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 ≥ λ 1 ≈ 8.17260 and m/m 1 ≥ λ 2 ≈ 12.91743, respectively. For m/m 1 λ 1 and m/m 1 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.

Dimer-atom scattering between two identical fermions and a third particle

“…As the mass ratio gets higher, modulations of the T -matrix become more apparent with multiple sign changes. We argued that this effect could be related to the "fall of a particle to the center" phenomenon [9,23] and to the emergence of three-body Efimov bound states [7,8].…”

“…This effect could be related to the "fall of a particle to the center" phenomenon [9,23], and to the emergence of threebody Efimov bound states [7,8], which are known to occur when the mass ratio is large. When the heavy A particles are separated from each other by a distance r ≪ a AB (or equivalently pa AB ≫ 1), it is known that an exchange of a light B particle mediates an effective −C/(m A r 2 ) attraction between A particles.…”

“…However, since three-body Efimov bound states emerges for larger mass ratios [7][8][9], this problem is not universal, and an additional parameter coming from the shortrange (or large-momentum) three-body physics is needed for an accurate description.…”

Bound States in a Quasi-Two-Dimensional Fermi Gas

“…In dimensions higher than one, few-body bound states can, for instance, impact the statistics of the many-body quasiparticle excitations. Indeed, for fermionic systems, the two-body bound state is fundamental to the understanding of the BCS-BEC crossover [1][2][3][4], while the existence of three-body bound states of fermions [5,6] with unequal masses can lead to dressed trimer quasiparticles in the highly polarized Fermi gas [7]. Even in one dimension (1D), few-body bound states can impact the many-body phase: It has already been shown that one can have a Luttinger liquid of trimers [8].…”

“…On the other hand, bound states of identical fermions are constrained to have odd angular momentum owing to Pauli exclusion and thus, even for attractive interactions, identical fermions are subject to a centrifugal barrier. For short-range s-wave [16] interactions in 3D, non-Efimov trimers consisting of two identical fermions with mass m " and one distinguishable particle with mass m # can only exist above the critical mass ratio m " =m # ' 8:2 [5], while Efimov trimers only appear once m " =m # * 13:6 [17]. However, the existence of larger (N þ 1)-body bound states involving N > 2 identical fermions remains largely unknown-it has only recently been shown that Efimov tetramers exist in 3D [18].…”