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arXiv:0806.3991 · Physical Review A

Low-energy resonances and bound states of aligned bosonic and fermionic dipoles

Krittika Kanjilal, D. Blume

Published Oct 16, 2008• 33 citations
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Abstract

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 ${a}_{00}$ and ${a}_{11}$ 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.

DOI
10.1103/physreva.78.040703

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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.
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Fundamental aspects of ultracold collisions between identical bosonic or fermionic dipoles are studied under quasi-two-dimensional (Q2D) confinement. In the strongly dipolar regime, bosonic and fermion species are found to share important collisional properties as a result of the confining geometry, which suppresses the inelastic rates irrespective of the quantum statistics obeyed. A potential negative is that the confinement causes dipole-dipole resonances to be extremely narrow, which could make it difficult to explore Q2D dipolar gases with tunable interactions. Such properties are shown to be universal, and a simple WKB model reproduces most of our numerical results. In order to shed light on the many-body behavior of dipolar gases in Q2D we have analyzed the scattering amplitude and developed an energy-analytic form of the pseudopotentials for dipoles.
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.
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