Broadband spectroscopy of quantum noise

Characterizing noise is key to the optimal control of the quantum system it affects. Using a single-qubit probe and appropriate sequences of $\pi$ and non-$\pi$ pulses, we show how one can characterize the noise a quantum bath generates across a wide range of frequencies -- including frequencies below the limit set by the probe's $\mathbb{T}_2$ time. To do so we leverage an exact expression for the dynamics of the probe in the presence of non-$\pi$ pulses, and a general inequality between the symmetric (classical) and anti-symmetric (quantum) components of the noise spectrum generated by a Gaussian bath. Simulation demonstrates the effectiveness of our method.