Precise frequency measurements are important in applications ranging from navigation and imaging to computation and communication. Here we outline the optimal quantum strategies for frequency discrimination and estimation in the context of quantum spectroscopy, and we compare the effectiveness of different readout strategies. Using a single NV center in diamond, we implement the optimal frequency discrimination protocol to discriminate two frequencies separated by 2 kHz with a single 44 μs measurement, a factor of ten below the Fourier limit. For frequency estimation, we achieve a frequency sensitivity of 1.6 µHz/Hz² for a 1.7 µT amplitude signal, which is within a factor of 2 from the quantum limit. Our results are foundational for discrimination and estimation problems in nanoscale nuclear magnetic resonance spectroscopy.

精确的频率测量在从导航和成像到计算和通信的应用中非常重要。在这里，我们概述了在量子光谱学中用于频率判别和估计的最佳量子策略，并且我们比较了不同读出策略的有效性。使用钻石中的单个NV中心，我们实施了最佳的频率区分协议，以一次44μs的测量来区分以2 kHz分开的两个频率，比傅立叶极限低10倍。对于频率估计，我们实现了1.6 µHz / Hz ²的频率灵敏度对于一个1.7 µT的幅度信号，该幅度是量子极限的2倍之内。我们的结果为纳米级核磁共振波谱的判别和估计问题奠定了基础。