Time-averaged quantum dynamics and the validity of the effective Hamiltonian model

Omar Gamel and Daniel F. V. James
Phys. Rev. A 82, 052106 – Published 8 November 2010

Abstract

We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the general equation to harmonic Hamiltonians, we confirm a previous formula for the effective Hamiltonian together with a additional decoherence term which should, in general, be included and whose vanishing provides the criteria for validity of the effective Hamiltonian approach. Finally, we apply the theory to examples of the ac Stark shift and three-level Raman transitions, recovering a decoherence effect in the latter.

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  • Received 9 July 2010

DOI:https://doi.org/10.1103/PhysRevA.82.052106

©2010 American Physical Society

Authors & Affiliations

Omar Gamel* and Daniel F. V. James

  • Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada

  • *ogamel@physics.utoronto.ca
  • dfvj@physics.utoronto.ca

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Issue

Vol. 82, Iss. 5 — November 2010

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