ensuremath{\perp}}$. In the dilute limit ($n{l}_{\ensuremath{\perp}}\ensuremath{\ll}1$, where $n$ is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length ${a}_{F}$ . When ${l}_{\ensuremath{\perp}}/{a}_{F}$ goes from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$, 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 ${a}_{F}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}n{l}_{\ensuremath{\perp}}^{2}$. In conclusion, we discuss experimental implications of these results.We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size ${l}_{\ensuremath{\perp}}$. In the dilute limit ($n{l}_{\ensuremath{\perp}}\ensuremath{\ll}1$, where $n$ is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length ${a}_{F}$. When ${l}_{\ensuremath{\perp}}/{a}_{F}$ goes from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$, 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 ${a}_{F}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}n{l}_{\ensuremath{\perp}}^{2}$. In conclusion, we discuss experimental implications of these results.

arXiv:cond-mat/0402276Physical Review LettersAug 25, 2004104 citations

Harmonically trapped Bose gases: Weakly-interacting regime and beyond

K. M. Daily, D. Blume

Bulletin of the American Physical SocietyJun 16, 20110 citations

n

is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length

{a}_{F}

. When ${l}_{\ensuremath{\perp}}/{a}_{F}$ goes from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$, 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 ${a}_{F}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}n{l}_{\ensuremath{\perp}}^{2}$. In conclusion, we discuss experimental implications of these results.