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Physical Review A

Spurious velocity dependence of free-space spontaneous emission

Martin Wilkens

Published Jan 1, 1993• 41 citations
Publisher

Abstract

It is shown that the standard calculation of the free-space spontaneous-emission rate leads to a spurious velocity dependence if the atomic motion is included nonrelativistically. The unphysical terms are of first order in v/c, akin to the nonrelativistic Doppler shift.
DOI
10.1103/physreva.47.671

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We show that the spontaneous emission of a moving atom inside a cavity is modified by two different mechanisms. The first one is a Doppler-induced detuning of the cavity line that leads to observable changes in the spontaneous emission rate for atomic velocities in excess of a characteristic velocity vcav{\mathit{v}}_{\mathrm{cav}}vcav​=c/Q, Q being the quality factor of the cavity. In addition, spatial mode effects can lead to a temporal modulation of the exponential decay rate. This modulation is observable for velocities that do not exceed another characteristic velocity vmod{\mathit{v}}_{\mathrm{mod}}vmod​ which is typically several orders of magnitude smaller than vcav{\mathit{v}}_{\mathrm{cav}}vcav​.
We argue that for moving atoms, the conventional dipole interaction must be supplemented by a so-called R\"ontgen term in order to obtain results which are trustworthy to order V/c in the atomic velocity. As an illustration, we include the R\"ontgen interaction in a Hamiltonian model to derive the angular distribution of photons spontaneously emitted by a freely moving atom. We find agreement with an independent calculation which is based on the transformation properties of such distribution under Lorentz boosts. This resolves the previously reported inconsistency of the conventional dipole interaction for moving atoms [Phys. Rev. A 47, 671 (1993)].
The spontaneous decay of a multilevel atom interacting with the electromagnetic field in free space is investigated with a unitary transformation method, which is introduced in order to include all rotating and counter-rotating terms in the Hamiltonian. By using the ground state of the total Hamiltonian, the evolution of the effective decay rate and the energy shift are calculated. When the atomic transition frequency is smaller than the central frequency of the spectrum, the Zeno effect dominates, and if the atomic transition frequency is larger than the central frequency, the anti-Zeno effect will dominate. The time evolution of the energy shift is obtained. The counter-rotating terms lead to a shift toward the low frequency region for the frequency distribution of the emitted photon.