Interaction of a two-level atom with a classical field in the context of Bohmian mechanics

TL;DR

This paper explores the use of Bohmian mechanics to analyze the trajectories and time spent by a two-level atom in a waveguide interacting with a localized external field, providing insights into quantum dynamics beyond standard quantum mechanics.

Contribution

It applies Bohmian mechanics to compute atomic trajectories and residence times in a waveguide with a localized field, offering a novel approach to quantum time measurements.

Findings

Bohmian trajectories calculated for a Gaussian wave packet.

Average time spent by particles in the field region determined.

Arrival-time distributions at the waveguide edges analyzed.

Abstract

We discuss Bohmian paths of the two-level atoms moving in a waveguide through an external resonance-producing field, perpendicular to the waveguide, and localized in a region of finite diameter. The time spent by a particle in a potential region is not well-defined in the standard quantum mechanics, but it is well-defined in the Bohmian mechanics. Bohm's theory is used for calculating the average time spent by a transmitted particle inside the field region and the arrival-time distributions at the edges of the field region. Using the Runge-Kutta method for the integration of the guidance law, some Bohmian trajectories were also calculated. Numerical results are presented for the special case of a Gaussian wave packet.