Non-perturbative treatment of non-Markovian dynamics of open quantum systems

Abstract

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments - one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (non-unitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, non-perturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open system dynamics.

5+4 pages, 2 figures, Close to the version accepted for publication in Physical Review Letters

References in corpus (15)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Protecting entanglement via the quantum Zeno effect
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach
• Performance of a quantum heat engine at strong reservoir coupling
• Universal Markovian reduction of Brownian particle dynamics
• Mesoscopic Spin-Boson Models of Trapped Ions
• The effect of dipole-dipole interaction for two atoms with different couplings in non-Markovian environment
• Non-Markovian quantum input-output networks
• Non-Markovian quantum state diffusion for absorption spectra of molecular aggregates
• Open systems with error bounds: spin boson model with spectral density variations
• Entanglement trapping in a non-stationary structured reservoir
• Improved scaling of Time-Evolving Block-Decimation algorithm through Reduced-Rank Randomized Singular Value Decomposition
• Quantum interference induced by initial system-environment correlations
• Pseudomodes and the corresponding transformation of the temperature-dependent bath correlation function

Cited by in corpus (15)

• Precursors of non-Markovianity
• Quantum Probes for Ohmic Environments at Thermal Equilibrium
• Heat transport through a superconducting artificial atom
• Rate operator unravelling for open quantum system dynamics
• Fingerprint and universal Markovian closure of structured bosonic environments
• Collective bath coordinate mapping of "hierarchy" in hierarchical equations of motion
• Kerr nonlinearity induced strong spin-magnon coupling
• Spin-boson model as a simulator of non-Markovian multiphoton Jaynes-Cummings models
• Correlations, information backflow, and objectivity in a class of pure dephasing models
• Dressed bound states at chiral exceptional points
• A solvable class of non-Markovian quantum multipartite dynamics
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• Modified coherence of quantum spins in a damped pure-dephasing model
• Equilibration and Typicality in Quantum Processes
• Finite-frequency noise in non-Markovian systems: A Markovian embedding approach