Molecular branch of a small highly-elongated Fermi gas with an impurity: Full three-dimensional versus effective one-dimensional description

Abstract

We consider an impurity immersed in a small Fermi gas under highly-elongated harmonic confinement. The impurity interacts with the atoms of the Fermi gas through an isotropic short-range potential with three-dimensional free-space s-wave scattering length $a_{3\text{d}}$. We investigate the energies of the molecular branch, i.e., the energies of the state that corresponds to a gas consisting of a weakly-bound diatomic molecule and "unpaired" atoms, as a function of the s-wave scattering length $a_{3\text{d}}$ and the ratio $\eta$ between the angular trapping frequencies in the tight and weak confinement directions. The energies obtained from our three-dimensional description that accounts for the dynamics in the weak and tight confinement directions are compared with those obtained within an effective one-dimensional framework, which accounts for the dynamics in the tight confinement direction via a renormalized one-dimensional coupling constant. Our theoretical results are related to recent experimental measurements.

4 figures (expanded version)

References in corpus (11)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time
• Precise characterization of ^6Li Feshbach resonances using trap-sideband resolved RF spectroscopy of weakly bound molecules
• Pairing in few-fermion systems with attractive interactions
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Coherent molecule formation in anharmonic potentials near confinement-induced resonances
• Three-body problem for ultracold atoms in quasi-one-dimensional traps
• Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas
• Three s-wave interacting fermions under anisotropic harmonic confinement: Dimensional crossover of energetics and virial coefficients
• Controlling integrability in a quasi-1D atom-dimer mixture

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• Tunneling dynamics of two interacting one-dimensional particles
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• One-dimensional Repulsive Fermi Gas in a Tunable Periodic Potential
• Quench dynamics of dipolar fermions in a one-dimensional harmonic trap
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results