Investigation of the Effect of Finite Pulse Errors on BABA Pulse Sequence Using Floquet-Magnus Expansion Approach

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.