Bound states of a light atom and two heavy dipoles in two dimensions

TL;DR

This paper investigates a three-body system in two dimensions consisting of a light particle and two heavy dipoles, analyzing bound states, wave functions, and effects of interactions, with implications for quantum information transfer.

Contribution

It provides an analytic wave function for the system, explores the spectrum and degeneracies, and studies the impact of dipole interactions and repulsion on bound states.

Findings

Bound states depend on mass ratio and interaction strength.

Degeneracies are related to radial and angular quantum numbers.

Large repulsion leads to disappearance of bound states into the continuum.

Abstract

We study a three-body system, formed by a light particle and two identical heavy dipoles, in two dimensions in the Born-Oppenheimer approximation. We present the analytic light-particle wave function resulting from an attractive zero-range potential between the light and each of the heavy particles. It expresses the large-distance universal properties which must be reproduced by all realistic short-range interactions. We calculate the three-body spectrum for zero heavy-heavy interaction as a function of light to heavy mass ratio. We discuss the relatively small deviations from Coulomb estimates and the degeneracies related to radial nodes and angular momentum quantum numbers. We include a repulsive dipole-dipole interaction and investigate the three-body solutions as functions of strength and dipole direction. Avoided crossings occur between levels localized in the emerging small and large-distance minima, respectively. The characteristic exchange of properties such as mean square radii are calculated. Simulation of quantum information transfer is suggested. For large heavy-heavy particle repulsion all bound states have disappeared into the continuum. The corresponding critical strength is inversely proportional to the square of the mass ratio, far from the linear dependence from the Landau criterion.