Transmission-based noise spectroscopy for quadratic qubit-resonator interactions

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 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.

Automated summary

We develop a theory to describe the transient transmission through noisy qubit-resonator systems, where quadratic interactions are present in superconducting and nanomechanical resonators coupled to solid-state qubits. By generalizing the quantum Langevin equations, we find that only linear and quadratic couplings allow for an analytical treatment using standard input-output theory. Focusing on quadratic couplings and arbitrary initial qubit coherences, we demonstrate that noise characteristics can be extracted from input-output measurements by analyzing the averaged fluctuations in transmission probability and phase. Our results extend the field of transmission-based noise spectroscopy and have immediate practical applications.