The driven-Markovian master equation based on the Lewis-Riesenfeld invariants theory
arXiv:2304.07956 · doi:10.1103/PhysRevA.106.052217
Abstract
We derive a Markovian master equation for driven open quantum systems based on the Lewis-Riesenfeld invariants theory, which is available for arbitrary driving protocols.The role of the Lewis-Riesenfeld invariants is to help us bypass the time-ordering obstacle in expanding the propagator of the free dynamics, such that the Lindblad operators in our driven-Markovian master equation can be determined easily. We also illustrate that, for the driven open quantum systems, the spontaneous emission and the thermal excitation induce the transitions between eigenstates of the Lewis-Riesenfeld invariant, but not the system Hamiltonian's. As an example, we present the driven-Markovian master equation for a driven two-level system coupled to a heat reservoir. By comparing to the exactly solvable models, the availability of the driven-Markovian master equation is verified. Meanwhile, the adiabatic limit and inertial limit of the driven-Markovian master equation are also discussed, which result in the same Markovian master equations as those presented before in the corresponding limits.
Including Erratum of Phys. Rev. A 106, 052217 (2022)
References in corpus (14)
- Shortcut to adiabatic passage in two and three level atoms
- Lewis-Riesenfeld invariants and transitionless tracking algorithm
- Dissipative Landau-Zener transitions of a qubit: bath-specific and universal behavior
- Gauging a quantum heat bath with dissipative Landau-Zener transitions
- Thermodynamics of Precision in Markovian Open Quantum Dynamics
- A thermodynamically consistent Markovian master equation beyond the secular approximation
- Dynamical invariants for quantum control of four-level systems
- Exact propagation of open quantum systems in a system-reservoir context
- Exact non-Markovian master equation for a driven damped two-level system
- Dynamical invariants and nonadiabatic geometric phases in open quantum systems
- Shortcuts to adiabaticity for open quantum systems and a mixed-state inverse engineering scheme
- Invariant-based inverse engineering of time-dependent, coupled harmonic oscillators
- Decoherence measurements in crystals of molecular magnets
- Analytic approach to dynamics of the resonant and off-resonant Jaynes-Cummings systems with cavity losses