Velocity-dependent dipole forces on an excited atom

TL;DR

This paper calculates velocity-dependent forces on an excited atom near ground state atoms or surfaces, revealing how these forces vary with distance and regime, including van der Waals and Rontgen components.

Contribution

It provides a detailed time-dependent analysis of velocity-dependent dipole forces, including both conservative and non-conservative components, in different regimes and configurations.

Findings

Van der Waals force dominates in the non-retarded regime and is antiparallel to velocity.

In the retarded regime, forces oscillate spatially and Rontgen component can dominate near surfaces.

All velocity-dependent interactions are linear in velocity at leading order.

Abstract

We present a time-dependent calculation of the velocity-dependent forces which act on an excited atomic dipole in relative motion with respect to ground state atoms of a different kind. Both, its interaction with a single atom and with a dilute atomic plate are evaluated. In either case, the total force consists of a conservative van der Waals component and a non-conservative Rontgen component. On physical grounds, the former corresponds to the velocity-dependent recoil experienced by the excited atom in the processes of absorption and emission of the photons that it exchanges with the ground state atoms on a periodic basis. The latter corresponds to the time-variation of the Rontgen momentum, which is also mediated by the periodic exchange of quasi-resonant photons. We find that, at leading order, all these interactions are linear in the velocity. In the non-retarded regime the van der Waals force dominates, being antiparallel to the velocity. On the contrary, in the retarded regime the velocity-dependent forces oscillate in space, van der Waals and Rontgen forces are of the same order in the atom-atom interaction, and the Rontgen component dominates in the atom-surface interaction.