Quantum harmonic oscillators are central to many modern quantum technologies. We introduce a method to determine the frequency noise spectrum of oscillator modes through coupling them to a qubit with continuously driven qubit-state-dependent displacements. We reconstruct the noise spectrum using a series of different drive phase and amplitude modulation patterns in conjunction with a data-fusion routine based on convex optimization. We apply the technique to the identification of intrinsic noise in the motional frequency of a single trapped ion with sensitivity to fluctuations at the sub-Hz level in a spectral range from quasi-DC up to 50 kHz.
@article{arxiv.2010.04375,
title = {Quantum oscillator noise spectroscopy via displaced cat states},
author = {Alistair R. Milne and Cornelius Hempel and Li Li and Claire L. Edmunds and Harry J. Slatyer and Harrison Ball and Michael R. Hush and Michael J. Biercuk},
journal= {arXiv preprint arXiv:2010.04375},
year = {2021}
}