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arXiv · 2604.21463

Dynamical Regimes of Finite-Length Transmission Lines in Circuit Quantum Electrodynamics

Fabio Borrelli·Giovanni Miano·Adrian Parra-Rodriguez·Carlo Forestiere
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Abstract

We study the emergence of continuum, discrete-multimode, and single-mode regimes in finite-length transmission lines capacitively coupled to transmon qubits. We show that the appropriate description is selected by the hierarchy among the qubit frequency $\omega_q$, the characteristic transmission line frequency $\omega_{\mathrm{TL}}$, and the characteristic coupling frequency $\omega_g$. In the long-line continuum limit, the transmission line acts as a structured reservoir described by a Drude--Lorentz spectral density; in the short-line limit, it reduces to an effective single-mode resonator; and, between these limits, it behaves as a discrete multimode coupler. This provides a unified cQED picture of the dynamical regimes of finite-length transmission lines in superconducting-circuit architectures.

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Fabio Borrelli, Giovanni Miano, Adrian Parra-Rodriguez, Carlo Forestiere. 2026-04-23. Dynamical Regimes of Finite-Length Transmission Lines in Circuit Quantum Electrodynamics. https://arxiv.org/abs/2604.21463

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