Dynamics of ultracold dipolar particles in a confined geometry and tilted fields

TL;DR

This paper develops a new theoretical framework for understanding the collision dynamics of ultracold dipolar particles in confined geometries and tilted fields, revealing how field orientation influences reaction rates and energy transfer.

Contribution

The authors introduce a tesseral harmonic-based formalism that conserves a quantum number during collisions and apply it to analyze KRb molecule interactions in tilted fields and optical lattices.

Findings

Tilted fields significantly alter reactive and inelastic collision rates.

Inelastic excitation can reduce kinetic energy in confined fermionic systems.

The formalism accurately describes dipolar interactions in complex geometries.

Abstract

We develop a collisional formalism adapted for the dynamics of ultracold dipolar particles in a confined geometry and in fields tilted relative to the confinement axis. Using tesseral harmonics instead of the usual spherical harmonics to expand the scattering wavefunction, we recover a good quantum number $\xi = \pm 1$ which is conserved during the collision. We derive the general expression of the dipole-dipole interaction in this convenient basis set as a function of the polar and azimuthal angles of the fields. We apply the formalism to the collision of fermionic and bosonic polar KRb molecules in a tilted electric field and in a one-dimensional optical lattice. The presence of a tilted field drastically changes the magnitude of the reactive and inelastic rates as well as the inelastic threshold properties at vanishing collision energies. Setting an appropriate strength of the confinement for the fermionic system, we show that the ultracold particles can even further reduce their kinetic energy by inelastic excitation to higher states of the confinement trap.