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arXiv · 2301.08551

Transmission-based noise spectroscopy for quadratic qubit-resonator interactions

Philipp M. Mutter·Guido Burkard
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Abstract

We develop a theory describing the transient transmission through noisy qubit-resonator systems with quadratic interactions as are found in superconducting and nanomechanical resonators coupled to solid-state qubits. After generalizing the quantum Langevin equations to arbitrary qubit-resonator couplings, we show that only the cases of linear and quadratic couplings allow for an analytical treatment within standard input-output theory. Focussing for the first time on quadratic couplings and allowing for arbitrary initial qubit coherences, it is shown that noise characteristics can be extracted from input-output measurements by recording both the averaged fluctuations in the transmission probability and the averaged phase. Our results represent an extension to the field of transmission-based noise spectroscopy with immediate practical applications.

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Philipp M. Mutter, Guido Burkard. 2023-01-20. Transmission-based noise spectroscopy for quadratic qubit-resonator interactions. https://doi.org/10.1103/physreva.107.052603

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