Robust microwave cavity control for NV ensemble manipulation

Nitrogen-vacancy (NV) center ensembles have the potential to improve a wide range of applications, including nuclear magnetic resonance spectroscopy at the microscale and nanoscale, wide-field magnetometry, and hyperpolarization of nuclear spins via the transfer of optically induced NV polarization to nearby nuclear spin clusters. These NV ensembles can be coherently manipulated with microwave cavities, that deliver strong and homogeneous drivings over large volumes. However, the pulse shaping for microwave cavities presents the challenge that the external controls and intracavity field amplitudes are not identical, leading to adverse effects on the accuracy of operations on the NV ensemble. In this paper, we introduce a method based on gradient ascent pulse engineering (GRAPE) to optimize external controls, resulting in robust pulses within the cavity while minimizing the effects of cavity ringings. The effectiveness of the method is demonstrated by designing both <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>π</a:mi></a:math> and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>π</b:mi><b:mo>/</b:mo><b:mn>2</b:mn></b:mrow></b:math> pulses. These optimized controls are then integrated into a PulsePol sequence, where numerical simulations reveal a resilience to detunings five times larger than those tolerated by the sequence constructed using standard controls.