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arXiv:1112.4934 · Physical Review A

Universal bound and scattering properties for two dipoles

Yujun Wang, Chris H. Greene

Published Feb 10, 2012• 14 citations
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Abstract

The bound state and low-energy scattering properties of two oriented dipoles are investigated for both bosonic and fermionic symmetries. Interestingly, a universal scaling emerges for the expectation value of the angular momentum for deeply bound two-dipole states. This scaling traces to the pendulum motion of two dipoles in the strong dipole regime. The low-energy scattering phase shifts of two dipoles also show universal behavior. These universal observations make connections to the scaling laws reported by Wang et al. [Phys. Rev. Lett. 106, 233201 (2011); Phys. Rev. Lett. 107, 233201 (2011)] for three dipoles.

DOI
10.1103/physreva.85.022704

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The bound state and low-energy scattering properties of two oriented dipoles are investigated for both bosonic and fermionic symmetries. Interestingly, a universal scaling emerges for the expectation value of the angular momentum for deeply bound two-dipole states. This scaling traces to the pendulum motion of two dipoles in the strong dipole regime. The low-energy scattering phase shifts of two dipoles also show universal behavior. These universal observations make connections to the scaling laws reported by Wang et al. [Phys. Rev. Lett. 106, 233201 (2011); Phys. Rev. Lett. 107, 233201 (2011)] for three dipoles.
The low-energy scattering properties of two aligned identical bosonic and identical fermionic dipoles are analyzed. Generalized scattering lengths are determined as functions of the dipole moment and the scattering energy. Near resonance, where a new bound state is being pulled in, all nonvanishing generalized scattering lengths diverge, with the a00{a}_{00}a00​ and a11{a}_{11}a11​ scattering lengths being dominant for identical bosons and identical fermions, respectively. Implications for the energy spectrum and the eigenfunctions of trapped two-dipole systems and for pseudopotential treatments are discussed.
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.
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.
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
This contribution reports recent investigations on low-energy scaling properties of three-body systems, by considering elastic s –wave collisions of a particle in a bound-state formed by the remaining two-body system. First, some previous results for the case of the halo nucleus 20 C will be revised, for the neutron– 19 C scattering properties near the critical condition for the occurrence of an excited bound state in 20 C, within a neutron–neutron– 18 C configuration. In our approach, we consider the Faddeev formalism with renormalized zero-range two-body interactions. Next, by considering the actual possibilities for verification of low-energy scaling properties in cold-atom laboratories, the approach is extended to atomic strongly-mass-imbalanced three-body systems, with two identical heavy particles and a light one. In this case, we consider that the heavy particle is being scattered by the light-heavy weakly-bound dimer. Our preliminary results for scattering observable are evidencing the universal scaling features.
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.