Quantum Theory of an Atom Near Partially Reflecting Walls
Abstract
First consider a dielectric medium of identical two-state atoms coupled by the radiation field to an initially excited atom outside the dielectric. From the Schrodinger equation follows a delay differential equation describing how the atom interacts with the dielectric by virtual photon exchanges. In the macroscopic limit of a continuous distribution of atoms in the dielectric, a simpler delay-differential equation is derived are applied in which a Fresnel reflection coefficient appears. The results is derived are applied to a model of an atom in a multimode Fabry-Perot resonator, and a general delay-differential equation is obtained for the probability amplitude of the initially excited state. This equation predicts well-known Rabi oscillations when the round-trip photon propagation time is negligible compared with the inverse of the Rabi frequency and the mirrors are highly reflective. For low mirror reflectivities Purcell's prediction that the emission rate is enhanced by the cavity Q factor is recovered. When the photon bounce time is large compared with the inverse Rabi frequency, Rabi oscillations do not occur. The Ewald-Oseen extinction theorem is discussed from the standpoint of quantum mechanics.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 15, 1987
- Accession Number
- ADA192564
Entities
People
- P. W. Milonni
- R. J. Cook
Organizations
- Air Force Research Laboratory