Optimal frequency measurements with quantum probes

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.

Advances in nano- and microscale NMR spectroscopy using diamond quantum sensors

“…However, more sophisticated pulse sequences have been established, extending the practical measurement time, and reaching theoretically arbitrary spectral resolution. 10,[63][64][65][66] Interested readers are referred to excellent reviews. 53,56,57 Further note that reliable information about the quantum state of the NV center can only be obtained by multiple read-outs to gain sufficient statistics (quantum mechanics is intrinsically probabilistic, spin projection noise).…”

Quantum metrology with imperfect measurements

“…Moreover, as the photon emissions are spontaneous and random, the same photon-number being recorded can actually come from both the dark and bright signals, albeit with different probabilities. These for the readout of an NV-centre are modelled as two Poissonian distributions of distinct means, depending also on the number of QND repetitions 76,77 , often approximated by Gaussians 53 -Fig. 6 | Attaining the optimal SS of precision in presence of measurement imperfections and local unitary control.…”

Advances in nano- and microscale NMR spectroscopy using diamond quantum sensors

“…After that, the experiment must be restarted, limiting the spectral resolution achievable to a few kHz. However, more sophisticated pulse sequences have been established, extending the practical measurement time, and reaching a theoretically arbitrary spectral resolution 10,[63][64][65][66] . Interested readers are referred to excellent reviews 53,56,57 .…”