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Efimov trimers in a harmonic potential and universality in three-body recombination

S. J. J. M. F. Kokkelmans, Portegies, JW Jim, Noam Gross, Zav Shotan, Lev Khaykovich

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

We report on experimental evidence of universality in ultracold 7Li atoms’three-body recombination loss in the vicinity of a Feshbach resonance [1]. We observe a recombination minimum and an Efimov resonance in regions of positive and negative scattering lengths. Both observed features lie deeply within the range of validity of the universal theory and we find that the relations between their widths and locations, are in an excellent agreement with the theoretical predictions. We also investigate the possibility to stabilize Efimov trimers in optical 1 attices. We present universal solutions of three bosons in a harmonic potential, for all ranges of the scattering length and harmonic oscillator length. We compare our results to the limiting cases, such as that of a vanishing trapping potential. The combination of being able to tune both length parameters gives rise to quite distinct solutions of these trimers, and allows for minimizing the inelastic losses.

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We report on experimental evidence of universality in ultracold 7Li atoms’three-body recombination loss in the vicinity of a Feshbach resonance [1]. We observe a recombination minimum and an Efimov resonance in regions of positive and negative scattering lengths. Both observed features lie deeply within the range of validity of the universal theory and we find that the relations between their widths and locations, are in an excellent agreement with the theoretical predictions. We also investigate the possibility to stabilize Efimov trimers in optical 1 attices. We present universal solutions of three bosons in a harmonic potential, for all ranges of the scattering length and harmonic oscillator length. We compare our results to the limiting cases, such as that of a vanishing trapping potential. The combination of being able to tune both length parameters gives rise to quite distinct solutions of these trimers, and allows for minimizing the inelastic losses.
We report on experimental evidence of universality in ultracold 7Li atoms' three-body recombination loss in the vicinity of a Feshbach resonance. We observe a recombination minimum and an Efimov resonance in regions of positive and negative scattering lengths, respectively, which are connected through the pole of the Feshbach resonance. Both observed features lie deeply within the range of validity of the universal theory, and we find that the relations between their properties, i.e., widths and locations, are in excellent agreement with the theoretical predictions.
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.
Universality is a fundamental property of diverse few-body systems such as atomic nuclei, simple molecules or ultracold atoms. It is related to a peculiar quantum mechanical phenomenon which was discovered by Russian theoretician Vitaly Efimov in the early 1970-s. A consequence of his prediction was the existence of an infinite number of bound energy levels for three particles even if a short-range two-body potential is just not deep enough to bind two particles together. This counterintuitive discovery attracted a great deal of interest but lacked an experimental verification for many years. Difficulties in finding a system where the inter-particle potential can be changed easily were answered recently with the experimental demonstration of Feshbach resonances in ultracold atoms. In the limit of zero collision energy the two-body interactions are determined by a single parameter, the scattering length a, which is defined by the low energy s-wave scattering phase-shift. In the vicinity of a Feshbach resonance this parameter diverges and thus can be readily tuned to large values and different signs by an experimentally easy-to-use change of the external magnetic field. A universal behavior is expected when a becomes the largest length scale in the system. In this case the three-body observables depend only on the scattering length and on a three-body parameter which serves as a boundary condition for the short range physics. The first experimental evidence for the existence of Efimov quantum states was reported in 2006 in a system of ultracold Cs atoms by the Innsbruck group. They investigated three-body recombination induced loss of atoms from a shallow optical trap and showed the enhancement of this loss at certain values of the scattering length. It was
We report on the measurement of four-body recombination rate coefficients in an atomic gas. Our results obtained with an ultracold sample of cesium atoms at negative scattering lengths show a resonant enhancement of losses and provide strong evidence for the existence of a pair of four-body states, which is strictly connected to Efimov trimers via universal relations. Our findings confirm recent theoretical predictions and demonstrate the enrichment of the Efimov scenario when a fourth particle is added to the generic three-body problem.
Under certain circumstances, three or more interacting particles may form bound states. Although the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associated four-body bound states. A total of 11 precisely determined three- and four-body features are found in the inelastic-loss spectrum. Their relative locations on either side of the resonance agree well with universal theory, whereas a systematic deviation from universality is found when comparing features across the resonance.
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.