A hierarchical equations of motion (HEOM) analog for systems with delay: illustrated on inter-cavity photon propagation

Abstract

Over the last two decades, the hierarchical equations of motion (HEOM) of Tanimura and Kubo have become the equation of motion-based tool for numerically exact calculations of system-bath problems. The HEOM is today generalized to many cases of dissipation and transfer processes through an external bath. In spatially extended photonic systems, the propagation of photons through the bath leads to retardation/delays in the coupling of quantum emitters. Here, the idea behind the HEOM derivation is generalized to the case of photon retardation and applied to the simple example of two dielectric slabs. The derived equations provide a simple reliable framework for describing retardation and may provide an alternative to path integral treatments.

References in corpus (40)

• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Matrix product states represent ground states faithfully
• Light interaction with photonic and plasmonic resonances
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Unconventional quantum optics in topological waveguide QED
• Effective mode volumes and Purcell factors for leaky optical cavities
• Quantization of quasinormal modes for open cavities and plasmonic cavity-QED
• Photonic Quantum Circuits with Time Delays
• A positive tensor network approach for simulating open quantum many-body systems
• Time-bin entangled photons from a quantum dot
• Semiconductor devices for entangled photon pair generation: a review
• Brillouin-Wigner perturbation theory in open electromagnetic systems
• Time-delayed quantum feedback control
• Numerically exact open quantum systems simulations for arbitrary environments using automated compression of environments
• Quasinormal mode approach to modelling light-emission and propagation in nanoplasmonics
• Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
• QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics
• Dissipation-assisted matrix product factorization
• Efficient simulation of non-Markovian system-environment interaction
• Exact dynamics of non-additive environments in non-Markovian open quantum systems
• Anisotropy-Induced Quantum Interference and Population Trapping Between Orthogonal Quantum Dot Exciton States in Semiconductor Cavity Systems
• Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain
• Non-Markovian features in semiconductor quantum optics: Quantifying the role of phonons in experiment and theory
• Efficient calculation of open quantum system dynamics and time-resolved spectroscopy with Distributed Memory HEOM (DM-HEOM)
• Quantized quasinormal mode description of non-linear cavity QED effects from coupled resonators with a Fano-like resonance
• Modelling quantum light-matter interactions in waveguide-QED with retardation and a time-delayed feedback: matrix product states versus a space-discretized waveguide model
• Quantum dynamics in photonic crystals
• Exact Simulation of Pigment-Protein Complexes Unveils Vibronic Renormalization of Electronic Parameters in Ultrafast Spectroscopy
• Efficient Real-Time Path Integrals for Non-Markovian Spin-Boson Models
• Energy flow in the Photosystem I supercomplex: comparison of approximative theories with DM-HEOM
• Comparison between continuous- and discrete-mode coherent feedback for the Jaynes-Cummings model
• Fluctuation-dissipation theorem and fundamental photon commutation relations in lossy nanostructures using quasinormal modes
• Enhanced TEMPO algorithm for quantum path integrals with off-diagonal system-bath coupling: applications to photonic quantum networks
• Revisiting Quantum Feedback Control: Disentangling the Feedback-induced Phase from the Corresponding Amplitude
• Non-equilibrium non-Markovian steady-states in open quantum many-body systems: Persistent oscillations in Heisenberg quantum spin chains
• Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space
• Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics using the Polaron Transformation in HEOM Space

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