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

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.

Comments are welcome

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• Exploring quantum thermodynamics with NMR
• Preparing tunable Bell-diagonal states on a quantum computer
• Hilbert-Schmidt quantum coherence in multi-qudit systems
• Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase-damping and amplitude damping noise channels
• The sudden change phenomenon of quantum discord
• Entanglement production by the magnetic dipolar interaction dynamics
• Complete complementarity relations in system-environment decoherent dynamics
• The Kraus representation for the dynamics of open quantum systems