Correlations of Continuous Weak Measurements on a Single Spin

In the last years, the nitrogen-vacancy defect in diamond has been established as an exceptional quantum sensor for physical quantities like magnetic and electric fields, capable of detecting the faint signal of only a few proton nuclear spin outside the diamond crystal [1]. In order to perform nuclear magnetic resonance spectroscopy (NMR) on such samples, a continuous readout scheme was developed by several different groups [2-4].
We explain how this scheme, when applied to the spectroscopic investigation of individual nuclear spins, can be understood as subsequent weak measurements of the nuclear spin with non-commuting measurement operators. When varying the parameters of the measurement, the observed nuclear spin signal deviates from the intrinsic Larmor precession, towards a regime where the signal is dominated by the measurement.

[1] Staudacher, T. et al. Science 339, 561-563 (2013).
[2] Schmitt, S. et al. Science 356, 832–837 (2017).
[3] Boss, J. M., Cujia, K. S., Zopes, J. & Degen, C. L. Science 356, 837–840 (2017).
[4] Bucher, D. B. et al. arXiv:1705.08887 [quant-ph] (2017).