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Defects in solid state materials provide an ideal, robust platform forquantum sensing. To deliver maximum sensitivity, a large ensemble ofnon-interacting defects hosting coherent quantum states are required. Controlof such an ensemble is challenging due to the spatial variation in both thedefect energy levels and in any control field across a macroscopic sample. Inthis work we experimentally demonstrate that we can overcome these challengesusing Floquet theory and optimal control optimization methods to efficientlyand coherently control a large defect ensemble, suitable for sensing. We applyour methods experimentally to a spin ensemble of up to 4 $\times$ 10$^9$nitrogen vacancy (NV) centers in diamond. By considering the physics of thesystem and explicitly including the hyperfine interaction in the optimization,we design shaped microwave control pulses that can outperform conventional($\pi$-) pulses when applied to sensing of temperature or magnetic field, witha potential sensitivity improvement between 11 and 78\%. Through dynamicalmodelling of the behaviour of the ensemble, we shed light on the physicalbehaviour of the ensemble system and propose new routes for furtherimprovement.

Optimal control of a nitrogen-vacancy spin ensemble in diamond for sensing in the pulsed domain