We develop a systematic approach to derive narrowband (NB) and passband (PB) composite sequences which can produce any preselected transition probability with any desired accuracy. The NB composite pulses are derived by successive cancellation of derivative terms in the propagator. The PB pulses are built by combining two $\pi /2$ NB pulses. Both the NB and the PB pulses feature vanishing wings on both sides of the central region around the target transition probability, and the PB pulses offer also a flat (broadband) top around the target probability. The NB sequences are particularly suitable for sensing and metrology applications, whereas the PB sequences can be very useful for qubit control in the case of tightly spaced laser-driven qubits for they ensure both selectivity (suppressed cross talk to neighbors) and robustness (suppressed laser pointing instability). Other possible applications include selective (NB) or both selective and robust (PB) control of close transitions in frequency space.

中文翻译：

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窄带和通带复合脉冲用于可变旋转

我们开发了一种系统的方法来导出窄带（NB）和通带（PB）复合序列，该序列可以产生具有任何所需精度的任何预选转换概率。NB复合脉冲是通过在传播器中连续消除导数项而得出的。PB脉冲是通过组合两个$\pi /2$NB脉冲。NB和PB脉冲均在目标跃迁概率附近的中央区域两侧均具有消失的翅膀，并且PB脉冲在目标概率附近也提供平坦（宽带）顶部。NB序列特别适合于传感和计量应用，而PB序列在紧密间隔的激光驱动量子位的情况下对于量子位控制非常有用，因为它们既确保了选择性（抑制了与邻居的串扰）又增强了鲁棒性（抑制了激光）指向不稳定）。其他可能的应用包括频率空间中近距离的选择性（NB）或选择性和鲁棒（PB）控制。