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

2010/07/31 by Omar Gamel, Daniel F. V. James · 11 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum optics and atomic interactions #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1103/physreva.82.052106

published as Phys. Rev. A 82, 052106 (2010) · 7 pages, 2 figures

arxiv created 2010/10/08 · openalex publication_date 2010/11/08 · arxiv updated 2013/03/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• Analysis of quantum semigroups with GKS–Lindblad generators: II. General

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