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Quantum-Atom Optics Downunder (QAO)

On Scattering Ground State Polar Molecules

Christopher Ticknor

Published Jan 1, 2007• 0 citations
Publisher

Abstract

We report a theoretical study on the nature of scattering polar molecules in the presence of an electric field in their absolute ground state. Most important is the illustration that the s-wave scattering length does not parametrize the scattering at low energies even when the electric field is non-zero. Furthermore we show that a simple semi-classical scattering cross section can be used to estimate the total cross section accurately for particular field and energy values.

DOI
10.1364/qao.2007.qme10

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We report a theoretical study on the nature of scattering polar molecules in the presence of an electric field in their absolute ground state. Most important is the illustration that the s-wave scattering length does not parametrize the scattering at low energies even when the electric field is non-zero. Furthermore we show that a simple semi-classical scattering cross section can be used to estimate the total cross section accurately for particular field and energy values.
We explore the total collisional cross section of ground-state polar molecules in an electric field at various energies, focusing on RbCs\mathrm{RbCs}RbCs and RbK\mathrm{RbK}RbK. An external electric field polarizes the molecules and induces strong dipolar interactions, leading to nonzero partial waves contributing to the scattering even as the collision energy goes to zero. This results in the need to compute scattering problems with many different values of total MMM to converge the total cross section. An accurate and efficient approximate total cross section is introduced and used to study the low-field temperature dependence. To understand the scattering of the polar molecules we compare a semiclassical cross section with the quantum unitarity limit. This comparison leads to the ability to characterize the scattering based on the value of the electric field and the collision energy. General and simple forms of the characteristic electric field and energy are given, enabling characterization of the scattering.
We present first steps toward understanding the ultracold scattering properties of polar molecules in strong electric field-seeking states. We have found that the elastic cross section displays a quasiregular set of potential resonances as a function of the electric field, which potentially offers intimate details about the intermolecular interaction. We illustrate these resonances in a ``toy'' model composed of pure dipoles, and in more physically realistic systems. To analyze these resonances, we use a simple WKB approximation to the eigenphase, which proves both reasonably accurate and meaningful. A general treatment of the Stark effect and dipolar interactions is also presented.
We explore the impact of the short-range interaction on the scattering of ground state polar molecules and study the transition from a weak to strong dipolar scattering over an experimentally reasonable range of energies and electric field values. In the strong dipolar limit, the scattering scales with respect to a dimensionless quantity defined by mass, induced dipole moment, and collision energy. The scaling has implications for all quantum mechanical dipolar scattering. Furthermore the universal scattering regime will readily be achieved with polar molecules at ultracold temperatures.
A detailed study is made of the nature of rotational Feshbach resonances in the elastic scattering of extremely-low-energy electrons by diatomic polar molecules. The bound-state properties of an electron in the field of a dipole rotator, determined previously, are used in establishing the resonance behavior of elastic-scattering phase shifts in the energy region below the first rotational excitation threshold. Feshbach resonances of very narrow widths are found in partial-wave scattering channels with total angular momenta greater than zero when the strength of the interaction potentials is somewhat less than that necessary to yield bound states of the same symmetry type, and very much less than those necessary to yield a "bound state" of the projected Hamiltonian QHQ\mathrm{QHQ}QHQ. The latter implies a non-negligible value of the resonance energy shift for polar molecules.
We investigate the scattering cross section of aligned dipolar molecules in low-temperature gases. Over a wide range of collision energies relevant to contemporary experiments, the cross section declines in inverse proportion to the collision speed, and is given nearly exactly by a simple semiclassical formula. At yet lower energies, the cross section becomes independent of energy, and is reproduced within the Born approximation to within corrections due to the s-wave scattering length. While these behaviors are universal for all polar molecules, nevertheless interesting deviations from universality are expected to occur in the intermediate energy range.
We investigate the scattering cross section of aligned dipolar molecules in low-temperature gases. Over a wide range of collision energies relevant to contemporary experiments, the cross section declines in inverse proportion to the collision speed, and is given nearly exactly by a simple semiclassical formula. At yet lower energies, the cross section becomes independent of energy, and is reproduced within the Born approximation to within corrections due to the s-wave scattering length. While these behaviors are universal for all polar molecules, nevertheless interesting deviations from universality are expected to occur in the intermediate energy range.