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EPJ Web of Conferences

Short-Range Interaction Impact on Two-Dimensional Dipolar Scattering

Eugene A. Koval, Oksana A. Koval

Published Jan 1, 2018• 2 citations
Publisher

Abstract

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.

DOI
10.1051/epjconf/201817306008

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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.

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A. Crubellier, Rosario González‐Férez, Christiane P. Koch +1 more

The definition of the scattering volume for $p$-wave collisions needs to be generalized in the presence of dipolar interactions for which the potential decreases with the interparticle separation as $1/{R}^{3}$. Here, we propose a way to define the scattering volume characterizing the short-range interactions in odd-parity waves, by analyzing the $p$-wave component of the two-body threshold wave function. Our approach uses an asymptotic model and introduces explicitly the anisotropic dipole-dipole interaction, which governs the ultracold collision dynamics at long range. The short-range interactions, which are essential to describe threshold resonances, are taken into account by a single parameter related to the nodal structure of the wave functions at short distances.

arXiv:1807.05783•Physical Review A•Mar 25, 2019•3 citations
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.
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 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.
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.
The definition of the scattering volume for ppp-wave collisions needs to be generalized in the presence of dipolar interactions for which the potential decreases with the interparticle separation as 1/R31/{R}^{3}1/R3. Here, we propose a way to define the scattering volume characterizing the short-range interactions in odd-parity waves, by analyzing the ppp-wave component of the two-body threshold wave function. Our approach uses an asymptotic model and introduces explicitly the anisotropic dipole-dipole interaction, which governs the ultracold collision dynamics at long range. The short-range interactions, which are essential to describe threshold resonances, are taken into account by a single parameter related to the nodal structure of the wave functions at short distances.