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arXiv:1908.08682 · Physical Review Letters

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

A. A. Wood, Lloyd C. L. Hollenberg, Robert E Scholten, A. Martin

Published Jan 17, 2020• 26 citations
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Abstract

The theory of angular momentum connects physical rotations and quantum spins together at a fundamental level. Physical rotation of a quantum system will therefore affect fundamental quantum operations, such as spin rotations in projective Hilbert space, but these effects are subtle and experimentally challenging to observe due to the fragility of quantum coherence. We report on a measurement of a single-electron-spin phase shift arising directly from physical rotation, without transduction through magnetic fields or ancillary spins. This phase shift is observed by measuring the phase difference between a microwave driving field and a rotating two-level electron spin system, and it can accumulate nonlinearly in time. We detect the nonlinear phase using spin-echo interferometry of a single nitrogen-vacancy qubit in a diamond rotating at 200 000 rpm. Our measurements demonstrate the fundamental connections between spin, physical rotation, and quantum phase, and they will be applicable in schemes where the rotational degree of freedom of a quantum system is not fixed, such as spin-based rotation sensors and trapped nanoparticles containing spins.

DOI
10.1103/physrevlett.124.020401

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We demonstrate that the internal magnetic states of a single nitrogen-vacancy defect, within a rotating diamond crystal, acquire geometric phases. The geometric phase shift is manifest as a relative phase between components of a superposition of magnetic substates. We demonstrate that under reasonable experimental conditions a phase shift of up to four radians could be measured. Such a measurement of the accumulation of a geometric phase, due to macroscopic rotation, would be the first for a single atom-scale quantum system.
Magnetic sensors are typically much more sensitive to oscillating (AC) magnetic fields than static (DC) fields, due to the presence of more noise at lower frequency, typically scaling with a 1/f1/f1/f dependence. For quantum magnetometers, this characteristic noise is reflected in the ensemble dephasing time T2∗T_2^*T2∗​, the relevant sensing time for a DC field, being much lower than the spin coherence time T2T_2T2​, 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 limited by the electron spin coherence time, T2T_2T2​. We rotate the host diamond with a period comparable to T2T_2T2​, such that the angle between the NV axis and the magnetic field to be detected changes as a function of time, upconverting the static magnetic field to an oscillating field in the physically rotating frame. Using spin-echo interferometry, we observe an order of magnitude improvement in DC magnetometer response compared to a conventional Ramsey experiments. Enhancements to our scheme could realise DC sensitivities equivalent to demonstrated AC magnetic field sensitivities with NV centres.