Time-local Heisenberg-Langevin equations and the driven qubit

Abstract

The time-local master equation for a driven boson system interacting with a boson environment is derived by way of a time-local Heisenberg--Langevin equation. Extension to the driven qubit fails---except for weak excitation---due to the lost linearity of the system-environment interaction. We show that a reported time-local master equation for the driven qubit is incorrect. As a corollary to our demonstration, we also uncover odd asymptotic behavior in the "repackaged" time-local dynamics of a system driven to a far-from-equilibrium steady state: the density operator becomes steady while time-dependent coefficients oscillate (with periodic singularities) forever.

6 pages; additional discussion, one additional figure, minor formatting changes

References in corpus (6)

• Input-output theory of cavities in the ultra-strong coupling regime: the case of a time-independent vacuum Rabi frequency
• Nonlinear response of the vacuum Rabi resonance
• Non-Markovian entanglement dynamics of noisy continuous variable quantum channels
• Exact non-Markovian cavity dynamics strongly coupled to a reservoir
• Non-Markovian quantum input-output networks
• Exact non-Markovian master equation for a driven damped two-level system

Cited by in corpus (10)

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• Estimating the degree of non-Markovianity using machine learning
• Comparison between continuous- and discrete-mode coherent feedback for the Jaynes-Cummings model
• Revisiting Quantum Feedback Control: Disentangling the Feedback-induced Phase from the Corresponding Amplitude
• Stabilizing quantum coherence against pure dephasing in the presence of quantum feedback at finite temperature
• Kernel-based quantum regressor models learn non-Markovianity
• Perturbation approach in Heisenberg equations for lasers
• Estimating the degree of non-Markovianity using variational quantum circuits