The Einstein's coefficients and the quantum theory

Olaf Stenzel

Vitaly V. Datsyuk, Saulius Juodkazis, Hiroaki Misawa

The rate of spontaneous electromagnetic emission in a cavity is the normalized output radiation rate in the classical electrodynamics and the Einstein $A$ coefficient in a quantum theory. We reveal the difference and similarity between the quantum and classical rates by calculations of the relative output power of the resonant spontaneous electric-dipole emission as a function of light absorption in a high-$Q$ cavity. We show that the relative resonant output power is equal to the relative width of a morphology-dependent resonance in the spectral dependence of the Einstein $A$ coefficient. The validity of the theory is demonstrated by numerical verification of an experimental result on a microsphere.

Seiya Abiko

Ophelliam Loiselet

We will present here a clear derivation of the Einstein's spontaneous coefficient using Boudet's theory of probability transition current and classical electromagnetism. It is a step toward the quantum mechanics expressed in terms of real 3D fields quantities.

David A. Holm, Murray Sargent

We transform our quantum theory of multiwave mixing, which is based on a reduced density operator, to the corresponding nondegenerate quantum-noise Langevin equations. We derive the diffusion coefficients from the drift coefficients using the generalized Einstein relation and illustrate the resulting quantum Langevin theory of multiwave mixing by specializing to the Reid and Walls degenerate theory of squeezed states of light.