Provably optimal controls for magnetometry in cluttered environments

The extreme fragility of quantum systems makes them ideally suited for sensing applications such as magnetometry, biological imaging and noise characterization for quantum computing. However, interpreting a qubit-based sensor's output is generally complicated by background clutter arising from both out-of-band spectral leakage, and ambiguity in signal origin when the implemented qubit drive is imperfect. Here we present a novel sensing protocol based on the optimal band-limited Slepian functions that overcomes both of these challenges. We construct Slepian-based controls using a finite-difference method that preserves the relevant spectral concentration while removing nonlinearities in the sensor response which arise when targeting ambient noise signatures that couple to the sensor's signal through an additive dephasing Hamiltonian term, such as magnetic field fluctuations. We experimentally implement a tomographic measurement framework which separates multi-axes contributions using projective measurements on a single trapped ion magnetometer. Experiments validate the spectral concentration of the new finite-difference controls and allow for simultaneous, narrowband spectrum reconstruction of both environmental dephasing and control noise fields.