Exact amplitudes of parametric processes in driven Josephson circuits

• URL: http://arxiv.org/abs/2501.07784v1
• Date: Tue, 14 Jan 2025 02:03:19 GMT
• Title: Exact amplitudes of parametric processes in driven Josephson circuits
• Authors: Roman Baskov, Daniel K. Weiss, Steven M. Girvin,
• Abstract summary: We present a general approach for analyzing arbitrary parametric processes in Josephson circuits within a single degree of freedom approximation. We obtain formally exact amplitudes (supercoefficients') of these parametric processes for driven SNAIL-based and SQUID-based circuits.
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• Abstract: We present a general approach for analyzing arbitrary parametric processes in Josephson circuits within a single degree of freedom approximation. Introducing a systematic normal-ordered expansion for the Hamiltonian of parametrically driven superconducting circuits we present a flexible procedure to describe parametric processes and to compare different circuit designs for particular applications. We obtain formally exact amplitudes (`supercoefficients') of these parametric processes for driven SNAIL-based and SQUID-based circuits. The corresponding amplitudes contain complete information about the circuit topology, the form of the nonlinearity, and the parametric drive, making them, in particular, well-suited for the study of the strong drive regime. We present a closed-form expression for supercoefficients describing circuits without stray inductors and a tractable formulation for those with it. We demonstrate the versatility of the approach by applying it to the estimation of Kerr-cat qubit Hamiltonian parameters and by examining the criterion for the emergence of chaos in Kerr-cat qubits. Additionally, we extend the approach to multi-degree-of-freedom circuits comprising multiple linear modes weakly coupled to a single nonlinear mode. We apply this generalized framework to study the activation of a beam-splitter interaction between two cavities coupled via driven nonlinear elements. Finally, utilizing the flexibility of the proposed approach, we separately derive supercoefficients for the higher-harmonics model of Josephson junctions, circuits with multiple drives, and the expansion of the Hamiltonian in the exact eigenstate basis for Josephson circuits with specific symmetries.

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