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New Journal of Physics

Three-body recombination of cold fermionic atoms

Hiroya Suno, Brett D. Esry, Chris H. Greene

Published May 30, 2003• 36 citations
Publisher

Abstract

Recombination of identical, spin-polarized fermions in cold three-body collisions is investigated. We parametrize the mechanisms for recombination in terms of the `scattering volume' V p and another length scale r 0 . Model two-body interactions were used within the framework of the adiabatic hyperspherical representation. We examine the recombination rate K 3 as a function of the collision energy E for various values of V p . Not only do we consider the dominant J Π = 1 + case, but also the next-leading order contributions from J Π = 1 - and 3 - . We discuss the behaviour near a two-body resonance and the expected universality of fermionic recombination. Comparisons with boson recombination are considered in detail.

DOI
10.1088/1367-2630/5/1/353

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Recombination of identical, spin-polarized fermions in cold three-body collisions is investigated. We parametrize the mechanisms for recombination in terms of the `scattering volume' V p and another length scale r 0 . Model two-body interactions were used within the framework of the adiabatic hyperspherical representation. We examine the recombination rate K 3 as a function of the collision energy E for various values of V p . Not only do we consider the dominant J Π = 1 + case, but also the next-leading order contributions from J Π = 1 - and 3 - . We discuss the behaviour near a two-body resonance and the expected universality of fermionic recombination. Comparisons with boson recombination are considered in detail.
Three-body recombination of identical, spin-polarized fermionic atoms in the ultracold limit is investigated using model interactions. The mechanisms for recombination are parametrized by the "scattering volume" V(p) and described in the framework of the adiabatic hyperspherical representation. We have calculated the recombination rate K3 as a function of V(p) and have found K3 proportional, variant |V(p)|(8/3) for small |V(p)|. Recombination near a two-body Feshbach resonance can thus be significant.
We study three-body recombination in two dimensions for systems interacting via short-range two-body interactions in the regime of large scattering lengths. Using the adiabatic hyperspherical representation, we derive semianalytical formulas for three-body recombination in both weakly and deeply bound diatom states. Our results demonstrate the importance of long-range corrections to the three-body potentials by showing how they alter the low-energy and scattering-length dependence of the recombination rate for both bosonic and fermionic systems, which exhibit suppressed recombination if compared to the three-dimensional case. We verify these results through numerical calculations of recombination for systems with finite-range interactions and supporting a few two-body bound states. We also study finite-range effects for the energies of the universal three-identical-bosons states and find a slow approach to universal predictions as a function of the scattering length.
This work treats resonant collisions between five identical ultracold bosons in the framework of the adiabatic hyperspherical representation. The five-body recombination rate coefficient is quantified using a semiclassical description in conjunction with an analysis of the lowest five-body hyperspherical adiabatic potential curves in a scattering length regime with no universal weakly bound tetramers, trimers, or dimers. A comparison is made between these results and the only existing experimental measurement of five-body loss in an ultracold gas of bosonic cesium atoms and with the lone theoretical estimation of the loss rate. The recombination rate for the process B + B + B + B + B → B 4 + B is also computed in a different regime of scattering lengths where there is one universal bound tetramer by implementing a few-channel quantum scattering calculation based on five-body hyperspherical potential curves and nonadiabatic couplings. Our calculations predict regions where five-body recombination can cause decay of the atom cloud in an ultracold gas that is even faster than 3-body and 4-body recombination, which can ideally be tested by using the current generation of box traps having nearly uniform density.
The atom-atom-anion three-body recombination (TBR) and collision induced dissociation (CID) processes of the 3He–3He–T− system at ultracold temperatures are investigated by solving the Schrödinger equation in the adiabatic hyperspherical representation. The variations of the TBR and CID rates with the collision energies in the ultracold temperatures are obtained. It is found that the JΠ = 1− symmetry dominates the TBR and CID processes in most of the considered collision energy range. The rate of TBR (CID) into (from) the l = 1 anion is larger than those for the l = 0 and l = 2 anions, with the l representing the rotational quantum number of 3HeT−. This can be understood via the nonadiabatic couplings among the different channels.
Three-body recombination in helium-helium--alkali-metal collisions at cold temperatures is studied using the adiabatic hyperspherical representation. The rates for the three-body recombination processes $^{4}\text{H}\text{e}+^{4}\text{H}\text{e}+X\ensuremath{\rightarrow}^{4}\text{H}\text{e}+^{4}\text{H}\text{e}X$ and $^{4}\text{H}\text{e}+^{4}\text{H}\text{e}+X\ensuremath{\rightarrow}{^{4}\text{H}\text{e}}_{2}+X$, with X=7LiX=^{7}\text{L}\text{i}X=7Li, 23Na^{23}\text{N}\text{a}23Na, 39K^{39}\text{K}39K, 85Rb^{85}\text{R}\text{b}85Rb, and 133Cs^{133}\text{C}\text{s}133Cs, are calculated at nonzero collision energies by including not only zero total angular momentum, J=0J=0J=0, states but also J>0J>0J>0 states. The three-body recombination rates show a relatively weak dependence on the alkali-metal species, differing from each other only by about one order of magnitude, except for the 4He-4He-23Na^{4}\text{H}\text{e-}^{4}\text{H}\text{e-}^{23}\text{N}\text{a}4He-4He-23Na system.