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Bulletin of the American Physical Society

Few-body physics for bosonic and fermionic dipoles

Yujun Wang

Published Jun 6, 2012• 0 citations
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Abstract

This invited talk, coauthored by Jose D’Incao and Chris Greene, will review our theoretical evidence that predicts an Efimov effect for three interacting bosonic polar molecules. Interestingly, the hyperspherical coordinate treatment shows a universal barrier which implies that the three-body parameter is rather accurately known in terms of the dipole length. It was not a foregone conclusion that three bosonic dipoles would exhibit Efimov physics, given that the original derivation and also subsequent work was for systems with short-range interactions only, and moreover, for systems having conserved angular momentum. Despite the fact that neither of these properties holds for three bosonic dipoles oriented in an external electric field, Efimov physics emerges naturally. For three fermionic dipoles in the same spin substate, on the other hand, there is no Efimov effect, but there is a single universal bound (or quasi-bound) state predicted to occur. Conditions under which these novel 3-dipole states could be observed experimentally will be discussed at the meeting.

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•Jan 1, 2011•0 citations
This invited talk, coauthored by Jose D’Incao and Chris Greene, will review our theoretical evidence that predicts an Efimov effect for three interacting bosonic polar molecules. Interestingly, the hyperspherical coordinate treatment shows a universal barrier which implies that the three-body parameter is rather accurately known in terms of the dipole length. It was not a foregone conclusion that three bosonic dipoles would exhibit Efimov physics, given that the original derivation and also subsequent work was for systems with short-range interactions only, and moreover, for systems having conserved angular momentum. Despite the fact that neither of these properties holds for three bosonic dipoles oriented in an external electric field, Efimov physics emerges naturally. For three fermionic dipoles in the same spin substate, on the other hand, there is no Efimov effect, but there is a single universal bound (or quasi-bound) state predicted to occur. Conditions under which these novel 3-dipole states could be observed experimentally will be discussed at the meeting.
Three oriented bosonic dipoles are treated by using the hyperspherical adiabatic representation, providing numerical evidence that the Efimov effect persists near a two-dipole resonance and in a system where angular momentum is not conserved. Our results further show that the Efimov features in scattering observables become universal, with a known three-body parameter; i.e., the resonance energies depend only on the two-body physics, which also has implications for the universal spectrum of the four-dipole problem. Moreover, the Efimov states should be long-lived, which is favorable for their creation and manipulation in ultracold dipolar gases. Finally, deeply bound two-dipole states are shown to be relatively stable against collisions with a third dipole, owing to the emergence of a repulsive interaction originating in the angular momentum nonconservation for this system.
In recent years extensive theoretical and experimental studies of universal few-body physics have advanced our understanding of universal Efimov physics. Whereas theory had been the driving force behind our understanding of Efimov physics for decades, recent experiments have contributed an unexpected discovery. Specifically, measurements have found that the so-called three-body parameter determining several properties of the system is universal, even though fundamental assumptions in the theory of the Efimov effect suggest that it should be a variable property that depends on the precise details of the short-range two- and three-body interactions. The present Letter resolves this apparent contradiction by elucidating previously unanticipated implications of the two-body interactions. Our study shows that the three-body parameter universality emerges because a universal effective barrier in the three-body potentials prevents the three particles from simultaneously getting close together. Our results also show limitations on this universality, as it is more likely to occur for neutral atoms but less likely to extend to light nuclei.
Armed with a new solution to the four-body problem, we reanalyze the recent Innsbruck observation of an Efimov resonance in three-body collisions of cesium atoms, and show that it provides evidence of new, universal four-body physics as well. Our theoretical treatment of four bosonic atoms in the limit of strong two-body attraction suggests a ubiquitous result: namely, that resonantly-bound states of all four atoms should occur whenever the two-body scattering length is a specific fraction (0.43) of the value where a three-body Efimov resonance occurs. A hitherto unanalyzed feature in the 2006 Innsbruck experiment supports this universal prediction, and it provides the first known evidence to date that a direct four-body recombination process plays a role. While we confirm the conclusion reached previously by some studies that no true Efimov effect exists for four particles, we demonstrate the existence of a universal class of four-body states that are intimately connected with three-body Efimov states.
The presence of few-body bound states is an important issue in the study of interacting bosonic systems due to the instability it introduces into the condensation. The problem is more interesting in two dimensions because the system can host only a finite number of bound states, in contrast to the Efimov effect in three dimensions. The authors considered a two-component bosonic system in two dimensions, with repulsive intra- and attractive inter-species interactions. They found that there is only one three-particle bound state and the binding energies for various scattering lengths fall on an universal curve, where the microscopic details are of no relevance. Their conclusion is pertinent for various systems such as excitons in quantum well structures and bosonic dipoles in bilayer geometries. They developed an efficient renormalization group type method, capable of handling both short- and long- range physics and free of numerical instabilities. This method also makes use of the Hopf coordinates and running basis to reduce the proliferation of hyperspherical harmonics appearing in alternative approaches, yielding significant saving in numerical implementations.
A quantum-mechanical description is presented for the three-body physics of shielded dipolar molecules, including a prediction of observable Efimov physics. Despite the anisotropic and long-range nature of the interaction, shielding enables a regime in which universality emerges already at the two-body level and extends to the three-body sector, where Efimov physics emerges. On the negative side of the scattering-length resonance, computed trimer binding energies display the characteristic scaling expected for Efimov resonances. Finally, the sudden approximation can be used to create trimer bound states, starting from positive energy trap states as a way to create or detect these molecular trimers. Moreover, the three-body parameter expressed in dipolar units is found to be universal.
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