A method for measuring small energy level shifts in a qubit by coherent amplification of their effect is proposed. It is based on the repeated application of the same interaction pulse in two manners: with the same phase of each subsequent pulse, and with an alternating phase shift of $\pi$ (i.e., a minus sign) from pulse to pulse. Two specific types of pulses are considered: a resonant $\pi$ pulse and an adiabatic chirped pulse, both of which produce population inversion with high fidelity. In the presence of a weak ambient external electric or magnetic field, the ensuing Stark or Zeeman shift leads to an energy level shift and hence a static detuning. In both the resonant and adiabatic approaches, a small level shift does not alter the transition probability very much; however, it can significantly change the dynamical phases in the propagator. The repeated application of the same pulse greatly amplifies the changes in the dynamical phases and maps them onto the populations. Hence the effect of the level shift can be measured with good accuracy. It is found that sequences of pulses with alternating phases deliver much greater error amplification and much steeper excitation profiles around resonance, thereby providing much higher sensitivity to small energy level shifts. Explicit analytic estimates of the sensitivity are derived using the well-known noncrossing Rosen-Zener and Rabi models and the level-crossing Demkov-Kunike model. This recipe provides a simple tool for rapid and accurate sensing of weak electric and magnetic fields by using the same pulse generating an inversion quantum gate, without sophisticated tomography or entangling operations.

中文翻译：

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通过能级位移效应的相干放大对弱电场和磁场进行量子传感

提出了一种通过相干放大效应来测量量子位中小能级位移的方法。它基于以两种方式重复应用相同的相互作用脉冲：每个后续脉冲的相位相同，以及交替相移为$\pi$（即，减号）从脉冲到脉冲。考虑了两种特定类型的脉冲：谐振$\pi$脉冲和绝热啁啾脉冲，两者都产生高保真粒子数反转。在存在微弱的环境外部电场或磁场的情况下，随之而来的斯塔克或塞曼位移会导致能级位移，从而导致静态失谐。在共振和绝热方法中，小的能级偏移不会对跃迁概率产生很大影响；然而，它可以显着改变传播器中的动态相位。相同脉冲的重复应用极大地放大了动态相位的变化并将它们映射到种群上。因此，可以以良好的精度测量电平偏移的影响。发现具有交替相位的脉冲序列在共振周围提供更大的误差放大和更陡峭的激励曲线，从而对小的能级变化提供更高的灵敏度。使用众所周知的非交叉 Rosen-Zener 和 Rabi 模型以及水平交叉 Demkov-Kunike 模型导出敏感性的显式分析估计。该配方提供了一种简单的工具，通过使用相同的脉冲生成反转量子门，快速准确地感测弱电场和磁场，无需复杂的断层扫描或纠缠操作。