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.

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Cited by in corpus (4)

• Kondo QED: The Kondo effect and photon trapping in a two-impurity Anderson model ultra-strongly coupled to light
• Quantization of optical quasinormal modes for spatially separated cavity systems with finite retardation
• WaveguideQED.jl: An Efficient Framework for Simulating Non-Markovian Waveguide Quantum Electrodynamics
• Input-Output Hierarchical Equations Of Motion