A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model

Abstract

We show that the effect of a Gaussian Bosonic environment linearly coupled to a quantum system can be simulated by a stochastic Lindblad master equation characterized by a set of ancillary Bosonic modes initially at zero temperature and classical stochastic fields. We test the method for Ohmic environments with exponential and polynomial cut-offs against, respectively, the Hierarchical Equations of Motion and the deterministic pseudomode model with respect to which the number of ancillary quantum degrees of freedom is reduced. For a subset of rational spectral densities, all parameters are explicitly specified without the need of any fitting procedure, thereby simplifying the modeling strategy. Interestingly, the classical fields in this decomposition must sometimes be imaginary-valued, which can have counter-intuitive effects on the system properties which we demonstrate by showing that they can decrease the entropy of the system, in contrast to real-valued fields.

arXiv comment41 pages, 11 figures

References in corpus (74)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Control of quantum phenomena: Past, present, and future
• Dephasing assisted transport: Quantum networks and biomolecules
• Environment-Assisted Quantum Transport
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Non-Markovian Quantum State Diffusion
• Open system dynamics with non-Markovian quantum trajectories
• General non-Markovian dynamics of open quantum systems
• Thermalizing Quantum Machines: Dissipation and Entanglement
• The non-Markovian stochastic Schrodinger equation for open systems
• Quantum feedback: theory, experiments, and applications
• Exact c-number Representation of Non-Markovian Quantum Dissipation
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance
• A non-Markovian decoherence theory for double dot charge qubit
• Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems
• Non-Markovian entanglement dynamics in the presence of system-bath coherence
• Correlation-dependent coherent to incoherent transitions in resonant energy transfer dynamics
• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Efficient simulation of finite-temperature open quantum systems
• Entanglement Dynamics of Two Qubits in a Common Bath
• Universal Markovian reduction of Brownian particle dynamics
• Virtual excitations in the ultra-strongly-coupled spin-boson model: physical results from unphysical modes
• The SLH framework for modeling quantum input-output networks
• Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
• A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems
• Electronic excitation dynamics in multichromophoric systems described via a polaron-representation master equation
• Mappings of open quantum systems onto chain representations and Markovian embeddings
• Auxiliary master equation approach to non-equilibrium correlated impurities
• Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
• A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach
• Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong coupling regime
• Optimized auxiliary oscillators for the simulation of general open quantum systems
• Simulating spin-boson dynamics with stochastic Liouville-von Neumann equations
• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations
• A Stochastic Liouvillian Algorithm to Simulate Dissipative Quantum Dynamics With Arbitrary Precision
• Coherent and incoherent dynamics in excitonic energy transfer: correlated fluctuations and off-resonance effects
• Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes
• Non-Markovian Dissipative Semiclassical Dynamics
• A multi-site variational master equation approach to dissipative energy transfer
• Non-Markovian Dynamics Impact on the Foundations of Statistical Mechanics
• Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum Limit
• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. II. Beyond Linear Response of Spin Baths
• Simulating Open Quantum Systems with Hamiltonian Ensembles and the Nonclassicality of the Dynamics
• Non-Markovian quantum input-output networks
• Bath induced coherence and the secular approximation
• Pulse-level noisy quantum circuits with QuTiP
• Open systems with error bounds: spin boson model with spectral density variations
• Periodically refreshed baths to simulate open quantum many-body dynamics
• Optimized auxiliary representation of a non-Markovian environment by a Lindblad equation
• Optimizing co-operative multi-environment dynamics in a dark-state-enhanced photosynthetic heat engine
• Quantum dynamics of incoherently driven V-type system: Analytic solutions beyond the secular approximation
• Exact semiclassical wave equation for stochastic quantum optics
• Stochastic Representation of Non-Markovian Fermionic Quantum Dissipation
• Quantifying the nonclassicality of pure dephasing
• Nonlinear interferometry approach to photonic sequential logic
• Relations for certain symmetric norms and anti-norms before and after partial trace
• Exact propagation of open quantum systems in a system-reservoir context
• When do weak-coupling approaches accurately capture the dynamics of complex quantum systems?
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
• Unraveling the topology of dissipative quantum systems
• Non-Markovianity in the optimal control of an open quantum system described by hierarchical equations of motion
• The Fermionic influence superoperator: a canonical derivation for the development of methods to simulate the influence of a Fermionic environment on a quantum system with arbitrary parity symmetry
• Transport Through a Correlated Interface: Auxiliary Master Equation Approach
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. II. Numerical Implementation
• An operator derivation of the Feynman-Vernon theory, with applications to the generating function of bath energy changes and to anharmonic baths
• Jumptime unraveling of Markovian open quantum systems
• Optical response of laser-driven charge-transfer complex described by Holstein-Hubbard model coupled to heat baths: Hierarchical equations of motion approach
• Efficient choice of coloured noises in stochastic dynamics of open quantum systems
• Non-Markovian Quantum Feedback Networks I: Quantum Transmission Lines, Lossless Bounded Real Property and Limit Markovian Channels

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• Markovian Embeddings of Non-Markovian Open System Dynamics
• Purified pseudomode model for nonlinear system-bath interactions
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