Numerical Engineering of Effective Hamiltonians for High-Resolution Nanoscale Magnetic Resonance Imaging and Spectroscopy

Synopsis

Effective Hamiltonian engineering has proven to be an incredibly powerful tool in the field of quantum control for ensuring the robustness of control sequences with respect to various unwanted Hamiltonian terms. It has also found great use in engineering control sequences for sensing and spectroscopy applications, where effective Hamiltonian engineering is used for enhancing the effect that a variation in the Hamiltonian has on the evolution of the system. We demonstrate a general framework for precise and efficient numerical evaluation of arbitrary time-dependent perturbation theory terms generally appearing in effective Hamiltonian treatments. We apply this capability to perform force detected magnetic resonance experiments using silicon nanowire-based transducers and achieve a factor of 500 reduction of the proton-spin resonance linewidth in a(50−nm)3 volume of polystyrene. We make use of the enhanced spin coherence times to perform Fourier-transform imaging of proton spins with a one-dimensional slice thickness below 2 nm.