Atom-dimer scattering for confined ultracold fermion gases

Abstract

We solve the three-body problem of an ultracold Fermi gas with parabolic confinement length $a_{\perp }$ and 3D scattering length $a$. On the two-body level, there is a Feshbach-type resonance at $a_{\perp }/a\approx 1.46$, and a dimer state for arbitrary $a_{\perp }/a$. The three-body problem is shown to be universal, an d described by the atom-dimer scattering length $a_{ad}$ and a range parameter $b_{ad}$. In the dimer limit $a_{\perp }/a\gg 1$, we find a repulsive zero-range atom-dimer interaction. For $a_{\perp }/a\ll -1$, however, the potential has long range, with $a_{ad}>0$ and $b_{ad}\gg a_{ad}$. There is no trimer state, and despite $a_{ad}=0$ at $a_{\perp }/a\approx 2.6$, there is no resonance enhancement of the interaction.

5 pages, 2 figures; to appear in PRL (revised version)

References in corpus (4)

• Observation of Bose-Einstein Condensation of Molecules
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Weakly bound dimers of fermionic atoms
• An exactly solvable model of the BCS-BEC crossover

Cited by in corpus (12)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Confinement-induced resonances for a two-component ultracold atom gas in arbitrary quasi-one-dimensional traps
• Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap
• Three-body problem for ultracold atoms in quasi-one-dimensional traps
• Multi-Channel Atomic Scattering and Confinement-Induced Resonances in Waveguides
• Charge and spin dynamics of interacting Fermions in a one dimensional harmonic trap
• Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas
• Calibration of Interaction Energy between Bose and Fermi Superfluids
• Nanoscale atomic waveguides with suspended carbon nanotubes
• Controlling integrability in a quasi-1D atom-dimer mixture
• Three-body bound states in a harmonic waveguide with cylindrical symmetry