Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas

Abstract

The four-body problem for an interacting two-species Fermi gas is solved analytically in a confined quasi-one-dimensional geometry, where the two-body atom-atom scattering length $a_{aa}$ displays a confinement-induced resonance. We compute the dimer-dimer scattering length $a_{dd}$, and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.

5 pages, 1 figure, published in Phys. Rev. Lett., breathing mode calculation added

References in corpus (21)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Observation of resonance condensation of fermionic atom pairs
• Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• Realization of Bose-Einstein condensates in lower dimensions
• Observation of Bose-Einstein Condensation of Molecules
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Experimental Study of the BEC-BCS Crossover Region in Lithium 6
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Weakly bound dimers of fermionic atoms
• Confinement induced molecules in a 1D Fermi gas
• Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance
• Collective oscillations of a 1D trapped Bose gas
• Atom-molecule coherence in Bose gases
• On the correct strong-coupling limit in the evolution from BCS superconductivity to Bose-Einstein condensation
• An exactly solvable model of the BCS-BEC crossover
• Quantitative comparison between theoretical predictions and experimental results for the BCS-BEC crossover
• Dilute Fermi gas in quasi-one-dimensional traps: From weakly interacting fermions via hard core bosons to weakly interacting Bose gas
• Interacting fermions in quasi-one-dimensional harmonic traps
• Atom-dimer scattering for confined ultracold fermion gases
• Three-body problem for ultracold atoms in quasi-one-dimensional traps

Cited by in corpus (32)

• Theory of ultracold Fermi gases
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Universal few-body physics and cluster formation
• Few-body physics with ultracold atomic and molecular systems in traps
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• Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap
• Highly polarized Fermi gases: One-dimensional case
• Realization of effective super Tonks-Girardeau gases via strongly attractive one-dimensional Fermi gases
• Bound states in a quasi-two-dimensional Fermi gas
• Quantum dynamics of resonant molecule formation in waveguides
• Born-Oppenheimer study of two-component few-particle systems under one-dimensional confinement
• A Pure Confinement Induced Trimer in One-Dimensional Atomic Waveguides
• Confinement-induced Resonances in Quasi-one-dimensional Traps with Transverse Anisotropy
• Solution of the BEC to BCS Quench in One Dimension
• Dark-soliton-like excitations in the Yang-Gaudin gas of attractively interacting fermions
• Quantum dark solitons in ultracold one-dimensional Bose and Fermi gases
• Collective mode damping and viscosity in a 1D unitary Fermi gas
• FFLO vs Bose-Fermi mixture in polarized 1D Fermi gas on a Feshbach resonance: a 3-body study
• Shifts and widths of Feshbach resonances in atomic waveguides
• Effective super Tonks-Girardeau gases as ground states of strongly attractive multi-component fermions
• Resonant d-wave scattering in harmonic waveguides
• The three-body pseudo-potential for atoms confined in one dimension
• Few-Boson Processes in the Presence of an Attractive Impurity under One-Dimensional Confinement
• Exact solution of the three-boson problem at vanishing energy
• Excitation spectrum and effective interactions of highly-elongated Fermi gas
• Molecular branch of a small highly-elongated Fermi gas with an impurity: Full three-dimensional versus effective one-dimensional description
• Controlling integrability in a quasi-1D atom-dimer mixture
• Correlated Gaussian Approach to Anisotropic Resonantly Interacting Few-Body Systems
• Strongly bound fermion pairs on a ring: a composite-boson approach
• Emergence of dark soliton signatures in a one-dimensional unpolarized attractive Fermi gas on a ring
• Achieving one-dimensionality with attractive fermions
• Effective theory for strongly attractive one-dimensional fermions