1105.4120 (Robert Hoeppner et al.)

A semiclassical optics derivation of Einstein's rate equations    [PDF]

Robert Hoeppner, Germán J. de Valcárcel, Eugenio Roldán

We provide a semiclassical optics derivation of Einstein's rate equations
(ERE) for a two-level system illuminated by a broadband light field, setting a
limit for their validity that depends on the light spectral properties (namely
on the height and width of its spectrum). Starting from the optical Bloch
equations for individual atoms, the ensemble averaged atomic inversion is shown
to follow ERE under two concurrent hypotheses: (i) the decorrelation of the
inversion at a given time from the field at later times, and (ii) a Markov
approximation owed to the short correlation time of the light field. The latter
is then relaxed, leading to effective Bloch equations for the ensemble average
in which the atomic polarization decay rate is increased by an amount equal to
the width of the light spectrum, what allows its adiabatic elimination for
large enough spectral width. Finally the use of a phase-diffusion model of
light allows us to check all the results and hypotheses through numerical
simulations of the corresponding stochastic differential equations.

View original: http://arxiv.org/abs/1105.4120