Controlling effective Hamiltonians: Broadband pulsed dynamic nuclear polarization by constrained random walk and non-linear optimization

We present constrained random walk (cRW) and figure of merit (FOM) based non-linear optimization procedures for systematic design and fundamental understanding of magnetic resonance experiments, addressing bilinear and linear effective Hamiltonians to provide broadband polarization transfer. cRW can be used directly for fast random experiment design or in combination with non-linear optimization or optimal control, leveraging the optimization of a FOM function for efficient control of linear and bilinear terms derived by exact effective Hamiltonian theory. The efficacy of the combined cRW and FOM-based optimization approach is demonstrated by the design of broadband dynamic nuclear polarization pulse sequences for static solids with an electron spin excitation bandwidth reaching 100 MHz.