We study the manifestations of universal four-body physics in ultracold dimer-dimer collisions. We show that resonant features associated with three-body Efimov physics and dimer-dimer scattering lengths are universally related. The emergence of universal four-boson states allows for the tunability of the dimer-dimer interaction, thus enabling the future study of ultracold molecular gases with both attractive and repulsive interactions. Moreover, our study of the interconversion between dimers and Efimov trimers shows that B2+B2-->B3+B rearrangement reactions can provide an efficient trimer formation mechanism. Our analysis of the temperature dependence of this reaction provides an interpretation of the available experimental data and sheds light on the possible experimental realization of rearrangement processes in ultracold gases.
We study the manifestations of universal four-body physics in ultracold dimer-dimer collisions. We show that resonant features associated with three-body Efimov physics and dimer-dimer scattering lengths are universally related. The emergence of universal four-boson states allows for the tunability of the dimer-dimer interaction, thus enabling the future study of ultracold molecular gases with both attractive and repulsive interactions. Moreover, our study of the interconversion between dimers and Efimov trimers shows that B2+B2-->B3+B rearrangement reactions can provide an efficient trimer formation mechanism. Our analysis of the temperature dependence of this reaction provides an interpretation of the available experimental data and sheds light on the possible experimental realization of rearrangement processes in ultracold gases.
We consider weakly bound bosonic and fermionic heteronuclear molecules (dimers) in ultracold atomic gases, where the interspecies interaction is characterized by a large positive scattering length. We develop a new theoretical approach to solve the four-body scattering problem, which is valid when the mass ratio between the constituent atoms is sufficiently large. This approach is then used to study elastic and inelastic dimer- dimer scattering processes in the case that the light constituent atoms are fermions, while the heavy atoms can be either fermions or bosons. Due to the Fermi statistics of the light atoms, the heavy atoms experience a strong repulsion at large intermolecular distances. This leads to suppression of the collisional relaxation to universal trimer (Efimov) states and/or deeply bound molecular states. We present the formation rate of Efimov trimers as a function of the three-body parameter for several experimentally interesting systems. The competition between the formation of trimers and relaxation to deeply bound molecules is analyzed, and prospects for future studies of these systems are discussed.
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
Ultracold gases of three distinguishable particles with large scattering lengths are expected to show rich few-body physics related to the Efimov effect. We have created three different mixtures of ultracold 6Li atoms and weakly bound 6Li2 dimers consisting of atoms in three different hyperfine states and studied their inelastic decay via atom-dimer collisions. We have found resonant enhancement of the decay due to the crossing of Efimov-like trimer states with the atom-dimer continuum in one mixture as well as minima of the decay in another mixture, which we interpret as a suppression of exchange reactions of the type |12+|3→|23+|1. Such a suppression is caused by interference between different decay paths and demonstrates the possibility of using Efimov physics to control the rate constants for molecular exchange reactions in the ultracold regime.
We discuss the collisional formation of Efimov trimers via ultracold four-body recombination. In particular, we consider the reaction A+A+A+B-->A_{3}+B with A and B ultracold atoms. We obtain expressions for the four-body recombination rate up to an overall constant and show that it reflects the three-body Efimov physics either as a function of collision energy or as a function of the two-body s-wave scattering length between A atoms. In addition, we briefly discuss issues important for experimentally observing this interesting and unexplored process.
Abstract We provide a general discussion on the importance of three-body Efimov physics for strongly interacting ultracold quantum gases. Using the adiabatic hyperspherical representation, we discuss a universal classification of three-body systems in terms of the attractive or repulsive character of the effective interactions. The hyperspherical representation leads to a simple and conceptually clear picture for the bound and scattering properties of three-body systems with strong s -wave interactions. Using our universal classification scheme, we present a detailed discussion of all relevant ultracold three-body scattering processes using a pathway analysis that makes evident the importance of Efimov physics in determining the energy and scattering length dependence of such processes. This article provides a general overview of the current status of the field and a discussion of various issues relevant to the lifetime and stability of ultracold quantum gases along with universal properties of ultracold, resonantly interacting, few-body systems.