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arXiv:1004.5420 · Physical Review Letters

Universal Rates for Reactive Ultracold Polar Molecules in Reduced Dimensions

Andrea Micheli, Zbigniew Idziaszek, Guido Pupillo, Mikhail A. Baranov, P. Zoller, Paul S. Julienne

Published Aug 13, 2010• 99 citations
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Abstract

Analytic expressions describe universal elastic and reactive rates of quasi-two-dimensional and quasi-one-dimensional collisions of highly reactive ultracold molecules interacting by a van der Waals potential. Exact and approximate calculations for the example species KRb show that stability and evaporative cooling can be realized for spin-polarized fermions at moderate dipole and trapping strength, whereas bosons or unlike fermions require significantly higher dipole or trapping strengths.

DOI
10.1103/physrevlett.105.073202

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Analytic expressions describe universal elastic and reactive rates of quasi-two-dimensional and quasi-one-dimensional collisions of highly reactive ultracold molecules interacting by a van der Waals potential. Exact and approximate calculations for the example species KRb show that stability and evaporative cooling can be realized for spin-polarized fermions at moderate dipole and trapping strength, whereas bosons or unlike fermions require significantly higher dipole or trapping strengths.
Universal collision rate constants are calculated for ultracold collisions of two like bosonic or fermionic heteronuclear alkali-metal dimers involving the species Li, Na, K, Rb, or Cs. Universal collisions are those for which the short range probability of a reactive or quenching collision is unity such that a collision removes a pair of molecules from the sample. In this case, the collision rates are determined by universal quantum dynamics at very long range compared to the chemical bond length. We calculate the universal rate constants for reaction of the reactive dimers in their ground vibrational state v = 0 and for vibrational quenching of non-reactive dimers with v ≥ 1. Using the known dipole moments and estimated van der Waals coefficients of each species, we calculate electric field dependent loss rate constants for collisions of molecules tightly confined to quasi-two-dimensional geometry by a one-dimensional optical lattice. A simple scaling relation of the quasi-two-dimensional loss rate constants with dipole strength, trap frequency and collision energy is given for like bosons or like fermions. It should be possible to stabilize ultracold dimers of any of these species against destructive collisions by confining them in a lattice and orienting them with an electric field of less than 20 kV cm(-1).
Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultralow collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of the reactive scattering mechanism. Here, we report on the ab initio calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters, we then develop a single-channel scattering model with flexible boundary conditions. Our calculations show that, at low temperatures (and in the absence of an external electric field), the reaction rates between molecules or between molecules and atoms have a resonant character as a function of the short-range parameters. We also find that both the isotropic and anisotropic van der Waals coefficients have significant contributions from dipole coupling to excited electronic states. Their values can differ dramatically from those solely obtained from the permanent dipole moment. A comparison with recently obtained reaction rates of fermionic 40 K 87 Rb shows that the experimental data cannot be explained by a model where the short-range scattering parameters are independent of the relative orbital angular momentum or partial wave.
We investigate collisions of polar molecules in quasi-2D traps in the presence of an external electric field perpendicular to the collision plane. We use the quantum-defect model characterized by two dimensionless parameters: yyy and sss. The first of them is related to the probability of the reaction at short distances, whereas the latter one defines the wave function phase at short distances. For yyy close to unity we obtain universal collision rates determined by the quantum reflection process from the long-range part of the interaction potential that depends only on the van der Waals coefficient, dipole-dipole interaction and the trap frequency. For small short-range reaction probabilities collision rates are highly nonuniversal and trap induced shape resonances are visible. For high dipole moments we observe the damping of reactive collisions, which can stabilize the ultracold gas of polar molecules. The calculations were performed with help of multichannel wave funcion propagation by imposing short-range boundary condition derived from the quantum-defect model.
We study polar alkali-metal dimer scattering in a quasi-one-dimensional geometry for both reactive and nonreactive species. Elastic and reactive rates are computed as a function of the amplitude of a static electric field within a purely long-range model with suitable boundary conditions at shorter range. We describe the diatomic molecules as rigid rotors and results are compared to the fixed-dipole approximation. We show in particular that for molecules with a sufficiently strong induced dipole moment oriented perpendicular to the trap axis, the long-range repulsive interaction leads to the suppression of short-range processes. Such shielding effect occurs for both reactive and nonreactive molecules, preventing two-body reactions as well as losses due to complex-mediated processes [M. Mayle et al., Phys. Rev. A 85, 062712 (2012)] from occurring. The present results demonstrate the possibility to suppress loss rates in current ultracold molecule experiments using one-dimensional confinement.
Recent experimental developments in the loading of ultracold KRb molecules into quasi-two-dimensional traps, combined with the ability to tune the ratio between elastic and loss (inelastic, reactive) collisions through application of an external electric field, are opening the door to achieving efficient evaporative cooling of reactive polar molecules. In this paper, we use Monte Carlo simulations and semianalytic models to study theoretically the experimental parameter regimes in which evaporative cooling is feasible under current trapping conditions. We investigate the effect of the anisotropic character of dipole-dipole collisions and reduced dimensionality on evaporative cooling. We also present an analysis of the experimentally relevant antievaporation effects that are induced by chemical reactions that take place when more than one axial vibrational state is populated.