Fig. 4: The excitation fidelity \(\langle {{{{{{{\boldsymbol{\rho }}}}}}}}| {I}_{{{{{{{{\rm{x}}}}}}}}} \rangle\) calculated for parallel pulse execution.
From: A digital twin for parallel liquid-state nuclear magnetic resonance spectroscopy
a Fidelity of the parallel hard pulse plotted against coupling strengths (\({{{{{{{\rm{c.s.}}}}}}}}=\left\vert {F}_{12}/{F}_{11}\right\vert\)). Each pulse has a 90° flip angle and lasts for 20 μs. b Fidelity of optimal control pulses applied in parallel under selected coupling strengths, ν0 and ν1 represent the resonance offset and radio frequency amplitudes, respectively. The radio frequency amplitude is determined based on the local B1 field, considering a fixed excitation power, resulting in slight variations of its range as the coupling strength is modified. The two channels are indicated as chn. 1 and chn. 2.
