Enhancing time-suspension sequences for the measurement of weak perturbations

We detail key features for implementation of time-suspension multiple-pulse line-narrowing sequences. This sequence class is designed to null the average Hamiltonian (H¯(⁰)) over the period of the multiple-pulse cycle, typically to provide for high-resolution isolation of evolution from a switched interaction, such as field gradients for imaging or small sample perturbations. Sequence designs to further ensure null contributions from correction terms (H¯((¹)) and H¯(²)) of the Magnus expansion are also well known, as are a variety of approaches to second averaging, the process by which diagonal content is incorporated in H¯(⁰) to truncate unwanted terms. In spite of such designs, we observed spin evolution not explicable by H¯(⁰) using 16-, 24- and 48-pulse time-suspension sequences. We found three approaches to effectively remove artifacts that included splitting of the lineshape into unexpected multiplets as well as chirped evolution. The noted approaches are simultaneously compatible for combination of their benefits. The first ensures constant power deposition from RF excitation as the evolution period is incremented. This removes chirping and allows more effective 2nd averaging. Two schemes for the latter are evaluated: the noted introduction of a diagonal term in H¯(⁰), and phase-stepping the line-narrowing sequence on successive instances during the evolution period. Either of these was sufficient to remove artifactual splittings and to further enhance resolution, while in combination enhancements were maintained. Finally, numerical simulations provide evidence that our experimental line-narrowing results with ⁷⁵As in crystalline GaAs approach performance limits of idealized sequences (e.g., with ideal square pulses, etc.). The three noted experimental techniques should likewise benefit ultimate implementation with switched interactions and corresponding new error contributions, which place further demand on sequence performance.