Quantum dynamics in a tiered non-Markovian environment

Abstract

We introduce a new analytical method for studying the open quantum systems problem of a discrete system weakly coupled to an environment of harmonic oscillators. Our approach is based on a phase space representation of the density matrix for a system coupled to a two-tiered environment. The dynamics of the system and its immediate environment are resolved in a non-Markovian way, and the environmental modes of the inner environment can themselves be damped by a wider `universe'. Applying our approach to the canonical cases of the Rabi and spin-boson models we obtain new analytical expressions for an effective thermalisation temperature and corrections to the environmental response functions as direct consequences of considering such a tiered environment. A comparison with exact numerical simulations confirms that our approximate expressions are remarkably accurate, while their analytic nature offers the prospect of deeper understanding of the physics which they describe. A unique advantage of our method is that it permits the simultaneous inclusion of a continuous bath as well as discrete environmental modes, leading to wide and versatile applicability.

Video abstract available at http://iopscience.iop.org/1367-2630/17/2/023063. 15 pages, 6 figures

References in corpus (32)

• Laser cooling of a nanomechanical oscillator into its quantum ground state
• Efficient simulation of strong system-environment interactions
• Non-Markovian Quantum State Diffusion
• A single NV defect coupled to a nanomechanical oscillator
• Sustained Quantum Coherence and Entanglement in the Avian Compass
• Hybrid circuit cavity quantum electrodynamics with a micromechanical resonator
• Dividing Quantum Channels
• The non-Markovian stochastic Schrodinger equation for open systems
• Non-classicality of the molecular vibrations assisting exciton energy transfer at room temperature
• Hierarchy of stochastic pure states for open quantum system dynamics
• Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems
• Long-Lived Electronic Coherence in Dissipative Exciton-Dynamics of Light-Harvesting Complexes
• Decoherence induced by interacting quantum spin baths
• Theory of Pseudomodes in Quantum Optical Processes
• Quantum control and entanglement in a chemical compass
• Genuine quantum trajectories for non-Markovian processes
• A general approach to quantum dynamics using a variational master equation: Application to phonon-damped Rabi rotations in quantum dots
• Quantum coherent biomolecular energy transfer with spatially correlated fluctuations
• Exciton dynamics and Quantumness of energy transfer in the Fenna-Matthews-Olson complex
• Microscopic derivation of the Jaynes-Cummings model with cavity losses
• Mappings of open quantum systems onto chain representations and Markovian embeddings
• Dynamics of the spin-boson model with a structured environment
• Observation of Entanglement Between Itinerant Microwave Photons and a Superconducting Qubit
• Spin-orbit-induced strong coupling of a single spin to a nanomechanical resonator
• An efficient method to calculate excitation energy transfer in light harvesting systems. Application to the FMO complex
• A multi-site variational master equation approach to dissipative energy transfer
• Nanomechanical resonant structures in single-crystal diamond
• Entanglement spectroscopy of a driven solid-state qubit and its detector
• Non-Markovian quantum state diffusion for absorption spectra of molecular aggregates
• Quantum thermometry using the ac Stark shift within the Rabi model
• Spectroscopy of a driven solid-state qubit coupled to a structured environment
• Non-Markoffian effects of a simple nonlinear bath

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• Photon-assisted tunneling and charge dephasing in a carbon nanotube double quantum dot
• Multiple single-photon generations in three-level atoms coupled to cavity with non-Markovian effects
• Optimisation of ultrafast singlet fission in 1D rings towards unit efficiency