Investigation of the effect of finite pulse errors on the BABA pulse sequence using the Floquet–Magnus expansion approach

Abstract

This paper presents the study of finite pulse widths for the BABA pulse sequence using the Floquet-Magnus expansion (FME) approach. In the FME scheme, the first order F1 is identical to its counterparts in average Hamiltonian theory (AHT) and Floquet theory (FT). However, the timing part in the FME approach is introduced via the Λ1 (t) function not present in other schemes. This function provides an easy way for evaluating the spin evolution during “the time in between” through the Magnus expansion of the operator connected to the timing part of the evolution. The evaluation of Λ1 (t) is useful especially for the analysis of the non-stroboscopic evolution. Here, the importance of the boundary conditions, which provides a natural choice of Λ1 (0) is ignored. This work uses the Λ1 (t) function to compare the efficiency of the BABA pulse sequence with δ – pulses and the BABA pulse sequence with finite pulses. Calculations of Λ1 (t) and F1 are presented.

Applications of Floquet–Magnus expansion, average Hamiltonian theory and Fer expansion to study interactions in solid state NMR when irradiated with the magic-echo sequence

“…Both theories still need more quantitative work to expand their use in the field of solid-state NMR. In the articles 22,23 , we studied spin dynamics under dipolar interactions using the FME. However, in this paper, we present the application of the AHT and FME approaches to the most useful interactions (CS, D, Q ) in solid-state NMR.…”

“…Instead, in this paper we studied Floquet-Magnus expansion (FME) 1,2,26,27 which is an alternative and unique approach in spin dynamics that shed new lights on both, AHT and FLT. This new scheme (FME), recently introduced to the solid-state NMR community had only been applied to Zeeman 31 and dipolar 22,23 interactions, and can be applied to any NMR interactions such as those investigated in this work.…”

Theories in Spin Dynamics of Solid-State Nuclear Magnetic Resonance Spectroscopy

“…In the above equations, the ( ) n t Λ functions with 1, 2, 3, n =  , represents the n th order term of the argument of the operator that introduces the frame such that the spin system operator is varying under the time independent Hamiltonian F . The evaluation of the function ( ) n t Λ is useful in many different ways, for instance, in rotating experiment of NMR, this function can be useful to quantify the level of productivity of double quantum terms [54] [55]. The FME propagator is given by:…”

“…effective Hamiltonian that will be useful to describe spin dynamics processes in solid-state NMR and understand different synchronized or non-synchronized experiments [34] [52]- [55]. Furthermore, our first applications of FE approach to study interactions in solid-state NMR when irradiated with the magic-echo sequence support this goal [52].…”

Progress in spin dynamics solid-state nuclear magnetic resonance with the application of Floquet–Magnus expansion to chemical shift anisotropy

“…The value and applicability of this approach lead Shirley 7 in 1965 to introduce this scheme to spectroscopy to solve the periodically time-dependent Schrodinger equation. From this initial introduction of FLT to quantum physics, the field of nuclear magnetic resonance spectroscopy has gained momentum with a continuous stream of conceptual advances and methodological innovations with new applications continuously increasing 19–24 . The two milestones theoretical approaches (AHT, FLT) and the two newly introduced theoretical approaches (FE, FME) used for NMR include:…”