Transmission-based noise spectroscopy for quadratic qubit-resonator interactions

TL;DR

This paper presents a theoretical framework for noise spectroscopy in qubit-resonator systems with quadratic interactions, enabling extraction of noise characteristics from transmission measurements, with potential practical applications.

Contribution

It extends the theory of transmission-based noise spectroscopy to quadratic qubit-resonator couplings, allowing analysis with arbitrary initial qubit states.

Findings

Analytical treatment of quadratic couplings within input-output theory.

Noise characteristics can be extracted from transmission and phase measurements.

Applicable to superconducting and nanomechanical resonator systems.

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.