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arXiv:1104.0656 · Physical Review A

Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

Diogo O. Soares-Pinto, M. H. Y. Moussa, Jonas Maziero, Eduardo Ribeiro DeAzevedo, Tito José Bonagamba, Roberto M. Serra, Lucas C. Céleri

Published Jun 28, 2011• 25 citations
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Abstract

We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-$1/2$ system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times ${T}_{1}$ and ${T}_{2}$ (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with ${T}_{1}$). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.

DOI
10.1103/physreva.83.062336

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