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Quantum sensors have recently achieved to detect the magnetic moment of fewor single nuclear spins and measure their magnetic resonance (NMR) signal.However, the spectral resolution, a key feature of NMR, has been limited byrelaxation of the sensor to a few kHz at room temperature. The spectralresolution of NMR signals from single nuclear spins can be improved by, e.g.,using quantum memories, however at the expense of sensitivity. Classicalsignals on the other hand can be measured with exceptional spectral resolutionby using continuous measurement techniques, without compromising sensitivity.To apply these techniques to single-spin NMR, it is critical to overcome theimpact of back action inherent of quantum measurements. Here we reportsequential weak measurements on a single $^{13}$C nuclear spin. The back-actionof repetitive weak measurements causes the spin to undergo a quantum dynamicsphase transition from coherent trapping to coherent oscillation. Single-spinNMR at room-temperature with a spectral resolution of 3.8 Hz is achieved. Theseresults enable the use of measurement-correlation schemes for the detection ofvery weakly coupled single spins.

High-resolution spectroscopy of single nuclear spins via sequential weak measurements