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AIP conference proceedings

Energetic dependencies of total cross section of quantum anisotropic scattering in two dimensions

Eugene A. Koval, Oksana A. Koval

Published Jan 1, 2019• 0 citations
Publisher

Abstract

The quantum anisotropic scattering in two dimensions is investigated using an example of a scattering of two arbitrarily oriented dipoles moving in a plane, that models the intermolecular interaction processes in ultracold gases of diatomic polar molecules in 1D optical traps. The aim of this paper is a numerical analysis of energetic dependencies of the total cross section. It confirmed the resonance nature of the peaks of the total cross section dependence on the parameters of the system (the short-range interaction radius; the tilt angle of the dipoles in respect with the Z-axis, perpendicular to the plane of motion).

DOI
10.1063/1.5130131

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The quantum anisotropic scattering in two dimensions is investigated using an example of a scattering of two arbitrarily oriented dipoles moving in a plane, that models the intermolecular interaction processes in ultracold gases of diatomic polar molecules in 1D optical traps. The aim of this paper is a numerical analysis of energetic dependencies of the total cross section. It confirmed the resonance nature of the peaks of the total cross section dependence on the parameters of the system (the short-range interaction radius; the tilt angle of the dipoles in respect with the Z-axis, perpendicular to the plane of motion).
We report numerical investigation of the short range interaction influence on the two-dimensional quantum scattering of two dipoles. The model simulates two ultracold polar molecules collisions in two spatial dimensions. The used algorithm allows us to quantitatively analyse the scattering of two polarized dipoles with account for strongly anisotropic nature of dipolar interaction. The strong dependence of the scattering total cross section on the short range interaction radius was discovered for threshold collision energies. We also discuss differences of calculated scattering cross section dependencies for different polarisation axis tilt angles.
The impact of the short-range interaction on the resonances' occurrence in the anisotropic dipolar scattering in a plane is numerically investigated for the arbitrarily oriented dipoles and for a wide range of collision energies. We reveal the strong dependence of the cross section of the two-dimensional (2D) dipolar scattering on the radius of short-range interaction, which is modeled by a hard wall potential and by the more realistic Lennard-Jones potential, and on the mutual orientations of the dipoles. We define the critical (magic) tilt angle of one of the dipoles, depending on the direction of the second dipole for arbitrarily oriented dipoles. We find that resonances arise only when this angle is exceeded. In contrast to the three-dimensional (3D) case, the energy dependencies of the boson (fermion) 2D scattering cross section grow (are reduced) with an energy decrease in the absence of the resonances. We show that the mutual orientation of dipoles strongly impacts the form of the energy dependencies, which begin to oscillate with the tilt angle increase, unlike the 3D dipolar scattering. The angular distributions of the differential cross section in the 2D dipolar scattering of both bosons and fermions are highly anisotropic at nonresonant points. The results of the accurate numerical calculations of the cross section agree well with the results obtained within the Born and eikonal approximations.
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.
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.
Analytic expressions for the differential cross sections of ultracold atoms and molecules that scatter primarily due to dipolar interactions are derived within the first-order Born approximation and are shown to agree with the partial wave expansion. These cross sections are applied to the problem of cross-dimensional rethermalization. Strikingly, the rate of rethermalization can vary by as much as a factor of 2, depending on the orientation of the dipoles. Thus the anisotropic dipole-dipole interaction can have a significant effect even on the behavior of a nondegenerate ultracold gas.
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.