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Journal of Mathematical Physics

Spectral properties of the two-photon absorption and emission process

Raffaella Carbone, Franco Fagnola, J. C. García, Roberto B. Quezada

Published Mar 1, 2008• 18 citations
Publisher

Abstract

The quantum Markov semigroup of the two-photon absorption and emission process has two extremal normal invariant states. Starting from an arbitrary initial state it converges toward some convex combination of these states as time goes to infinity (approach to equilibrium). We compute the exact exponential rate of this convergence showing that it depends only on the emission rates. Moreover, we show that off-diagonal matrix elements of any initial state go to zero with an exponential rate which is smaller than the exponential rate of convergence of the diagonal part. In other words quantum features of a state survive longer than the relaxation time of its classical part.

DOI
10.1063/1.2890700

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We consider a sequence of operators [Formula: see text] that describes the time evolution of normal states of an open quantum system. Our objective is to analyze the asymptotic behavior of [Formula: see text], where [Formula: see text] is an arbitrary initial normal state. Our focus is on specific situations in which the operators [Formula: see text] are produced by various quantum Markov semigroups of weak coupling limit-type. To tackle this problem, we introduce a new result concerning exponential convergence to equilibrium in the trace norm for quantum Markov semigroups, provided that their induced semigroups have a spectral gap. Moreover, applications to quantum annealing are discussed.
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