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

This paper presents a study of finite pulse widths for the BABA pulse sequence using the FloquetMagnus 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 Lambda 1(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 Lambda 1(t) is particularly useful for the analysis of the non-stroboscopic evolution. Here, the importance of the boundary conditions, which provide a natural choice of Lambda 1(0), is ignored. This work uses the function to compare the efficiency of the BABA pulse sequence with delta-pulses and the BABA pulse sequence with finite pulses. Calculations of Lambda 1(t) and F1 are presented.