Composite pulses for ultrabroad-band and ultranarrow-band excitation

Abstract

We introduce ultrabroad-band composite pulses (CPs), which maximize (at the expense of a finite error tolerance $\ensuremath{\epsilon}$) the pulse area range wherein the population inversion remains above $1\ensuremath{-}\ensuremath{\epsilon}$. We present such CPs for error thresholds $\ensuremath{\epsilon}=0.01$, 0.001, and 0.0001 in two versions: CPs with different pulse areas of the constituent pulses, used as control parameters, and with equal pulse areas. The former CPs naturally outperform the CPs of identical pulses, which in turn outperform conventional broad-band CPs obtained by annulling the population inversion derivatives at a single point. Moreover, we derive double-compensation CPs, which correct errors in both the pulse area and the detuning. They outperform the corresponding conventional CPs as well. By using the same error-tolerance approach, we construct ultranarrow-band CPs, which squeeze the population inversion in as narrow a range as possible while keeping the excitation outside this range below the error threshold $\ensuremath{\epsilon}$.