Commutativity of the adiabatic elimination limit of fast oscillatory components and the instantaneous feedback limit in quantum feedback networks

Abstract

We show that, for arbitrary quantum feedback networks consisting of several quantum mechanical components connected by quantum fields, the limit of adiabatic elimination of fast oscillator modes in the components and the limit of instantaneous transmission along internal quantum field connections commute. The underlying technique is to show that both limits involve a Schur complement procedure. The result shows that the frequently used approximations, for instance to eliminate strongly coupled optical cavities, are mathematically consistent.

arXiv comment38 pages, 10 figures, minor typos corrected and minor editorial changes. Published in Journal of Mathematical Physics

References in corpus (6)

• Quantum Feedback Networks: Hamiltonian Formulation
• The Langevin equation from Markovian Quantum Central Limits
• Quantum Flows as Markovian Limit of Emission, Absorption and Scattering Interactions
• Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem
• Adiabatic elimination in quantum stochastic models
• Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode

Cited by in corpus (18)

• The SLH framework for modeling quantum input-output networks
• Coherent controllers for optical-feedback cooling of quantum oscillators
• Specification of photonic circuits using Quantum Hardware Description Language
• Backaction driven, robust, steady-state long-distance qubit entanglement over lossy channels
• Design of nanophotonic circuits for autonomous subsystem quantum error correction
• Transformation of quantum photonic circuit models by term rewriting
• Singular Perturbation Approximations for General Linear Quantum Systems
• On structure-preserving transformations of the Ito generator matrix for model reduction of quantum feedback networks
• Gauge subsystems, separability, and robustness in autonomous quantum memories
• Zeno Dynamics for Open Quantum Systems
• On The Scattering Process in Quantum Optics
• Pole placement design for quantum systems via coherent observers
• Tangential Interpolatory Projection for Model Reduction of Linear Quantum Stochastic Systems
• Characteristic Operator Functions for Quantum Input-Plant-Output Models & Coherent Control
• Coherent LQG Control, Free-Carrier Oscillations, Optical Ising Machines and Pulsed OPO Dynamics
• Towards generic adiabatic elimination for bipartite open quantum systems
• The Stratonovich Formulation of Quantum Feedback Network Rules
• On the Quasi-Balanceable Class of Linear Quantum Stochastic Systems