1201.5797 (Jean-Bernard Bru et al.)

Characterization of the Quasi-Stationary State of an Impurity Driven by
Monochromatic Light I - The Effective Theory    [PDF]

Jean-Bernard Bru, Walter de Siqueira Pedra, Matthias Westrich

We consider an impurity ($N$--level atom) driven by monochromatic light in a
host environment which is a fermionic thermal reservoir. The external light
source is a time--periodic perturbation of the atomic Hamiltonian stimulating
transitions between two atomic energy levels $E_{1}$ and $E_{N}$ and thus acts
as an optical pump. The purpose of the present work is the analysis of the
effective atomic dynamics resulting from the full microscopic time--evolution
of the compound system. We prove, in particular, that the atomic dynamics of
population relaxes for large times to a quasi-stationary state, that is, a
stationary state up to small oscillations driven by the external light source.
This state turns out to be uniquely determined by a balance condition. The
latter is related to \textquotedblleft generalized Einstein
relations\textquotedblright relations of spontaneous/stimulated
emission/absorption rates, which are conceptually similar to the
phenomenological relations derived by Einstein in 1916. As an application we
show from quantum mechanical first principles how an inversion of population of
energy levels of an impurity in a crystal can appear. Our results are based on
the spectral analysis of the generator of the evolution semigroup related to a
non--autonomous Cauchy problem effectively describing the atomic dynamics.

View original: http://arxiv.org/abs/1201.5797