Pushing the sensitivity of nuclear magnetic resonance spectroscopy down to the single nuclear spin limit is a long-standing goal, and would find applications both in quantum computing and in high-precision spectroscopy. So far, the only mechanisms to detect individual nuclear spins is using an electron spin in close proximity, which couples via hyperfine interaction and acts as a local antenna. Therefore, individual nuclear spin detection requires single electron spin readout. 

Until recently, detection of single electron spins has been limited to electrical or optical readout, which achieves single electron spin detection only for certain specific systems, thus limiting the range of study. Our group has recently developed a new method to detect electron spins at 10~mK. By coupling the electron spin to a low-mode-volume, high-quality-factor resonator, the radiative relaxation rate of the spin is enhanced by the Purcell effect. The spontaneous emission is detected by a novel detector relying on superconducting transmon qubit, the SMPD. As it relies solely on the magnetic dipole coupling of the spin magnetic moment to a resonator, this all-microwave method should be in principle broadly applicable to a large range of unpaired electron spin systems.

In this presentation, we demonstrate a range of new methods to readout and measure the spectrum of individual nuclear spins coupled to an electron spin, itself measured by microwave photon counting. We apply these methods to the operation of a two-nuclear-spin-qubit register, and to the high-resolution spectroscopy of an individual nuclear-spin-9/2 impurity.