Stochastic Bloch-Redfield theory: quantum jumps in a solid-state environment

Abstract

We discuss mapping the Bloch-Redfield master-equation to Lindblad form and then unravelling the resulting evolution into a stochastic Schrödinger equation according to the quantum-jump method. We give two approximations under which this mapping is valid. This approach enables us to study solid-state-systems of much larger sizes than is possible with the standard Bloch-Redfield master-equation, while still providing a systematic method for obtaining the jump operators and corresponding rates. We also show how the stochastic unravelling of the Bloch-Redfield equations becomes the kinetic Monte Carlo (KMC) algorithm in the secular approximation when the system-bath-coupling operators are given by tunnelling-operators between system-eigenstates. The stochastic unravelling is compared to the conventional Bloch-Redfield approach with the superconducting single electron transistor (SSET) as an example.

12 pages, 7 figures

References in corpus (9)

• Low- and high-frequency noise from coherent two-level systems
• Staying positive: going beyond Lindblad with perturbative master equations
• Stochastic pure state representation for open quantum systems
• Derivation of Markovian master equations for spatially correlated decoherence
• Orthogonal jumps of wavefunction in white-noise potentials
• Quantum trajectories for the realistic measurement of a solid-state charge qubit
• Model for monitoring of a charge qubit using a radio-frequency quantum point contact including experimental imperfections
• Influence of two-level fluctuators on adiabatic passage techniques
• Structured environments in solid state systems: crossover from Gaussian to non-Gaussian behavior

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