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Europhysics Letters (EPL)

Efimov states for systems with negative scattering lengths

S. Jonsell

Published Aug 30, 2006• 31 citations
Publisher

Abstract

The recent experimental results showing the existence of an Efimov state (Kraemer T. et al. , Nature , 440 (2006) 315) are used to fix the three-body parameter for cesium. With the value of this parameter known, several three-body properties can be calculated quantitatively, without any other information about the boson-boson interaction. Finite-temperature results for the rate of formation of dimers are found to agree very well with the experimental results. Properties of bound Efimov states and predissociative Efimov resonances are calculated. The lifetime of the predissociative resonances are calculated using the complex coordinate rotation method. For Efimov states confined by an external harmonic potential there are significant changes to both energies and lifetimes if the oscillator length is comparable to or smaller than the two-body scattering length.

DOI
10.1209/epl/i2006-10235-1

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The recent experimental results showing the existence of an Efimov state (Kraemer T. et al. , Nature , 440 (2006) 315) are used to fix the three-body parameter for cesium. With the value of this parameter known, several three-body properties can be calculated quantitatively, without any other information about the boson-boson interaction. Finite-temperature results for the rate of formation of dimers are found to agree very well with the experimental results. Properties of bound Efimov states and predissociative Efimov resonances are calculated. The lifetime of the predissociative resonances are calculated using the complex coordinate rotation method. For Efimov states confined by an external harmonic potential there are significant changes to both energies and lifetimes if the oscillator length is comparable to or smaller than the two-body scattering length.
Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the particular type of the two-body interaction potential. Efimov's scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. This resonance develops into a continuum resonance at non-zero collision energies, and we observe a shift of the resonance position as a function of temperature. We also report on a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point from which to explore the universal properties of resonantly interacting few-body systems.
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.
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.
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.
We report the observation of a three-body recombination resonance in an ultracold gas of cesium atoms at a very large negative value of the s-wave scattering length. The resonance is identified as the second triatomic Efimov resonance, which corresponds to the situation where the first excited Efimov state appears at the threshold of three free atoms. This observation, together with a finite-temperature analysis and the known first resonance, allows the most accurate demonstration to date of the discrete scaling behavior at the heart of Efimov physics. For the system of three identical bosons, we obtain a scaling factor of 21.0(1.3), close to the ideal value of 22.7.
We report the observation of a three-body recombination resonance in an ultracold gas of cesium atoms at a very large negative value of the s-wave scattering length.The resonance is identified as the second triatomic Efimov resonance, which corresponds to the situation where the first excited Efimov state appears at the threshold of three free atoms.This observation, together with a finite-temperature analysis and the known first resonance, allows the most accurate demonstration to date of the discrete scaling behavior at the heart of Efimov physics.For the system of three identical bosons, we obtain a scaling factor of 21.0(1.3),close to the ideal value of 22.7.