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

Abstract

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, ...

Dissipation-induced rotation of suspended ferromagnetic nanoparticles

“…(2.3) the Barnett field. This emergent magnetic field is responsible for the Barnett effect (magnetization by rotation) 34 and its existence has been recently confirmed experimentally for different spin systems [35][36][37] . In this context, it is of interest to analyze the role of the Barnett field in the dissipation-induced rotation of suspended ferromagnetic nanoparticles.…”

T2 -limited sensing of static magnetic fields via fast rotation of quantum spins

“…The experimental setup and methods are depicted in Fig. 1 and are similar to those described previously [18,19]. A diamond containing an ensemble of NV centers is mounted to the spindle of an electric motor that rotates at 200,000 rpm (3.33 kHz).…”

“…In this work, we demonstrate a quantum magnetometry method based on an ensemble of rotating spin qubits which can detect DC magnetic fields with a sensitivity ultimately limited by T 2 , rather than T * 2 . Our technique upconverts the DC magnetic field to AC by rotating the host diamond crystal with a period comparable to T 2 [18,19] in a way that modulates the coupling between the NV center and the magnetic field to be detected. With the NV crystal axis at an angle θ NV to the rotation axis and a small target DC magnetic field transverse to the rotation axis, the Zeeman shift of the NV is modulated at the rotation frequency in proportion to the DC field.…”

Observation of a Quantum Phase from Classical Rotation of a Single Spin

“…Solid-state spin qubits such as the nitrogen-vacancy (NV) center in diamond [1,2] provide promising testbeds of how classical rotation affects quantum systems [3], due to their long coherence times of up to several milliseconds [4] and the robust nature of the host substrate. As the natural quantization axis of the NV is set by the host diamond crystal orientation, rotating the crystal rotates the qubit, and the effects of other phenomena such as magnetic fields can be examined independently [5,6]. In this work we observe a phase shift between a single NV qubit in a classically rotating diamond and an external microwave field used to drive quantum rotations.…”