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Three-Body Recombination in Ultracold Systems: Prediction of Weakly-Bound Atomic Trimer Energies

L. Tomio, V. S. Filho, Marcelo Takeshi Yamashita, A. Gammal, T. Frederico

Published Jan 1, 2003• 4 citations
OpenAlex

Abstract

Abstract. The three-body recombination coefficient of an ultracold atomic system, together with the corresponding two-body scattering length a, allow us to predict the energy E3 of the shallow trimer bound state, using a universal scaling function. The production of dimers in trapped Bose-Einstein con-densates, from three-body recombination processes, in the regime of short magnetic pulses near a Feshbach resonance, is also studied in line with the experimental observation. 1

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Weakly bound atomic trimers in ultracold traps

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The experimental three-atom recombination coefficients of the atomic states ${}^{23}\mathrm{Na}|{F=1,m}_{F}=\ensuremath{-}1〉,$ ${}^{87}\mathrm{Rb}|{F=1,m}_{F}=\ensuremath{-}1〉,$ and ${}^{85}\mathrm{Rb}|{F=2,m}_{F}=\ensuremath{-}2〉,$ together with the corresponding two-body scattering lengths, allow predictions of the trimer bound-state energies for such systems in a trap. The recombination parameter is given as a function of the weakly bound trimer energies, which are in the interval $1<m(a/\ensuremath{\Elzxh}{)}^{2}{E}_{3}<6.9$ for large positive scattering lengths $a.$ The contribution of a deep-bound state to our prediction, in the case of ${}^{85}\mathrm{Rb}|{F=2,m}_{F}=\ensuremath{-}2〉,$ for a particular trap, is shown to be relatively small.

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arXiv:physics/0304052•Physical Review Letters•Sep 18, 2003•279 citations
Abstract. The three-body recombination coefficient of an ultracold atomic system, together with the corresponding two-body scattering length a, allow us to predict the energy E3 of the shallow trimer bound state, using a universal scaling function. The production of dimers in trapped Bose-Einstein con-densates, from three-body recombination processes, in the regime of short magnetic pulses near a Feshbach resonance, is also studied in line with the experimental observation. 1
The experimental three-atom recombination coefficients of the atomic states ${}^{23}\mathrm{Na}|{F=1,m}_{F}=\ensuremath{-}1〉,$ ${}^{87}\mathrm{Rb}|{F=1,m}_{F}=\ensuremath{-}1〉,$ and ${}^{85}\mathrm{Rb}|{F=2,m}_{F}=\ensuremath{-}2〉,$ together with the corresponding two-body scattering lengths, allow predictions of the trimer bound-state energies for such systems in a trap. The recombination parameter is given as a function of the weakly bound trimer energies, which are in the interval $1<m(a/\ensuremath{\Elzxh}{)}^{2}{E}_{3}<6.9$ for large positive scattering lengths a.a.a. The contribution of a deep-bound state to our prediction, in the case of ${}^{85}\mathrm{Rb}|{F=2,m}_{F}=\ensuremath{-}2〉,$ for a particular trap, is shown to be relatively small.
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.
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.
Few-body effects play an important role for the understanding of ultracold quantum gases. We make use of an effective field theory approach to investigate various aspects of universal few-body physics close to a Feshbach resonance. That is the regime where the scattering length is large compared to all other length scales of the system and thus determines the observables. It is also the regime where the Efimov effect whose main characteristic is the occurrence of a sequence of three-body bound states becomes important. At unitarity, i.e., for diverging scattering length, the ratio of binding energies of neighboring states approaches a constant. The existence of those trimers can be captured by a single three-body parameter and influences observables such as recombination rates. Starting from adequate Lagrangians, we derive atom-dimer scattering amplitudes that contain all information of interest about the three-particle systems. With this method, we first investigate the scattering of atoms and dimers at finite temperature in the presence of the Efimov effect. We calculate the dimer relaxation rate and obtain good agreement with available experimental data. Furthermore, heteronuclear mixtures exhibiting large interspecies scattering length are studied in detail. If bosons are the majority species, the Efimov effect occurs in an S-wave channel and we are able to compute three-body recombination and dimer relaxation rates. The results are compared to the outcome of two existing experiments. For mainly fermionic systems, the Efimov effect is only present in an overall P-wave and three-body recombination at threshold vanishes. However, in mixtures of atoms and dimers, scattering cross sections and dimer relaxation show the typical Efimov behavior of log-periodicity. We also consider two-dimensional Bose gases, where the Efimov effect does not occur. For those systems, we derive an equation including the first non-universal corrections and deduce three-body observables such as binding energies and atom-dimer scattering parameters.
A new narrow three-atom loss resonance associated with an Efimov trimer crossing the three-atom threshold has recently been discovered in a many-body system of ultracold 6Li^{6}\mathrm{Li}6Li atoms in the three lowest hyperfine spin states at a magnetic field near 895 G. O'Hara and coworkers have used measurements of the three-body recombination rate in this region to determine the complex three-body parameter associated with Efimov physics. Using this parameter as the input, we calculate the universal predictions for the spectrum of Efimov states and for the three-body recombination rate in the universal region above 600 G where all three scattering lengths are large. We predict an atom-dimer loss resonance at $672\ifmmode\pm\else\textpm\fi{}2$ G associated with an Efimov trimer disappearing through an atom-dimer threshold. We also predict an interference minimum in the three-body recombination rate at $759\ifmmode\pm\else\textpm\fi{}1$ G where the three-spin mixture may be sufficiently stable to allow experimental study of the many-body system.