Advanced Hamiltonian engineering in spin ensembles for enhanced sensing and control

The study of many-body quantum systems, and specifically spin systems, is a main pillar of quantum physics. As part of this research direction, various experimental platforms have emerged which allow for controlled experiments in this context, with nitrogen vacancy (NV) ensembles in diamond being one of them. In order to realize relevant experiments in the NV system, advanced controlled schemes are required in order to generate the required interacting spin Hamiltonians, as well as to robustly control such dense spin ensembles. Here we tackle both issues: we develop a framework for Hamiltonian engineering based on the icosahedral symmetry group, demonstrating its advantages over existing schemes in terms of obtainable interacting Hamiltonians; we develop and demonstrate robust control pulses based on rapid adiabatic passage (RAP), which result in improved coherence times and sensing.