2008/08/31 by O. I. Kartavtsev, A. V. Malykh, S. A. Sofianos · 1 citation
Physics and Astronomy · #physics.atom-ph
paper · pdf · doi:10.1134/s1063776109030017
published as ZhETF 135, 419 (2009)
arxiv created 2008/10/24 · arxiv updated 2015/05/12
The universal three-body dynamics in ultra-cold binary gases confined to one-dimensional motion are studied. The three-body binding energies and the (2 + 1)-scattering lengths are calculated for two identical particles of mass m and a different one of mass m1, which interactions is described in the low-energy limit by zero-range potentials. The critical values of the mass ratio m/m1, at which the three-body states arise and the (2 + 1)-scattering length equals zero, are determined both for zero and infinite interaction strength λ1 of the identical particles. A number of exact results are enlisted and asymptotic dependences both for m/m1 → ∞ and λ1 → -∞ are derived. Combining the numerical and analytical results, a schematic diagram showing the number of the three-body bound states and the sign of the (2 + 1)-scattering length in the plane of the mass ratio and interaction-strength ratio is deduced. The results provide a description of the homogeneous and mixed phases of atoms and molecules in dilute binary quantum gases.