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arXiv:1302.5925 · Physical Review Letters

Atom Loss Resonances in a Bose-Einstein Condensate

Christian B. Langmack, Dane Hudson Smith, Eric Braaten

Published Jul 9, 2013• 6 citations
arXivHTMLPDF

Abstract

Atom loss resonances in ultracold trapped atoms have been observed at scattering lengths near atom-dimer resonances, at which Efimov trimers cross the atom-dimer threshold, and near two-dimer resonances, at which universal tetramers cross the dimer-dimer threshold. We propose a new mechanism for these loss resonances in a Bose-Einstein condensate of atoms. As the scattering length is ramped to the large final value at which the atom loss rate is measured, the time-dependent scattering length generates a small condensate of shallow dimers coherently from the atom condensate. The coexisting atom and dimer condensates can be described by a low-energy effective field theory with universal coefficients that are determined by matching exact results from few-body physics. The classical field equations for the atom and dimer condensates predict narrow enhancements in the atom loss rate near atom-dimer resonances and near two-dimer resonances due to inelastic dimer collisions.

DOI
10.1103/physrevlett.111.023003

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•Oct 25, 2011•1 citation
Atom loss resonances in ultracold trapped atoms have been observed at scattering lengths near atom-dimer resonances, at which Efimov trimers cross the atom-dimer threshold, and near two-dimer resonances, at which universal tetramers cross the dimer-dimer threshold. We propose a new mechanism for these loss resonances in a Bose-Einstein condensate of atoms. As the scattering length is ramped to the large final value at which the atom loss rate is measured, the time-dependent scattering length generates a small condensate of shallow dimers coherently from the atom condensate. The coexisting atom and dimer condensates can be described by a low-energy effective field theory with universal coefficients that are determined by matching exact results from few-body physics. The classical field equations for the atom and dimer condensates predict narrow enhancements in the atom loss rate near atom-dimer resonances and near two-dimer resonances due to inelastic dimer collisions.
In several experiments with ultracold trapped atoms, a narrow loss feature has been observed near an atom-dimer resonance, at which there is an Efimov trimer at the atom-dimer threshold. The conventional interpretation of these loss features is that they are produced by the avalanche mechanism, in which the energetic atom and dimer from three-body recombination undergo secondary elastic collisions that produce additional atoms with sufficient energy to escape from the trapping potential. We use Monte Carlo methods to calculate the average number of atoms lost and the average heat generated by recombination events in a Bose-Einstein condensate and in a thermal gas. We improve on previous models by taking into account the energy dependence of the cross sections, the spatial structure of the atom cloud, and the elastic scattering of the atoms. We show that the avalanche mechanism cannot produce a narrow loss feature near the atom-dimer resonance. The number of atoms lost from a recombination event can be more than twice as large as the three that would be obtained in the absence of secondary collisions. However, the resulting loss feature is broad and its peak is at a scattering length that is larger than the atom-dimer resonance and depends on the trap depth.
An Efimov trimer near the atom-dimer threshold can increase the atom loss rate in ultracold trapped atoms through the avalanche mechanism proposed by Zaccanti et al. A three-body recombination event creates an energetic atom and dimer, whose subsequent elastic collisions produce additional atoms with sufficient energy to escape from the trapping potential. We use Monte Carlo methods to calculate the average number of atoms lost and the average heat generated by recombination events in both a Bose-Einstein condensate and a thermal gas. We take into account the energy-dependence of the cross sections and the spatial structure of the atom cloud. While the number of atoms lost in a recombination event can be much larger than the value 3, we find that the avalanche mechanism does not produce a narrow loss feature near the atom-dimer resonance.
We derive a universal formula for the rate constant $\ensuremath{\beta}$ for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length aaa. We show that $\ensuremath{\beta}$ is determined by aaa and by 2 three-body parameters that also determine the binding energies and widths of Efimov states. The rate constant $\ensuremath{\beta}$ scales like $\ensuremath{\hbar}a∕m$ near the resonance, but the coefficient is a periodic function of ln(a)\mathrm{ln}(a)ln(a) that may have resonant enhancement at values of aaa that differ by multiples of 22.7.
Three-body systems with large scattering length display universal phenomena associated with a discrete scaling symmetry. These phenomena include resonant enhancement of three-body loss rates when an Efimov three-body resonance is at the scattering threshold. In particular, there can be resonant peaks in the atom-dimer relaxation rate for large positive scattering length. We improve upon earlier studies and calculate the atom-dimer relaxation rate as a function of temperature using a Bose-Einstein distribution for the thermal average. As input, we use calculations of the atom-dimer scattering phase shifts from effective field theory.
We study the collisional properties of an ultracold mixture of cesium atoms and dimers close to a Feshbach resonance near 550 G in the regime of positive sss-wave scattering lengths. We observe an atom-dimer loss resonance that is related to Efimov's scenario of trimer states. The resonance is found at a value of the scattering length that is different from a previous observation at low magnetic fields. This indicates nonuniversal behavior of the Efimov spectrum for positive scattering lengths. We compare our observations with predictions from effective field theory and with a recent model based on the van der Waals interaction. We present additional measurements on pure atomic samples in order to check for the presence of a resonant loss feature related to an avalanche effect, as suggested by observations in other atomic species. We could not confirm the presence of such a feature.
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.