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.

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

References in corpus (4)

• Quantum Feedback Networks: Hamiltonian Formulation
• The Langevin equation from Markovian Quantum Central Limits
• Adiabatic elimination in quantum stochastic models
• Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode

Cited by in corpus (5)

• Singular Perturbation Approximations for General Linear Quantum Systems
• Zeno Dynamics for Open Quantum Systems
• On The Scattering Process in Quantum Optics
• Characteristic Operator Functions for Quantum Input-Plant-Output Models & Coherent Control
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