Three-body recombination in one dimension

Abstract

We study the three-body problem in one dimension for both zero-and finite-range interactions using the adiabatic hyperspherical approach. Particular emphasis is placed on the threshold laws for recombination, which are derived for all combinations of the parity and exchange symmetries. For bosons, we provide a numerical demonstration of several universal features that appear in the three-body system, and discuss how certain universal features in three dimensions are different in one dimension. We show that the probability for inelastic processes vanishes as the range of the pairwise interaction is taken to zero and demonstrate numerically that the recombination threshold law manifests itself for large scattering length.

Born-Oppenheimer study of two-component few-particle systems under one-dimensional confinement

“…[23], but no such four-body calculations have appeared in the literature. In a hyperspherical calculation, the additional derivative discontinuity in the angular wave function is treated analytically, and the hyperradial potential curves are calculated as the solution to a single transcendental equation [21,23]. The HHHL Born-Oppenheimer calculation for bosons can be extended to arbitrary λ by choosing a b-spline basis set that satisfies the boundary condition, …”

“…More recent theory work includes the calculation of the three-boson hyperradial potential curves [18][19][20], three-body recombination rates and threshold laws [21], and benchmark quality hyperspherical calculations of three-boson binding energies and scattering amplitudes [22]. The three-body problem for unequal masses has been studied in free space [23] and in an optical lattice [24].…”

Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement

“…The number of the three-body even-parity (P = 0) bound states n can be determined for large m/m 1 , using the one-channel approximation in (10) and the effective potential −κ 2 (ρ)/ρ 2 , from (22). Within the framework of the quasi-classical approximations and taking into account the large-ρ asymptotic dependence (22), one obtains the relation m/m 1 ≈ C(n + δ) 2 in the limit of large n and m/m 1 .…”

“…Experiments with ultra-cold gases in the one-dimensional (1D) and quasi-1D traps have been recently performed [1,11,12,13], amid the rapidly growing interest to the investigation of mixtures of ultra-cold gases [14,15,16,17,18,19,20]. Different aspects of the three-body dynamics in 1D have been analyzed in a number of recent papers, e. g., the bound-state spectrum of two-component compound in [21], low-energy three-body recombination in [22], application of the integral equations in [23], and variants of the hyperradial expansion in [24,25,26].…”

Few-boson processes in the presence of an attractive impurity under one-dimensional confinement

“…col , where κ min is the hyperangular quantum number for the lowest three-body hyperspherical harmonic in the limit of large hyper-radius R → ∞ [35]. In general, κ min is an irrational number determined purely by the masses of the collision partners.…”