Simultaneous soft pulses applied at nearby frequencies

The rotation of a spin subject to an on-resonance soft pulse and simultaneously to a soft pulse at a nearby frequency may strongly deviate from the desired rotation expected for a single on-resonance pulse. The deviation is the result of transient frequency shifts of the spin caused by the off-resonance irradiation. We show that the resulting error can be corrected by shifting the frequency of the on-resonance pulse in such a way that it tracks the shift of the spin frequency. Experimentally, the effectiveness of this simple and intuitive method is demonstrated for simultaneous inversions at nearby frequencies in the case of both coupled and uncoupled spins. Simulations predict that the correction technique is effective for arbitrary pulse shapes and tip angles and is particularly useful when the frequency window of the shaped pulse is two to eight times the frequency separation between the chemical shifts of the two spins.