Arbitrarily accurate composite pulse sequences (4 pages)

Chingiz Kabytayev, Todd J. Green, Kaveh Khodjasteh +3 more

Ruth Shewmon, Jaroslaw Labaziewicz, Yufei Ge +2 more

Boyan T. Torosov, Nikolay V. Vitanov

Composite pulse sequences, which produce arbitrary predefined rotations of a two-state system at an angle $\ensuremath{\theta}$ on the Bloch sphere, are presented. The composite sequences can contain arbitrarily many pulses and can compensate experimental errors in the pulse amplitude and duration to any desired order. A special attention is devoted to two classes of $\ensuremath{\pi}/2$ sequences---symmetric and asymmetric---the phases of which are given by simple formulas in terms of rational multiples of $\ensuremath{\pi}$ for any number of constituent pulses. This allows one to construct arbitrarily accurate $\ensuremath{\pi}/2$ composite rotations. These $\ensuremath{\pi}/2$ composite sequences are used to construct three classes of arbitrarily long composite $\ensuremath{\theta}$ sequences by pairing two $\ensuremath{\pi}/2$ composite sequences, one of which is shifted by a phase $\ensuremath{\pi}\ensuremath{-}\ensuremath{\theta}$ with respect to the other one.

Boyan T. Torosov, Nikolay V. Vitanov

We present three classes of symmetric broadband composite pulse sequences. The composite phases are given by analytic formulas (rational fractions of $\ensuremath{\pi}$) valid for any number of constituent pulses. The transition probability is expressed by simple analytic formulas and the order of pulse area error compensation grows linearly with the number of pulses. Therefore, any desired compensation order can be produced by an appropriate composite sequence; in this sense, they are arbitrarily accurate. These composite pulses perform equally well as or better than previously published ones. Moreover, the current sequences are more flexible as they allow total pulse areas of arbitrary integer multiples of $\ensuremath{\pi}$.