Exact results for the 1D mixed Bose-Fermi interacting gas

A Fermi-Bose mapping method is used to determine the exact ground states of several models of mixtures of strongly interacting ultracold gases in tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D spin-aligned Fermi gas with infinitely strong zero-range attractions). We detail the case of a Bose-Fermi mixture with TG boson-boson (BB) and boson-fermion (BF) interactions. Exact results are given for density profiles in a harmonic trap, single-particle density matrices, momentum distributions, and density-density correlations. Since the ground state is highly degenerate, we analyze the splitting of the ground manifold for large but finite BB and BF repulsions.A Fermi-Bose mapping method is used to determine the exact ground states of several models of mixtures of strongly interacting ultracold gases in tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D spin-aligned Fermi gas with infinitely strong zero-range attractions). We detail the case of a Bose-Fermi mixture with TG boson-boson (BB) and boson-fermion (BF) interactions. Exact results are given for density profiles in a harmonic trap, single-particle density matrices, momentum distributions, and density-density correlations. Since the ground state is highly degenerate, we analyze the splitting of the ground manifold for large but finite BB and BF repulsions.

arXiv:0706.1797Physical Review LettersDec 5, 2007119 citations

Strongly Interacting Fermi and Bose-Fermi Gases

Ye-Ryoung Lee, Jae Hyuk Choi, Caleb A. Christensen +4 more

Bulletin of the American Physical SocietyMay 29, 20100 citations

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

FFLO vs Bose-Fermi mixture in a two channel model of a 1D Fermi gas: a 3-body study

Stefan K. Baur, John B. Shumway, Erich J. Mueller

Bulletin of the American Physical SocietyMay 23, 20090 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.