Magnetic pseudo-fields in a rotating electron-nuclear spin system

Analogous to the precession of a Foucault pendulum observed on the rotating Earth, a precessing spin observed in a rotating frame of reference appears frequency-shifted. This can be understood as arising from a magnetic pseudo-field(1,2) in the rotating frame that nevertheless has physically significant consequences, such as the Barnett effect(3). To detect these pseudo-fields, a rotating-frame sensor is required(4). Here we use quantum sensors, nitrogen-vacancy (NV) centres, in a rapidly rotating diamond to detect pseudo-fields in the rotating frame. Whereas conventional magnetic fields induce precession at a rate proportional to the gyromagnetic ratio, rotation shifts the precession of all spins equally, and thus primarily affect C-13 nuclear spins in the sample. We are thus able to explore these effects via quantum sensing in a rapidly rotating frame, and define a new approach to quantum control using rotationally induced nuclear spin-selective magnetic fields. This work provides an integral step towards realizing precision rotation sensing and quantum spin gyroscopes.