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Physical Review Letters

Properties of Pseudopotentials for Higher Partial Waves

J. H. Macek, James Sternberg

Published Jul 10, 2006• 26 citations
Publisher

Abstract

Contact psuedopotentials for relative angular momentum greater than zero are of interest for the study of cold atomic gases. For bosons, it is known that when the s-wave scattering length becomes infinite, an infinite number of three-body bound states, called Efimov states, are predicted by such potentials. Realistic potentials also exhibit the such states, thus a study of the Efimov effect for contact psuedopotentials for higher partial waves and fermions is important for the study of cold atoms. In this Letter we analyze three-body states of three particles interacting via psuedopotentials for higher partial waves and show that there is an Efimov effect for three fermions interacting via p-wave psuedopotentials.

DOI
10.1103/physrevlett.97.023201

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Contact psuedopotentials for relative angular momentum greater than zero are of interest for the study of cold atomic gases. For bosons, it is known that when the s-wave scattering length becomes infinite, an infinite number of three-body bound states, called Efimov states, are predicted by such potentials. Realistic potentials also exhibit the such states, thus a study of the Efimov effect for contact psuedopotentials for higher partial waves and fermions is important for the study of cold atoms. In this Letter we analyze three-body states of three particles interacting via psuedopotentials for higher partial waves and show that there is an Efimov effect for three fermions interacting via p-wave psuedopotentials.
Using the framework of effective field theory, we present a detailed study of the Efimov effect in higher partial waves for systems of two identical particles and a third distinguishable particle. Depending on the total angular momentum LLL, the two identical particles must be bosons or fermions. We derive analytical expressions for the elastic and inelastic atom-dimer scattering cross sections as well as the atom-dimer relaxation rate at the dimer breakup threshold. For the experimentally most relevant case of P-waves, we numerically calculate the atom-dimer scattering cross sections and relaxation rates as a function of the scattering length, three-body parameter, and mass ratio for energies away from the breakup threshold.
A class of universal ``three-body'' bound states has been recently predicted theoretically for identical fermions interacting at ppp-wave resonance in two dimensions. This phenomenon is called the super Efimov effect since the binding energies of the states follow a intriguing double exponential scaling. However, experimental resolution of this scaling is expected to meet formidable challenges. In this work, we introduce a thermodynamic quantity, the three-body contact ${C}_{\ensuremath{\theta}}$, to quantify three-body correlations in a two-dimensional gas composed of the resonantly interacting fermions; the contact ${C}_{\ensuremath{\theta}}$ is the consequence of the underlying universal super Efimov effect in the many-body context. We show how ${C}_{\ensuremath{\theta}}$ affects physical observables such as the radio-frequency spectrum, the momentum distribution, and the atom loss rate. The signature of the elusive super Efimov effect can be pinned down by the detection of the three-body contact ${C}_{\ensuremath{\theta}}$ via these observables in the many-body system.
The interaction of two atoms at energies in the microkelvin range is mainly characterized by one parameter, namely, the s-wave scattering length. Efimov showed that when the scattering length was effectively infinite, i.e. much larger than the natural length scale of the atoms, a large number of three-body bound states could form even when the two-body system supported only one weakly bound state, or possibly none at all. The states are bound in an effective 1/ R 2 potential and therefore form a series with a characteristic energy spacing. These states are called Efimov states and are conceptually important since they indicate a new way to form aggregates of particles. They bear some relation to vibrationally bound states of three atoms. The theory of these states and their relation to vibrational binding is reviewed in light of recent experimental measurements.
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.
Whether the Efimov effect is possible, in principle, for ppp-wave or higher partial-wave interactions is a fundamental question. Recently, there has been a claim that three nonrelativistic particles with resonant ppp-wave interactions exhibit the Efimov effect. We point out that the assumed ppp-wave scattering amplitude inevitably causes a negative probability. This indicates that the Efimov states found there cannot be realized in physical situations. We also restate our previous argument that the Efimov effect, defined as an infinite tower of universal bound states characterized by discrete scale invariance, is impossible for ppp-wave or higher partial-wave interactions.