Bimodal Floquet theory of phase-modulated heteronuclear decoupling experiments in solid-state NMR spectroscopy

Low power supercycled TPPM decoupling

Improving the spectral sensitivity and resolution of biological solids is one of the long-standing problems in nuclear magnetic resonance (NMR) spectroscopy. In this report, we introduce low-power supercycled variants of two-pulse phase-modulated (TPPM) sequence for heteronuclear decoupling. The utility of the sequence is shown by improvements in the transverse relaxation time of observed nuclei (with 1H decoupling) with its application to different samples (uniformly 13C, 15N, 2H-labeled GB1 back-exchanged with 25% H2O and 75% D2O, uniformly 13C, 15N, 2H-labeled human derived Asyn fibril back-exchanged with 100% H2O and uniformly 13C, 15N -labeled human derived Asyn fibril) at fast MAS using low radiofrequency (RF) fields. To understand the effect of spinning speed, the transverse relaxation time is monitored under different spinning frequencies. In comparison to existing heteronuclear decoupling sequences, the supercycled TPPM (sTPPM) sequence significantly improves the spectral sensitivity and resolution and is robust towards B1 inhomogeneity and decoupler offset.

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.