Wave packet motion in a quantized electromagnetic field: Analytic results

TL;DR

This paper provides an analytic framework to understand how quantum fluctuations of light influence electron motion, revealing that wave packet broadening depends strongly on the quantum state of the electromagnetic field.

Contribution

It offers an exact analytic solution for a charged particle interacting with a multimode quantized electromagnetic field, enabling detailed analysis of quantum effects on electron dynamics.

Findings

Position expectation values are weakly affected by quantum state variations.

Wave packet broadening depends strongly on the quantum state of the field.

Quantum uncertainties of the radiation are imprinted onto the particle's spatial uncertainty.

Abstract

We investigate the dynamics of a charged particle interacting with a multimode quantized electromagnetic field and obtain an analytic solution for the full electron--field system. This framework enables the calculation of position expectation values and uncertainties for arbitrary wave packets and field states, allowing us to identify quantum corrections to the corresponding classical motion. While the corrections to the position expectation value are weak and largely insensitive to the quantum state of the field, the wave packet broadening exhibits a pronounced dependence on the field state. In particular, the quantum uncertainty of the radiation is directly imprinted onto the spatial uncertainty of the particle. We illustrate these effects for Gaussian wave packets interacting with coherent, Fock, and squeezed states, including bright squeezed vacuum. The interaction with a finite-duration laser pulse is also analyzed as a multimode example. Our results provide a transparent analytic route toward understanding how quantum fluctuations of light influence electron dynamics in strong-field settings.