Continuous Bloch sphere mapping of nuclear states via weak measurement

We report on a strategy for the continuous mapping of nuclear spin states on a Bloch sphere for minute long periods. Our approach exploits nuclear spins initialized in Floquet prethermal transverse states on a Bloch sphere via spin-lock quantum control, and their non-destructive interrogation spins via homodyned weak measurement. Signal-to-noise gains are provided by hyperpolarizing the nuclear spins via coupling to optically pumped electrons. We demonstrate the technique for hyperpolarized ¹³C nuclear spins in diamond, and show the Bloch-sphere mapping of quantum states for up to 50s. We apply it to the continuous ``tracking’’ of magnetic fields with Floquet prethermal ¹³C quantum sensors. Overall this work opens intriguing possibilities for continuously interrogated quantum sensors and in mapping phase diagrams of driven out-of-equilibrium phases of quantum matter.