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
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
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.
The Efimov states are three-body bound states, which appear universally when the s-wave scattering length between the particles is resonantly large.Since the Efimov states and their characteristic discrete scale invariance have recently been observed in ultracold atoms, the Efimov states and their associated few-body phenomena have attracted widening interest both theoretically and experimentally.In this thesis, I theoretically study the Efimov physics and related phenomena, focusing on the following three topics: (i) Universal three-body physics for a mass-imbalanced Fermi system (Chapter 3).For a system of two identical spinless (i.e., spin-polarized) fermions and one distinguishable particle which interact via a short-range potential with a large s-wave scattering length, two classes of universal three-body bound states have been known to appear in different regimes of the mass ratio: the Efimov trimers and the Kartavtsev-Malykh trimers, which feature the discrete and continuous scale invariance, respectively.I have found the third class of universal three-body bound states, which I call the "crossover trimers".The crossover trimers show neither the discrete nor continuous scale invariance.I have identified the regions of these three classes of trimers as a function of the mass ratio and the s-wave scattering length, and shown that the Kartavtsev-Malykh trimers and the Efimov trimers can continuously transform into each other via the crossover trimers as the mass ratio and the s-wave scattering length are varied.Owing to the presence of the crossover trimers, the Kartavtsev-Malykh trimers dissociate into a particle and a dimer when the s-wave scattering length is varied, inducing resonances in the particle-dimer scattering.I have calculated the elastic particle-dimer scattering lengths in arbitrary angular-momentum channels, and shown that the particle-dimer resonances indeed occur.From the resonance positions, I have found accurate values of the critical mass ratios at which the Kartavtsev-Malykh trimers in the higher angular-momentum channels appear. (ii) Universal three-body parameter (Chapter 4).In the Efimov physics, the three-body parameter fixes the short-range three-body phase and hence the scale of the energy spectrum.Until quite recently, it has been widely held that the threebody parameter should depend on the short-range part of the inter-atomic potential, and hence vary almost randomly between different atomic species and hyperfine states.However, mounting evidence in recent experiments suggests otherwise.While some theoretical studies have succeeded in reproducing the universal behavior in the three-body parameter, the underlying physical mechanism has remained unclear and controversial.In this thesis, I elucidate the physical origin of the universal three-body parameter.I propose that a non-adiabatic deformation of the three-body wave function induced by a universal two-body correlation results in a universal three-body repulsion, which prevents three particles from coming close and renders the three-body parameter universal.This mechanism is verified by reproducing the universal three-body repulsion with a simple model wave function.The mechanism found here suggests that the three-body parameter would also be universal for non-van der Waals types of potentials.For various classes of deep two-body potentials, it is shown that the effective range is the relevant length scale to characterize the two-body correlation and sets the three-body parameter.Depending on the shape of the two-body correlation, there
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.
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.
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.