Spontaneous emission of a moving atom in a waveguide of rectangular cross section

TL;DR

This paper investigates how the spontaneous emission rate and emitted photon frequency of a moving two-level atom in a rectangular waveguide are affected by the atom's motion and position, revealing directional frequency shifts and modified emission rates.

Contribution

It provides a first-order analytical study of the effects of atomic motion on spontaneous emission in a waveguide, including frequency shifts and emission rate variations.

Findings

Emitted photon frequency can be shifted above or below the transition frequency.

The spontaneous emission rate for a moving atom can be larger than that of a fixed atom.

Photon frequency shifts depend on the direction of emission relative to initial atomic motion.

Abstract

We study the spontaneous emission (SE) of an excited two-level nonrelativistic system (TLS) interacting with the vacuum in a waveguide of rectangular cross section. All TLS's transitions and the center-of-mass motion of the TLS are taken into account. The SE rate and the carried frequency of the emitted photon for the TLS initial being at rest is obtained, it is found in the first order of the center of mass (c.m.) that the frequency of the emitted photon could be smaller or larger than the transition frequency of the TLS but the SE rate is smaller than the SE rate $\Gamma_{f}$ of the TLS fixed in the same waveguide. The SE rate and the carried frequency of the emitted photon for the TLS initial being moving is also obtained in the first order of the c.m.. The SE rate is larger than $\Gamma_{f}$ but it is independent of the initial momentum. The carried frequency of the emitted photon is creased when it travels along the direction of the initial momentum and is decreased when it travels in the opposite direction of the initial momentum.