Movies S1 to S4 from the manuscript Optimal control pulses for the 1.2 GHz (28.2 T) NMR spectrometers

Movie S2. The effect of a hard pulse and a UR-90◦ pulse. The simulation was generated by solving the Liouville-von Neumann equation for the dynamics of isolated single spins under the influence of a 90◦-hard (rectangular pulse in simulation) pulse shown in the top panel and under the influence of a UR 90 ◦ 1 H (650 μs, 8 kHz RFA, ±7.5 kHz BW, ±20% Δ𝜈1 pulse as shown in the bottom panel.

Both the pulses were miscalibrated to ±10% in simulation and the effect of this is shown as spins in the orange color that had -10% B1 miscalibration, in magenta for spins with 0% B1 miscalibration, and dark purple color for spins under +10% B1 miscalibration. In all the three cases we had 11 spins that were spread across a bandwidth of ±7.5 kHz. The Bloch spheres show the transformation of all three orthogonal magnetization components under the above two pulses.

Movie S3. Simulation showing the symmetry relation between the pulse shape and the spin trajectories. The simulation was generated by solving the Liouville-von Neumann equation for the dynamics of isolated single spins under the influence of a UR 180 ◦ 1 H (700 μs, 8 kHz RFA, ±7.5 kHz BW, ±20% Δ𝜈1) without a symmetry in the top panel and a UR 180 ◦ 15 N (700 μs, 5 kHz RFA, ±3 kHz BW, ±20% Δ𝜈1 with a mirror symmetry in the bottom panels.

The effect of the a bove pulses is shown for a single on resonance spin starting as I z operator state in the first column, as I x state in the second column and as I y operator state in the last column. The Bloch spheres are aligned along the unitary rotation (x-axis) axis of the pulses to observe the symmetry relations between the shapes and the spin trajectories. Movie S4.

The effect of the BSCa(CO)URBOP 180 ◦ pulse and the BSCa(CO)URBOP 90 ◦ pulse. The simulation was generated by solving the Liouville-von Neumann equation for the dynamics of isolated single spins under the influence of the BSCa(CO)URBOP 180 ◦ (300 μs, 15kHz RFA, 12.6 (9) kHz BW, ±20% Δ𝜈1) pulse is shown in the top panel and under the influence of the BSCa(CO)URBOP 90 ◦ (290 μs, 15 kHz RFA, 12.6 (9) kHz BW, ±20% Δ𝜈1) pulse is shown in the bottom panel.

The influence of these pulses on CO spins (in green color) spread over 9 kHz and Ca spins (in orange color) spread over 12.6 kHz is shown on all the Bloch spheres. The Bloch spheres show the transformation of all three orthogonal magnetization components under the above two pulses.