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arXiv:1610.06153 · ChemPhysChem

Near Threshold Effects on Recombination and Vibrational Relaxation in Efimov Systems

Di Shu, I. Simbotin, Robin Côté

Published Oct 19, 2016• 5 citations
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Abstract

Abstract We investigate the energy dependence of inelastic processes in systems which possess Efimov states. We consider the three‐body recombination rate K3 where three free atoms interact to produce an atom–dimer pair, and the relaxation rate Krel where an atom quenches a weakly bound state of a dimer near an Efimov resonance to more deeply bound levels. Using a model capturing the key features of the Efimov problem, we identify new energy regimes for K3, namely the near threshold resonance (NTR) regime behavior E−2 for negative scattering lengths and the near threshold suppression (NTS) regime behavior E2 for positive scattering lengths. We also confirm a previously found oscillatory behavior of K3 at higher energy E. Finally, we find that Krel behaves as E−1 in the NTR regime.

DOI
10.1002/cphc.201600971

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Abstract We investigate the energy dependence of inelastic processes in systems which possess Efimov states. We consider the three‐body recombination rate K3 where three free atoms interact to produce an atom–dimer pair, and the relaxation rate Krel where an atom quenches a weakly bound state of a dimer near an Efimov resonance to more deeply bound levels. Using a model capturing the key features of the Efimov problem, we identify new energy regimes for K3, namely the near threshold resonance (NTR) regime behavior E−2 for negative scattering lengths and the near threshold suppression (NTS) regime behavior E2 for positive scattering lengths. We also confirm a previously found oscillatory behavior of K3 at higher energy E. Finally, we find that Krel behaves as E−1 in the NTR regime.
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.
We find that universal three-body physics extends beyond the threshold regime to non-zero energies. For ultracold atomic gases with a negative two-body s-wave scattering length near a Feshbach resonance, we show that the resonant peaks characteristic of Efimov physics persist in three-body recombination to higher collision energies. For this and other inelastic processes, we use the adiabatic hyperspherical representation to derive universal analytical expressions for their dependence on the scattering length, the collision energy and—for narrow resonances—the effective range. These expressions are supported by full numerical solutions of the Schrödinger equation and display log-periodic dependence on energy characteristic of Efimov physics. This dependence is robust and might be used to experimentally observe several Efimov features.
We describe three-body collisions close to a Feshbach resonance by taking into account two-body scattering processes involving both the open and the closed channels. We extract the atom-dimer scattering length and the three-body recombination rate, predicting the existence at negative scattering length of a sharp minimum in the recombination losses due to the presence of a shallow bound level. We obtain very good agreement with the experimental results in atomic 133Cs^{133}\mathrm{Cs}133Cs of Kraemer et al. [Nature (London) 440, 315 (2006)], and predict the position of Efimov resonances in a gas of 39K^{39}\mathrm{K}39K atoms.
Efimov physics refers to universal phenomena associated with a discrete scaling symmetry in the three-body problem with a large scattering length. The first experimental evidence for Efimov physics was the recent observation of a resonant peak in the three-body recombination rate for 133Cs^{133}\mathrm{Cs}133Cs atoms with large negative scattering length. There can also be resonant peaks in the atom-dimer relaxation rate for large positive scattering length. We calculate the atom-dimer relaxation rate as a function of temperature and show how measurements of the relaxation rate can be used to determine accurately the parameters that govern Efimov physics.
The resonant profile of the rate coefficient for three-body recombination into a shallow dimer is investigated for mass-imbalanced systems. In the low-energy limit, three atoms collide with zero-range interactions, in a regime where the scattering lengths of the heavy–heavy and the heavy–light subsystems are positive and negative, respectively. For this physical system, the adiabatic hyperspherical representation is combined with a fully semi-classical method and we show that the shallow dimer recombination spectra display an asymmetric lineshape that originates from the coexistence of Efimov resonances with Stückelberg interference minima. These asymmetric lineshapes are quantified utilizing the Fano profile formula. In particular, a closed-form expression is derived that describes the width of the corresponding Efimov resonances and the Fano lineshape asymmetry parameter q. The profile of Efimov resonances exhibits a q-reversal effect as the inter- and intra-species scattering lengths vary. In the case of a diverging asymmetry parameter, i.e., |q|→∞, we show that the Efimov resonances possess zero width and are fully decoupled from the three-body and atom–dimer continua, and the corresponding Efimov metastable states behave as bound levels.
A fundamental aspect of scattering is the appearance of resonances, which appear in many systems. Although their effect is often lost due to averaging at room temperatures or higher, they can become dominant features at low or ultralow temperatures, where only a few partial waves contribute to the scattering process. Our ability to form and manipulate ultracold molecules provides the seed to study in a precise and controlled fashion the role of single partial waves, and state-to-state processes in chemical systems. We explore resonances occurring due to the existence of a quasi-bound state in the entrance channel of a scattering system and explain the energy scaling due to these near threshold resonances (NTR) based on the properties of the Jost functions. We also investigate the threshold resonance effects in the Efimov systems which have been studied in a variety of context, such as three-body Coulomb systems and nuclear three-body systems. Numerical schemes based on Milne's phase-amplitude approach are formulated to analyze NTR effects. We present a simple and practical approach to solve the long-standing problem of finding the non-oscillatory solution to Milne's equation. Our numerical approach also gives an integral representation of scattering phase shift and allows us to compute ultra-narrow shape resonances.