Ramsey interferometry is a widely used tool for precisely measuring transition frequencies between two energy levels of a quantum system, with applications in time keeping, precision spectroscopy, quantum optics, and quantum information. Often, the coherence time of the quantum system surpasses the one of the oscillator probing the system, thereby limiting the interrogation time and associated spectral resolution. Correlation spectroscopy overcomes this limitation by probing two quantum systems with the same noisy oscillator for a measurement of their transition frequency difference; this technique has enabled very precise comparisons of atomic clocks. Here, we extend correlation spectroscopy to the case of multiple quantum systems undergoing strong correlated dephasing. We model Ramsey correlation spectroscopy with $N$ particles as a multiparameter phase estimation problem and demonstrate that multiparticle correlations can assist in reducing the measurement uncertainties even in the absence of entanglement. We derive precision limits and optimal sensing techniques for this problem and compare the performance of probe states and measurement with and without entanglement. Using one- and two-dimensional ion Coulomb crystals with up to 91 qubits, we experimentally demonstrate the advantage of measuring multiparticle correlations for reducing phase uncertainties and apply correlation spectroscopy to measure ion-ion distances, transition frequency shifts, laser-ion detunings, and path-length fluctuations. Our method can be straightforwardly implemented in experimental setups with globally coherent qubit control and qubit-resolved single-shot readout and is, thus, applicable to other physical systems such as neutral atoms in tweezer arrays.

中文翻译：

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具有多量子位增强相位估计的相关光谱

拉姆齐干涉测量是一种广泛使用的工具，用于精确测量量子系统两个能级之间的跃迁频率，其应用领域包括计时、精密光谱、量子光学和量子信息。通常，量子系统的相干时间超过探测系统的振荡器的相干时间，从而限制了询问时间和相关的光谱分辨率。相关光谱通过探测具有相同噪声振荡器的两个量子系统来测量它们的跃迁频率差，从而克服了这一限制；这项技术使得原子钟的比较变得非常精确。在这里，我们将相关光谱扩展到经历强相关相移的多个量子系统的情况。我们对拉姆齐相关光谱进行建模$氮$粒子作为多参数相位估计问题，并证明即使在没有纠缠的情况下，多粒子相关性也可以帮助减少测量不确定性。我们针对这个问题得出了精度限制和最佳传感技术，并比较了有和没有纠缠的探针状态和测量的性能。使用具有多达 91 个量子位的一维和二维离子库仑晶体，我们通过实验证明了测量多粒子相关性对于降低相位不确定性的优势，并应用相关光谱来测量离子间距离、跃迁频率偏移、激光离子失谐和路径长度波动。我们的方法可以在具有全局相干量子位控制和量子位解析单次读出的实验装置中直接实现，因此适用于其他物理系统，例如镊子阵列中的中性原子。