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arXiv:1106.6133 · Physical Review Letters

Universal Three-Body Physics for Fermionic Dipoles

Yujun Wang, José Paulo D'Incao, Chris H. Greene

Published Nov 29, 2011• 35 citations
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Abstract

Our present study of the universal physics for three oriented fermionic dipoles in the hyperspherical adiabatic representation predicts a single long-lived three-dipole state, which exists in only one three-body symmetry and forms near a two-dipole resonance. Our analysis reveals the spatial configuration of the universal state and the scaling of its binding energy and lifetime with the strength of the dipolar interaction. In addition, three-body recombination of fermionic dipoles is found to be important even at ultracold energies. An additional finding is that an effective long-range repulsion arises between a dipole and a dipolar dimer that is tunable via dipolar interactions.

DOI
10.1103/physrevlett.107.233201

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Our present study of the universal physics for three oriented fermionic dipoles in the hyperspherical adiabatic representation predicts a single long-lived three-dipole state, which exists in only one three-body symmetry and forms near a two-dipole resonance. Our analysis reveals the spatial configuration of the universal state and the scaling of its binding energy and lifetime with the strength of the dipolar interaction. In addition, three-body recombination of fermionic dipoles is found to be important even at ultracold energies. An additional finding is that an effective long-range repulsion arises between a dipole and a dipolar dimer that is tunable via dipolar interactions.
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.
We study three-body recombination in two dimensions for systems interacting via short-range two-body interactions in the regime of large scattering lengths. Using the adiabatic hyperspherical representation, we derive semianalytical formulas for three-body recombination in both weakly and deeply bound diatom states. Our results demonstrate the importance of long-range corrections to the three-body potentials by showing how they alter the low-energy and scattering-length dependence of the recombination rate for both bosonic and fermionic systems, which exhibit suppressed recombination if compared to the three-dimensional case. We verify these results through numerical calculations of recombination for systems with finite-range interactions and supporting a few two-body bound states. We also study finite-range effects for the energies of the universal three-identical-bosons states and find a slow approach to universal predictions as a function of the scattering length.
We use universality in two-body dipolar physics to study three-body recombination. We present results for the universal structure of weakly bound two-dipole states that depend only on the s-wave scattering length (a). We study threshold three-body recombination rates into weakly bound dimer states as a function of the scattering length. A Fermi golden rule analysis is used to estimate rates for different events mediated by the dipole-dipole interaction and a phenomenological contact interaction. The three-body recombination rate in the limit where a≫D contains terms which scale as a{4}, a{2}D{2}, and D4, where D is the dipolar length. When a≪D, the three-body recombination rate scales as D4.
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.
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.
Recombination of identical, spin-polarized fermions in cold three-body collisions is investigated. We parametrize the mechanisms for recombination in terms of the `scattering volume' V p and another length scale r 0 . Model two-body interactions were used within the framework of the adiabatic hyperspherical representation. We examine the recombination rate K 3 as a function of the collision energy E for various values of V p . Not only do we consider the dominant J Π = 1 + case, but also the next-leading order contributions from J Π = 1 - and 3 - . We discuss the behaviour near a two-body resonance and the expected universality of fermionic recombination. Comparisons with boson recombination are considered in detail.