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arXiv:physics/0506104 · Physical Review A

Long-range scattering resonances in strong-field-seeking states of polar molecules

Christopher Ticknor, John L. Bohn

Published Sep 15, 2005• 59 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.72.032717

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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 character of a novel set of ``field-linked'' states that were predicted by Avdeenkov and Bohn [Phys. Rev. Lett. 90, 043006 (2003)]. These states exist at ultralow temperatures in the presence of an electrostatic field, and their properties are strongly dependent on the field's strength. We clarify the nature of these quasibound states by constructing their wave functions and determining their approximate quantum numbers. As the properties of field-linked states are strongly defined by anisotropic dipolar and Stark interactions, we construct adiabatic surfaces as functions of both the intermolecular distance and the angle that the intermolecular axis makes with the electric field. Within an adiabatic approximation we solve the two-dimensional Schr\"odinger equation to find bound states, whose energies correlate well with resonance features found in fully converged multichannel scattering calculations.
Abstract Scattering resonances are an essential tool for controlling the interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances 1 , which have been extensively studied in various platforms 1–7 , are not expected to exist in most ultracold polar molecules because of the fast loss that occurs when two molecules approach at a close distance 8–10 . Here we demonstrate a new type of scattering resonance that is universal for a wide range of polar molecules. The so-called field-linked resonances 11–14 occur in the scattering of microwave-dressed molecules because of stable macroscopic tetramer states in the intermolecular potential. We identify two resonances between ultracold ground-state sodium–potassium molecules and use the microwave frequencies and polarizations to tune the inelastic collision rate by three orders of magnitude, from the unitary limit to well below the universal regime. The field-linked resonance provides a tuning knob to independently control the elastic contact interaction and the dipole–dipole interaction, which we observe as a modification in the thermalization rate. Our result provides a general strategy for resonant scattering between ultracold polar molecules, which paves the way for realizing dipolar superfluids 15 and molecular supersolids 16 , as well as assembling ultracold polyatomic molecules.
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.
The collisional stability of ultracold polar molecules in electrostatic traps is considered. Rate constants for collisions that drive molecules from weak-electric-field-seeking to strong-field-seeking states are estimated using a simple model that emphasizes long-range dipolar forces. The rate constants for collisional losses are found to vary substantially as a function of molecular parameters used in the model, such as dipole moment, mass, and the splitting of the molecular $\ensuremath{\Lambda}$ doublet. Varying these parameters over physically reasonable ranges yields rate constants as low as ${10}^{\ensuremath{-}20} {\mathrm{cm}}^{3}/\mathrm{sec}$ and as high as ${10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{sec}.$ Nevertheless, the loss rates rise dramatically in the presence of the externally applied trapping electric field. For this reason it is argued that electrostatic traps are likely to be less stable against collisional losses than their magnetic counterparts.
The elastic scattering amplitudes of indistinguishable, bosonic, strongly polar molecules possess universal properties at the coldest temperatures due to wave propagation in the long-range dipole-dipole field. Universal scattering cross sections and anisotropic threshold angular distributions, independent of molecular species, result from careful tuning of the dipole moment with an applied electric field. Three distinct families of threshold resonances also occur for specific field strengths, and can be both qualitatively and quantitatively predicted using elementary adiabatic and semiclassical techniques. The temperatures and densities of heteronuclear molecular gases required to observe these universal characteristics are predicted.