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arXiv:1103.5902 · Physical Review A

Three-body radio-frequency association of Efimov trimers

Timur V. Tscherbul, Seth T. Rittenhouse

Published Dec 9, 2011• 10 citations
arXivHTMLPDF

Abstract

We present a theoretical analysis of rf association of Efimov trimers in a two-component Bose gas with short-range interactions. Using the adiabatic hyperspherical formalism to solve the quantum three-body problem, we obtain universal expressions for three-body rf association rates as a function of the $s$-wave scattering length $a>0$. We find that the association rates scale as ${a}^{\ensuremath{-}2}$ in the limit of large $a$, and diverge as ${a}^{3}{a}_{ad}^{3}$ whenever an Efimov state crosses the atom-dimer threshold (where ${a}_{ad}$ stands for the atom-dimer scattering length). Our calculations show that trimer formation rates as large as $\ensuremath{\sim}$10${}^{\ensuremath{-}21}$ cm${}^{6}$/s can be achieved with rf Rabi frequencies on the order of 1 MHz, suggesting that direct rf association is a powerful tool for making and probing few-body quantum states in ultracold atomic gases.

DOI
10.1103/physreva.84.062706

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We present a theoretical analysis of rf association of Efimov trimers in a two-component Bose gas with short-range interactions. Using the adiabatic hyperspherical formalism to solve the quantum three-body problem, we obtain universal expressions for three-body rf association rates as a function of the sss-wave scattering length a>0a>0a>0. We find that the association rates scale as a\ensuremath−2{a}^{\ensuremath{-}2}a\ensuremath−2 in the limit of large aaa, and diverge as a3aad3{a}^{3}{a}_{ad}^{3}a3aad3​ whenever an Efimov state crosses the atom-dimer threshold (where aad{a}_{ad}aad​ stands for the atom-dimer scattering length). Our calculations show that trimer formation rates as large as \ensuremath∼\ensuremath{\sim}\ensuremath∼10\ensuremath−21{}^{\ensuremath{-}21}\ensuremath−21 cm6{}^{6}6/s can be achieved with rf Rabi frequencies on the order of 1 MHz, suggesting that direct rf association is a powerful tool for making and probing few-body quantum states in ultracold atomic gases.
Few-Body Problem Seemingly simple, quantum mechanical few-body systems are notoriously difficult to describe. Efimov trimers, three-body bound states with interactions tuned to be in close vicinity of the formation of two-body bound states, are the most tractable of these systems, with relevance, for example, in nuclear physics. Observed recently in ultracold atomic gases through their signatures in the rate of inelastic three-body collisions, Efimov trimers are predicted to appear at interaction strengths whose ratios are universally specified. By measuring binding energy as a function of interaction strength, Lompe et al. (p. 940 ) directly observed the association of three distinguishable atoms into a bound state. This technique may enable more precise studies of the trimer state, potentially revealing the nature of nonuniversal corrections suggested by prior experiments.
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.
This thesis reports on experiments studying the few-body physics of three distinguishable fermionic atoms with large scattering lengths. The experiments were performed with ultracold gases of fermionic 6Li atoms in three different hyperfine states. By tuning the strength of the interactions between the atoms with Feshbach resonances and measuring the rate constants for inelastic three-atom and atom-dimer collisions the intersections of two universal trimer states with the three-atom and atom-dimer continuum could be located. Subsequently, one of these Efimov states was directly observed with RF-association spectroscopy. Using this technique the binding energy of this Efimov state was measured as a function of the strength of the interparticle interactions. The experiments presented in this thesis provide a nearly complete understanding of the universal few-body physics of three-component Fermi gases of 6Li atoms. This understanding will be the foundation for future studies of the many-body physics of three-component Fermi gases.
The quantum mechanics of three interacting particles gives rise to fundamental and universal phenomena, such as the staircase of Efimov trimers predicted in the context of nuclear physics and observed in ultracold gases. Here, we observe a novel type of halo trimer using radio-frequency spectroscopy in an ultracold mixture of Na 23 and K 40 atoms. The trimers consist of two light bosons and one heavy fermion, and they have the structure of a Feshbach dimer weakly bound to one additional boson. We find that the trimer peak closely follows the dimer resonance over the entire range of explored interaction strengths and across an order-of-magnitude variation of the dimer energy, as reproduced by our theoretical analysis. The presence of this halo trimer is of direct relevance for many-body physics in ultracold mixtures and the association of ultracold molecules.
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 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.