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arXiv:quant-ph/0605242

Microscopic Theory of the Photon Recoil of an Atom in a Dielectric

Hao Fu, P. R. Berman

Published May 29, 2006• 0 citations
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Abstract

An atom recoils when it undergoes spontaneous decay. In this paper we present a microscopic calculation of the recoil of a source atom imbedded in a dielectric medium. We find that the source atom recoils with the canonical photon momentum $n\hbar k_{0,}$ where $n$ is the index of refraction and $\hbar k_{0}$ is the photon momentum calculated at the source atom atomic frequency $ω_{0}$. We also show explicitly how the energy is conserved with the photon inside the medium.

DOI
10.48550/arxiv.quant-ph/0605242

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An atom recoils when it undergoes spontaneous decay. In this paper we present a microscopic calculation of the recoil of a source atom imbedded in a dielectric medium. We find that the source atom recoils with the canonical photon momentum nℏk0,n\hbar k_{0,}nℏk0,​ where nnn is the index of refraction and ℏk0\hbar k_{0}ℏk0​ is the photon momentum calculated at the source atom atomic frequency ω0ω_{0}ω0​. We also show explicitly how the energy is conserved with the photon inside the medium.
We consider the recoil momentum of a spontaneously emitting atom in a dispersive dielectric, first from a microscopic approach, in which the dielectric is treated as a collection of atoms and the field is quantized in vacuum , and, then, from the macroscopic approach of quantizing the field in the dielectric. The atom's recoil momentum differs from both the Abraham and Minkowski forms of the field momentum, and this difference is explained in terms of a dispersive contribution to the momentum acquired by the medium.
We consider the spontaneous emission in an absorbing medium by calculating the quantum flow of energy from an emitting atom. For this purpose, we extend the analysis by Power and Thirunamachandran of quantized Maxwell fields in the vicinity of an atom in the free space to a situation where the emitter is in a dielectric medium. We represent the quantum flow in terms of the non-equal time commutators involving electric and magnetic fields, as well as the local displacement field. The commutators are calculated applying a previously developed microscopic theory of quantization of radiation in dielectrics. Consequently, we derive from first principles the rate of spontaneous emission in an absorbing medium containing local field factors and other refractive contributions. The results support the previous introduction of the (virtual cavity) local field correction by Barnett et al on a phenomenological basis, as well as our previous approach in which the spontaneous emission is considered as a resonance energy transfer to the far-zone atoms. A distinctive feature of the present formalism is that it deals with the spontaneous emission directly by calculating the quantum flow from the emitting atom. Therefore, the method is free from divergences appearing in other approaches analysing the spontaneous decay in absorbing media.
Decay of an excited molecule (atom) has been considered in an absorbing dielectric. The decay rate has been derived calculating the total rate of excitation transfer to the surrounding species. The contribution due to the far-zone energy transfer yields the rate of photon emission in the absorbing medium. The analysis is based on a microscopic QED theory of energy transfer in condensed phases. As a result, effects due to discreteness of the medium (such as the local field effects) are reflected intrinsically in the decay rates. The microscopic approach supports the previous introduction of the local field factors on a phenomenological basis.
A systematic shift of the photon recoil momentum due to the index of refraction of a dilute gas of atoms has been observed. The recoil frequency was determined with a two-pulse light grating interferometer using near-resonant laser light. The results show that the recoil momentum of atoms caused by the absorption of a photon is n variant Planck's k, where n is the index of refraction of the gas and k is the vacuum wave vector of the photon. This systematic effect must be accounted for in high-precision atom interferometry with light gratings.
Decay of an excited molecule ~atom! has been considered in an absorbing dielectric. The decay rate has been derived calculating the total rate of excitation transfer to the surrounding species. The contribution due to the far-zone energy transfer yields the rate of photon emission in the absorbing medium. The analysis is based on a microscopic QED theory of energy transfer in condensed phases. As a result, effects due to discreteness of the medium ~such as the local field effects! are reflected intrinsically in the decay rates. The microscopic approach supports the previous introduction of the local field factors on a phenomenological basis.