Reactive collisions of two ultracold particles in a harmonic trap

TL;DR

This paper studies how two ultracold particles in a harmonic trap behave when they can react and be lost, using models that include complex scattering lengths and finite-range potentials, revealing decay rates and energy properties.

Contribution

It introduces a detailed analysis of reactive ultracold particles in a harmonic trap using complex scattering lengths and finite-range models, advancing understanding of decay processes.

Findings

Eigenenergies become complex, indicating decay rates.

Finite interaction range affects reactive scattering properties.

Universal complex scattering length relates to van der Waals interactions.

Abstract

We consider two ultracold particles confined in spherically symmetric harmonic trap and interacting via isotropic potential with absorbing boundary conditions at short range that models reactive scattering. First, we apply the contact pseudopotential with complex scattering length and investigate the properties of eigenergies and eigenfunctions for different trap states as a function of real and imaginary part of the scattering length. In the analyzed case the eigenenergies take complex values, and their imaginary part can be interpreted in terms of decay rates. Then we introduce the model of a square well with absorbing boundary conditions that is later used to investigate the effects of the finite range of interaction on the properties of a reactive scattering in the trap. Finally, we analyze the decay rates for some reactive alkali dimer molecules assuming short-range probability of reaction equal to unity. In this case the complex scattering length is given by universal value related to the mean scattering length of van der Waals interaction between molecules.