Abstract
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.
Highlights
Quantum sensing uses platforms such as photons, ions, solidstate defects, and their quantum properties as resources to estimate physical quantities as precisely as possible[1,2]
We extend our studies by explicitly analyzing the influence of imperfect readout of our sensor qubit and perform a detailed comparison between two readout strategies.We show that these results can be applied to find the optimal protocol for frequency estimation[15,16,17,18,19] and we use this protocol to experimentally estimate the value of a single unknown frequency
nuclear magnetic resonance (NMR) can be used to answer “yes–no”. Questions such as whether a certain toxin or metabolite is present in the sample
Summary
Quantum sensing uses platforms such as photons, ions, solidstate defects, and their quantum properties as resources to estimate physical quantities as precisely as possible[1,2]. The performance depends on the sensing and readout protocols, which should optimize the ratio of the sensor response for the parameter of interest[3,4] to readout noise[5]. Finding optimal protocols is crucial to enabling efficient estimation. One of the major applications of quantum sensing is nanoscale nuclear magnetic resonance (NMR) spectroscopy in which a nanoscale quantum sensor replaces the macroscopic inductive coil and interacts with a sample of nuclear spins[6,7,8,9]. Pioneering work with the nitrogen-vacancy (NV) center in diamond[10,11], has demonstrated nanoscale spatial resolution[6,7,12,13,14] with single spin sensitivity[9]. Understanding and realizing the limits of quantum measurements is important in spectroscopy wherein frequency encodes energy, spatial, and structural information
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