Time Dependent Markovian Quantum Master Equation

Abstract

We construct a quantum Markovian Master equation for a driven system coupled to a thermal bath. The derivation utilizes an explicit solution of the propagator of the driven system. This enables the validity of the Master equation to be extended beyond the adiabatic limit. The Non-Adiabatic Master Equation (NAME) is derived employing the weak system-bath coupling limit. The NAME is valid when a separation of timescales exists between the bath dynamics and the external driving. In contrast to the adiabatic Master equation, the NAME leads to coupled equations of motion for the population and coherence. We employ the NAME to solve the example of an open driven time-dependent harmonic oscillator. For the harmonic oscillator the NAME predicts the emergence of coherence associated with the dissipation term. As a result of the non-adiabatic driving the thermalization rate is suppressed. The solution is compared with both numerical calculations and the adiabatic Master equation.

References in corpus (27)

• Fast quantum gates for neutral atoms
• Quantum Thermodynamics
• Geometric Manipulation of Trapped Ions for Quantum Computation
• A single-atom heat engine
• Quantum Annealing and Analog Quantum Computation
• Experimental Observation of a Generalized Gibbs Ensemble
• Quantum heat engines and refrigerators: Continuous devices
• Robustness of adiabatic quantum computation
• The quantum harmonic Otto cycle
• Irreversible Performance of a Quantum Harmonic Heat Engine
• Quantum Adiabatic Markovian Master Equations
• Controlling open quantum systems: Tools, achievements, and limitations
• Entropy production and thermodynamic power of the squeezed thermal reservoir
• Quantum Refrigerator and the III-law of Thermodynamics
• Fast quantum gates for cold trapped ions
• Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
• Markovian Master Equation and Thermodynamics of Two-level System in Strong Laser Field
• Markovian Quantum Master Equation beyond Adiabatic Regime
• The Quantum Adiabatic Approximation and the Geometric Phase
• Entropy production and non-Markovian dynamical maps
• Noise Resistant Quantum Control Using Dynamical Invariants
• Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems
• The production rate of the system-bath mutual information
• A third-order exceptional point effect on the dynamics of a single particle in a time-dependent harmonic trap
• Secular master equation for adiabatically time dependent systems
• Complete positivity and thermodynamics in a driven open quantum system
• Probing microscopic models for system-bath interactions via parametric driving

Cited by in corpus (74)

• Shortcuts to adiabaticity: concepts, methods, and applications
• Quantum stochastic processes and quantum non-Markovian phenomena
• Optimal cycles for low-dissipation heat engines
• Strong Coupling Thermodynamics of Open Quantum Systems
• Thermodynamic Geometry of Microscopic Heat Engines
• Thermodynamic length in open quantum systems
• Identifying optimal cycles in quantum thermal machines with reinforcement-learning
• Work fluctuations in slow processes: quantum signatures and optimal control
• Completely positive master equation for arbitrary driving and small level spacing
• Shortcut to Equilibration of an Open Quantum System
• Quantum Signatures in the Quantum Carnot Cycle
• A thermodynamically consistent Markovian master equation beyond the secular approximation
• Superconducting-like heat current: Effective cancellation of current-dissipation trade off by quantum coherence
• Maximum power and corresponding efficiency for two-level heat engines and refrigerators: optimality of fast cycles
• Quantum finite-time thermodynamics: insight from a single qubit engine
• Finite-time quantum Stirling heat engine
• Exact solution of time-dependent Lindblad equations with closed algebras
• Thermodynamics of Optical Bloch Equations
• Why and when is pausing beneficial in quantum annealing?
• Fast Route to Thermalization
• Superadiabatic thermalization of a quantum oscillator by engineered dephasing
• Open system dynamics from thermodynamic compatibility
• Optimal nonequilibrium thermometry in Markovian environments
• Maximum power heat engines and refrigerators in the fast-driving regime
• Quantum thermo-dynamical construction for driven open quantum systems
• Optimal Control for Closed and Open System Quantum Optimization
• Unification of the first law of quantum thermodynamics
• From non-equilibrium Green's functions to quantum master equations for the density matrix and out-of-time-order correlators: steady state and adiabatic dynamics
• A Landau-Zener Lindblad equation and work extraction from coherences
• Geometric-Arithmetic Master Equation in Large and Fast Open Quantum Systems
• Quantum jump approach to microscopic heat engines
• Dynamical invariant based shortcut to equilibration in open quantum systems
• Quantum collisional thermostats
• Inertial Theorem: Overcoming the quantum adiabatic limit
• Measurement-based quantum Otto engine with a two-spin system coupled by anisotropic interaction: enhanced efficiency at finite times
• A Quantum Otto Engine with Shortcuts to Thermalization and Adiabaticity
• Non-Markovian dynamics under time-translation symmetry
• Thermodynamics of Permutation-Invariant Quantum Many-Body Systems: A Group-Theoretical Framework
• Reservoir-engineering shortcuts to adiabaticity
• Model-free optimization of power/efficiency tradeoffs in quantum thermal machines using reinforcement learning
• Exact finite-time correlation functions for multi-terminal setups: Connecting theoretical frameworks for quantum transport and thermodynamics
• Markovian and non-Markovian master equations versus an exactly solvable model of a qubit in a cavity
• Benchmarking quantum gates and circuits
• Optimal control of dissipation and work fluctuations for rapidly driven systems
• Non-Markovian N-spin chain quantum battery in thermal charging process
• Nonequilibrium phononic first-order phase transition in a driven fermion chain
• Exceptional points and exponential sensitivity for periodically driven Lindblad equations
• The driven-Markovian master equation based on the Lewis-Riesenfeld invariants theory
• Self-consistency of optimizing finite-time Carnot engines with the low-dissipation model
• Time dependent Markovian master equation beyond the adiabatic limit
• Temporally correlated quantum noise in driven quantum systems
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Thermal effects on a nonadiabatic spin-flip protocol of spin-orbit qubits
• Controlling thermodynamics of a quantum heat engine with modulated amplitude drivings
• Quantum thermochemical engines
• Beyond-adiabatic Quantum Admittance of a Semiconductor Quantum Dot at High Frequencies: Rethinking Reflectometry as Polaron Dynamics
• Heat-based circuits using quantum rectification
• Optimizing Floquet engineering for non-equilibrium steady states with gradient-based methods
• The failure of semiclassical approach in the dissipative fully-connected Ising model
• Comment on "Universal Lindblad equation for open quantum systems"
• Nonlinear response theory for lossy superconducting quantum circuits
• Control of open quantum systems: Manipulation of a qubit coupled to a thermal bath by an external driving field
• Quantum transport phenomena induced by time-dependent fields
• Dynamics of a driven open double two-level system and its entanglement generation
• Interplay between external driving, dissipation and collective effects in the Markovian and non-Markovian regimes
• Is there any reasonable dynamics for quantum subsystems within the unitary-only quantum theory?
• Re-examining Einstein's $B$ coefficient and rate equations with the Rabi model
• Universally Robust Control of Open Quantum Systems
• Counterdiabatic driving for periodically driven open quantum systems
• Coherent dynamical control of quantum processes
• Topological advantage for adsorbate chemisorption on conjugated chains
• Nonadiabatic evolution and thermodynamics for a boundary-driven system with a weak intrasubsystem interaction
• Non-equilibrium Dynamics of Three-Level Absorption Refrigerator at Third-Order Liouvillian Exceptional Points
• Experimental verification of the inertial theorem control protocols