Abstract
A general approach is introduced for the efficient simultaneous optimization of pulses that compensate each otherʼs 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.
Highlights
Sequences of coherent and well-defined pulses play an important role in the measurement and control of quantum systems
Rectangular pulses: At first sight, it may be surprising that the quality factor Φ = 0.62 of a Ramsey sequence based on simple rectangular pulses is markedly better than the performance based on highly optimized s2-COOP0 pulses of comparable duration
Their performance is significantly better than the quality factor Φ that is reached by rectangular pulses, which is marked in figure 5 by an open rectangle
Summary
Sequences of coherent and well-defined pulses play an important role in the measurement and control of quantum systems. Most experiments do consist of a single pulse, but of highly orchestrated sequences of pulses that are separated by delays, which are either constant or which are varied in a systematic way [1] This opens up additional opportunities to improve the overall performance of experiments beyond what is achievable by combining the best possible individually optimized (composite or shaped) pulses. This makes it possible to leverage on the interplay within a pulse sequence and to exploit the potential of the pulses to compensate each others imperfections in a given pulse sequence. A special focus will be put on the analysis of the available degrees of freedom and the scaling of overall pulse sequence performance as a function of pulse durations
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