Understanding multi-quantum NMR through secular approximation

Unravelling the mechanism of polarization transfer from spin-1/2 to spin-1 system in solids

An analytic theory based on the concept of "effective-fields" is proposed to explain the mechanism of polarization transfer from spin I = 1/2 to spin S = 1 in non-rotating (static) solids. Employing an isolated two-spin model system, the matching conditions responsible for polarization transfer in cross-polarization (CP) experiments are identified and described in terms of the single-transition operators. In contrast to other existing treatments, the polarization transfer among spins is quantified through analytic expressions highlighting the individual contributions emerging from all plausible CP matching conditions. The interplay between the CP matching conditions observed in experiments is outlined in both isotropic and anisotropic systems and verified through comparison between simulations based on analytic and exact numerical methods. The predictions emerging from the analytic theory are verified over a wide range of experimentally relevant parameters and could be beneficial in the optimization of the CP experiments.

A perspective on the relative merits/demerits of time-propagators based on Floquet theorem

The present report examines the nuances of analytic methods employed in the derivation of evolution operators in periodically driven quantum systems based on Floquet theorem. Specifically, time-propagators of the form, U(t) = P(t)e-iH̄t defined in the Hilbert space (of finite dimension), are derived through generalized multimodal expansion of the operators involved. While Floquet methods defined in the extended Hilbert space (of infinite dimension) have remained the method of choice for the description of time-evolution at non-stroboscopic time-intervals, the expansion schemes discussed do present an attractive option for similar studies in the standard Hilbert space. Nevertheless, the convergence criteria and suitability of such methods deserve formal validation in problems of experimental relevance. Employing examples comprising periodic Hamiltonians from magnetic resonance spectroscopy, the exactness of Floquet based time-propagators in the Schrödinger and interaction representation is discussed. Through rigorous comparisons between simulations emerging from analytic and exact numerical methods, the relative merits and demerits of different formulations of Floquet based methods are also discussed.

Theory of radio-frequency pulses on periodically driven three-level systems: challenges and perspectives

Nuances of multiple-quantum transitions in periodically driven systems is discussed through analytical methods based on time propagators derived from Floquet theory.