Low-energy three-body dynamics in binary quantum gases

Abstract

The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. Two identical fermions of the mass $m$ and a particle of the mass $m_1$ with the zero-range two-body interaction in the states of the total angular momentum L=1 are considered. Using the boundary condition model for the s-wave interaction of different particles, both eigenvalue and scattering problems are treated by solving hyper-radial equations, whose terms are derived analytically. The dependencies of the three-body binding energies on the mass ratio $m/m_1$ for the positive two-body scattering length are calculated; it is shown that the ground and excited states arise at $m/m_1\ge {\lambda }_1\approx 8.17260$ and $m/m_1\ge {\lambda }_2\approx 12.91743$, respectively. For $m/m_1 \alt λ_1$ and $m/m_1 \alt λ_2$, the relevant bound states turn to narrow resonances, whose positions and widths are calculated. The 2 + 1 elastic scattering and the three-body recombination near the three-body threshold are studied and it is shown that a two-hump structure in the mass-ratio dependencies of the cross sections is connected with arising of the bound states.

16 pages

References in corpus (5)

• Observation of Phase Separation in a Strongly-Interacting Imbalanced Fermi Gas
• Interaction-driven Dynamics of 40K / 87Rb Fermi-Bose Gas Mixtures in the Large Particle Number Limit
• Two-species fermion mixtures with population imbalance
• Universal low-energy properties of three two-dimensional particles
• On the stability of Bose-Fermi mixtures

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• Diagrammatic Monte Carlo study of mass-imbalanced Fermi-polaron system
• Crossover trimers connecting continuous and discrete scaling regimes
• High-temperature limit of the resonant Fermi gas
• Small mass- and trap-imbalanced two-component Fermi systems
• Three-body problem in a two-dimensional Fermi gas
• Efimov states embedded in the three-body continuum
• Efimov physics and universal trimer in spin-orbit coupled ultracold atomic mixtures