Faddeev-Jackiw quantisation of nonreciprocal quasi-lumped electrical networks

• URL: http://arxiv.org/abs/2401.09120v1
• Date: Wed, 17 Jan 2024 10:49:43 GMT
• Title: Faddeev-Jackiw quantisation of nonreciprocal quasi-lumped electrical networks
• Authors: A. Parra-Rodriguez and I. L. Egusquiza
• Abstract summary: We present an exact method for obtaining canonically quantisable Hamiltonian descriptions of nonreciprocal quasi-lumped electrical networks. We show how our method seamlessly facilitates the characterisation of general nonreciprocal, dissipative linear environments.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Following a consistent geometrical description previously introduced in Parra-Rodriguez et al. (2023), we present an exact method for obtaining canonically quantisable Hamiltonian descriptions of nonlinear, nonreciprocal quasi-lumped electrical networks. Utilising the Faddeev-Jackiw method once more, we identify and classify all possible singularities arising in the quest for Hamiltonian descriptions of general quasi-lumped element networks, and we offer systematic solutions to them--a major challenge in the context of canonical circuit quantisation. Accordingly, the solution relies on the correct identification of the reduced classical circuit-state manifold, i.e., a mix of flux and charge fields and functions. Starting from the geometrical description of the transmission line, we provide a complete program including lines coupled to one-port lumped-element networks, as well as multiple lines connected to nonlinear lumped-element networks. On the way, we naturally extend the canonical quantisation of transmission lines coupled through frequency-dependent, nonreciprocal linear systems, such as practical circulators. Additionally, we demonstrate how our method seamlessly facilitates the characterisation of general nonreciprocal, dissipative linear environments. This is achieved by extending the Caldeira-Leggett formalism, utilising continuous limits of series of immittance matrices. We expect this work to become a useful tool in the analysis and design of electrical circuits and of special interest in the context of canonical quantisation of superconducting networks. For instance, this work will provide a solid ground for a precise input-output theory in the presence of nonreciprocal devices, e.g., within waveguide QED platforms.

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