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

Defects in solid-state materials provide an ideal, robust platform for quantum sensing. To deliver maximum sensitivity, a large ensemble of noninteracting defects hosting quantum states with long coherence is required. Control of such an ensemble is challenging due to the spatial variation in both the defect energy levels and in any control field across a macroscopic sample. In this work, we experimentally demonstrate that we can overcome these challenges using Floquet theory and optimal control optimization methods to efficiently and coherently control a large defect ensemble, suitable for sensing. We apply our methods experimentally to a spin ensemble of up to 4×10⁹ nitrogen-vacancy centers in diamond. By explicitly including the hyperfine interaction to the intrinsic ¹⁴N nuclear spin in the optimization, we design shaped microwave control pulses that can outperform conventional (π) pulses when applied to sensing schemes, with an improvement in the strength of ensemble response of between 11% and 78%. Through simulation of the ensemble dynamics, we shed light on the bandwidth limitations of large-ensemble reinitialization and propose alternative routes for further improvement.