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 e ect 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 a ect 13 C nuclear spins in the sample. We are thus able to explore these e ects 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.A spin measured by an observer in a rotating frame appears to precess faster or slower depending on , the rotational angular frequency of the frame. This can be thought of as arising from an effective magnetic field 1,2 B Ω = /γ in the rotating frame, with γ the spin gyromagnetic ratio. Despite being referred to as 'fictitious' fields, rotationally induced magnetic pseudo-fields have measurable effects, in the same way that spin-state-dependent vector light shifts 5 and artificial gauge fields 6 have real effects. In the Barnett effect 3 , for example, the effective magnetic field generated by physically rotating an initially unmagnetized rod of iron leads to polarization of the constituent electron spins along the rotation axis, and magnetization of the iron sample. In this work, we explore for the first time quantum sensing of pseudo-fields in the physically rotating frame, using solid-state qubits that detect rotational pseudo-fields and simultaneously are uniquely suited to exploring quantum control with rotation.Exploring rotational pseudo-fields imposes considerable experimental challenges, as the sensor must be in the rotating frame 4,7 . Nuclear spin gyroscopes operate on a similar principle, where it is the sensing apparatus that executes rotations about a gas of nuclear spins 8 . Magic-angle spinning 9 nuclear magnetic resonance (NMR) experiments routinely study rapid rotations of more than 10 kHz in nuclear spin systems, and recent work has used a pickup coil rotating with the sample to measure the rotational pseudo-field 4,10,11 . However, NMR-based experiments require a strong polarizing magnetic field (much larger than the pseudo-fields) to obtain a signal, limiting these experiments to detection of small perturbations due to rotation. Both nuclear spin gyroscopes and pickup coils are operated essentially classically, with limited scope to fully study the effects of rotational pseudo-fields on quantum systems.Solid-state spin systems, ...

Single-qubit sensing in a physically rotating reference frame with defect centers in diamond.

Diamond-based quantum magnetometers are more sensitive to oscillating (AC) magnetic fields than static (DC) fields because the crystal impurity-induced ensemble dephasing time T * 2 , the relevant sensing time for a DC field, is much shorter than the spin coherence time T2, which determines the sensitivity to AC fields. Here we demonstrate measurement of DC magnetic fields using a physically rotating ensemble of nitrogen-vacancy centres at a precision ultimately limited by T2 rather than T * 2 . The rotation period of the diamond is comparable to T2 and the angle between the NV axis and the target magnetic field changes as a function of time, thus upconverting the static magnetic field to an oscillating field in the physically rotating frame. Using spin-echo interferometry of the rotating NV centres, we are able to perform measurements for over a hundred times longer compared to a conventional Ramsey experiment. With modifications our scheme could realise DC sensitivities equivalent to demonstrated NV center AC magnetic field sensitivities of order 0.1 nT Hz −1/2 .

No abstract