Concurrently optimized cooperative pulses in robust quantum control: application to broadband Ramsey-type pulse sequence elements

A general approach is introduced for the efficient simultaneous optimization of pulses that compensate each other's imperfections within the same scan. This is applied to Ramsey-type experiments for a broad range of frequency offsets and scalings of the pulse amplitude, resulting in pulses with significantly shorter duration compared to individually optimized broadband pulses. The advantage of the cooperative pulse approach is demonstrated experimentally for the case of two-dimensional nuclear Overhauser enhancement spectroscopy. In addition to the general approach, a symmetry-adapted analysis of the optimization of Ramsey sequences is presented. Furthermore, the numerical results led to the disovery of a powerful class of pulses with a special symmetry property, which results in excellent performance in Ramsey-type experiments. A significantly different scaling of pulse sequence performance as a function of pulse duration is found for characteristic pulse families, which is explained in terms of the different numbers of available degrees of freedom in the offset dependence of the associated Euler angles. (paper)