Tailoring the optimal control cost function to a desired output: application to minimizing phase errors in short broadband excitation pulses

Pattern pulses: design of arbitrary excitation profiles as a function of pulse amplitude and offset

“…In the present study, we used pulse durations between 2 and 6 ms and up to 24000 optimization parameters, which resulted in practical pulses. This study as well as previous studies (18,19,21) clearly show that state of the art spectrometers can inplement complicated pulses defined in a shape file with the same ease as much simpler pulses. We expect that the ability to create virtually arbitrary excitation patterns as a function of ν 0 and ν 1 will find numerous applications in NMR spectroscopy and imaging.…”

“…We expect that the ability to create virtually arbitrary excitation patterns as a function of ν 0 and ν 1 will find numerous applications in NMR spectroscopy and imaging. after the excitation pulse, x magnetization is brought back to the z axis by a time reversed broadband excitation pulse (BEBOP-tr) (18,19,20,21), and during the delay δ any remaining transverse magnetization is dephased by applying a gradient G 2 . Finally, in the presence of G 1 , the stored z magnetization is rotated to the x axis by a BEBOP pulse and the FID is recorded.…”

“…For example, for a broadband excitation pulse which is also robust with respect to rf amplitude variations due to pulse miscalibration or due to rf inhomogeneity, both ∆ν 0 and ∆ν 1 should be large, see e.g. (18)(19)(20)(21)(23)(24)(25)(26)(27). In contrast, for offset-selective or rf amplitude-selective pulses, ∆ν 0 or ∆ν 1 should be small, respectively (4,5,22,(28)(29)(30)(31)(32)(33)(34)(35)(36).…”

“…In contrast, the number of pulse parameters that can be optimized by optimal control based algorithms can be several orders of magnitude larger compared to conventional approaches. In NMR, this approach has been used so far to design bandselective pulses (9,(15)(16)(17), robust broadband excitation and inversion pulses (18)(19)(20)(21) and to explore the physical limits of pulse performance (20). Here, we demonstrate the design of pulses which create arbitrary patterns as a function of offset and rf amplitude.…”

Optimization of segmented linear Paul traps and transport of stored particles

“…Open loop optimal control has proved to be successful for the optimization of short broadband RF pulses in NMR experiments [48]. In a similar manner in ion trap based quantum computing tailored, light pulses can speed up and improve manipulation of the ions [49,50].…”