  Single-qubit sensing protocols can be used to measure qubit-bath coupling
parameters. However, for sufficiently large coupling, the sensing protocol
itself perturbs the bath, which is predicted to result in a characteristic
response in the sensing measurements. Here, we observe this bath perturbation,
also known as a quantum quench, by preparing the nuclear spin bath of a
nitrogen-vacancy (NV) center in polarized initial states and performing
phase-resolved spin echo measurements on the NV electron spin. These
measurements reveal a time-dependent phase determined by the initial state of
the bath. We derive the relationship between sensor phase and Gaussian spin
bath polarization, and apply it to reconstruct both the axial and transverse
polarization components. Using this insight, we optimize the transfer
efficiency of our dynamic nuclear polarization sequence. This technique for
directly measuring bath polarization may assist in preparing high-fidelity
quantum memory states, improving nanoscale NMR methods, and investigating
non-Gaussian quantum baths.
