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 $\ensuremath{\pi}$ and non-$\ensuremath{\pi}$ 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-$\ensuremath{\pi}$ pulses and a general inequality between the symmetric (classical) and antisymmetric (quantum) components of the noise spectrum generated by a Gaussian bath. We analyze the robustness of our method on state-preparation and measurement errors and pulse imperfection. Simulation demonstrates the effectiveness of our method.