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.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.

arXiv:quant-ph/0605242May 29, 20060 citations

Photon momentum in a medium with negative group velocity

I.M. Frank

ZhETF Pisma RedaktsiiuOct 1, 19780 citations

Recoil and Photon Momentum in a Dielectric

Peter W. Milonni, Robert W. Boyd

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 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.

Laser PhysicsJan 1, 200525 citations

Quantum optics of dielectrics in momentum-space

Michael E. Crenshaw

Optics CommunicationsMar 5, 20045 citations

Canonical and kinetic forms of the electromagnetic momentum in anad hocquantization scheme for a dispersive dielectric

J. C. Garrison, R. Y. Chiao

An ad hoc quantization scheme for the electromagnetic field in a weakly dispersive, transparent dielectric leads to the definition of canonical and kinetic forms for the momentum of the electromagnetic field in a dispersive medium. The canonical momentum is uniquely defined as the operator that generates spatial translations in a uniform medium, but the quantization scheme suggests two possible choices for the kinetic momentum operator, corresponding to the Abraham or the Minkowski momentum in classical electrodynamics. Another implication of this procedure is that a wave packet containing a single dressed photon travels at the group velocity through the medium. The physical significance of the canonical momentum has already been established by considerations of energy and momentum conservation in the atomic recoil due to spontaneous emission, the Cerenkov effect, the Doppler effect, and phase matching in nonlinear optical processes. In addition, the data of the Jones and Leslie radiation pressure experiment is consistent with the assignment of one $\ensuremath{\hbar}\mathbf{k}$ unit of canonical momentum to each dressed photon. By contrast, experiments in which the dielectric is rigidly accelerated by unbalanced electromagnetic forces require the use of the Abraham momentum.An ad hoc quantization scheme for the electromagnetic field in a weakly dispersive, transparent dielectric leads to the definition of canonical and kinetic forms for the momentum of the electromagnetic field in a dispersive medium. The canonical momentum is uniquely defined as the operator that generates spatial translations in a uniform medium, but the quantization scheme suggests two possible choices for the kinetic momentum operator, corresponding to the Abraham or the Minkowski momentum in classical electrodynamics. Another implication of this procedure is that a wave packet containing a single dressed photon travels at the group velocity through the medium. The physical significance of the canonical momentum has already been established by considerations of energy and momentum conservation in the atomic recoil due to spontaneous emission, the Cerenkov effect, the Doppler effect, and phase matching in nonlinear optical processes. In addition, the data of the Jones and Leslie radiation pressure experiment is consistent with the assignment of one $\ensuremath{\hbar}\mathbf{k}$ unit of canonical momentum to each dressed photon. By contrast, experiments in which the dielectric is rigidly accelerated by unbalanced electromagnetic forces require the use of the Abraham momentum.

arXiv:quant-ph/0406222Physical Review ANov 30, 200467 citations

Relaxation of Photon Density in a Resonant Medium

Yu. A. Vdovin

Journal of Experimental and Theoretical PhysicsAug 1, 19660 citations

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.