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Abstract
This paper presents a study of finite pulse widths for the BABA pulse sequence using the Floquet–Magnus expansion (FME) approach. In the FME scheme, the first order 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
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
is particularly useful for the analysis of the non-stroboscopic evolution. Here, the importance of the boundary conditions, which provide a natural choice of
, is ignored. This work uses the
function to compare the efficiency of the BABA pulse sequence with
and the BABA pulse sequence with finite pulses. Calculations of
and
are presented.
Acknowledgements
Eugene S. Mananga acknowledges Professor Georges El Fakhri and the support from the United States National Institute of Health (T32 EB013180) at Harvard Medical School and Massachusetts General Hospital. This paper is dedicated to the memory of Emeritus University Distinguished Professor of Physics Herman Z. Cummins of The City University of New York who was a great mentor.