Quantum Oscillator Noise Spectroscopy via Displaced Cat States

Quantum harmonic oscillators are central to many modern quantum technologies. We introduce a method determine the frequency noise spectrum of oscillator modes through coupling them qubit with continuously driven qubit-state-dependent displacements. reconstruct using series different drive phase and amplitude modulation patterns in conjunction data-fusion routine based on convex optimization. apply technique identification intrinsic motional single trapped ion sensitivity fluctuations at sub-Hz level spectral range from quasi-dc up 50 kHz.