Trapped Modes in Linear Quantum Stochastic Networks with Delays

Abstract

Networks of open quantum systems with feedback have become an active area of research for applications such as quantum control, quantum communication and coherent information processing. A canonical formalism for the interconnection of open quantum systems using quantum stochastic differential equations (QSDEs) has been developed by Gough, James and co-workers and has been used to develop practical modeling approaches for complex quantum optical, microwave and optomechanical circuits/networks. In this paper we fill a significant gap in existing methodology by showing how trapped modes resulting from feedback via coupled channels with finite propagation delays can be identified systematically in a given passive linear network. Our method is based on the Blaschke-Potapov multiplicative factorization theorem for inner matrix-valued functions, which has been applied in the past to analog electronic networks. Our results provide a basis for extending the Quantum Hardware Description Language (QHDL) framework for automated quantum network model construction (Tezak \textit{et al.} in Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci. 370(1979):5270-5290, to efficiently treat scenarios in which each interconnection of components has an associated signal propagation time delay.

References in corpus (4)

• Photonic Quantum Circuits with Time Delays
• Quantum Feedback Networks: Hamiltonian Formulation
• Time-delayed quantum feedback control
• Linear Quantum Feedback Networks

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• Quantum non-Markovian collision models from colored-noise baths
• Quantum stabilization of a single-photon emitter in a coupled microcavity--half-cavity system
• Input-Output Hierarchical Equations Of Motion
• Generating nonclassical states of motion using spontaneous emission
• The Stratonovich Formulation of Quantum Feedback Network Rules