${T}_{2}$-limited sensing of static magnetic fields via fast rotation of quantum spins

$T_{2}$ -limited sensing of static magnetic fields via fast rotation of quantum spins

A. A. Wood, A. G. Aeppli, E. Lilette, Y. Y. Fein, A. Stacey, L. C. L. Hollenberg, R. E. Scholten, and A. M. Martin

Phys. Rev. B 98, 174114 – Published 28 November 2018

Abstract

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 $T_{2}$ , which determines the sensitivity to ac fields. Here we demonstrate measurement of dc magnetic fields using a physically rotating ensemble of nitrogen-vacancy centers at a precision ultimately limited by $T_{2}$ rather than $T_{2}^{*}$ . The rotation period of the diamond is comparable to $T_{2}$ and the angle between the nitrogen-vacancy (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 centers, we are able to perform measurements for over 100 times longer compared to a conventional Ramsey experiment. With modifications our scheme could realize dc sensitivities equivalent to demonstrated NV center ac magnetic field sensitivities of order $0.1 nT {Hz}^{- 1 / 2}$ .

Received 15 August 2018

DOI:https://doi.org/10.1103/PhysRevB.98.174114

Physics Subject Headings (PhySH)

NV centers Quantum sensing

Diamond Nitrogen vacancy centers in diamond

Optically detected magnetic resonance

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

A. A. Wood, A. G. Aeppli, E. Lilette, Y. Y. Fein, A. Stacey, L. C. L. Hollenberg, R. E. Scholten, and A. M. Martin

School of Physics, University of Melbourne, Victoria 3010, Australia

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Vol. 98, Iss. 17 — 1 November 2018

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Images

Figure 1
Experimental configuration and rotational up-conversion procedure. (a) Outline of the NV center in diamond showing coordinate frame and effective two-level system. (b) A diamond containing an ensemble of NV centers is mounted to a high-speed electric motor that rotates the diamond around an axis $z$ at up to $200 000$ rpm (3.33 kHz). One of the four NV orientation classes ( $z^{'}$ ) makes an angle of $θ_{NV} \approx 4^{\circ}$ to the rotation axis. A $5.7 mT$ magnetic bias field is aligned parallel to $z$ . When a transverse magnetic field $B_{y}$ is applied, the Zeeman shift of the NV becomes time dependent since it is proportional to $B (t) \cdot \hat{z^{'}}$ in the NV frame. The time-dependent magnetic field can then be measured with a spin-echo pulse sequence performed in the physically rotating frame, with the relevant sensing time scale now determined by $T_{2}$ rather than the ensemble dephasing time $T_{2}^{*}$ . (c) Experimental setup. The motor controller outputs a pulse synchronous with the rotation which triggers an FPGA pulse generator. The FPGA outputs a spin echo pulse sequence, consisting of laser preparation and readout pulses (separated by one rotation period) and a $π / 2 − π − π / 2 (3 π / 2)$ microwave pulse sequence with pulse spacing $τ / 2$ . Laser light is focused onto the center of the diamond rotation with a high-NA objective, which also collects the emitted photoluminesence and directs it onto an avalanche photodiode.
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Figure 2
Coherence of rotating NV ensemble. (a) Stationary NV Ramsey data (gray circles) and NV spin-echo signal at $B_{z} = 5.7 mT$ when stationary (blue circles) and when rotating at 3.33 kHz (orange squares). A rotationally induced magnetic pseudofield adds to $B_{z}$ for the rotating data, shifting the position of the ${}^{13}C$ revivals. Refer to Fig. 3 for representative error bounds. (b) Detail of Ramsey contrast showing $T_{2}^{*}$ decay envelope due to quasistatic ensemble dephasing. The oscillations present in the Ramsey data are due to the ${}^{14}N$ nuclear hyperfine interaction. Inset: for comparison, the decay envelopes of rotating and stationary spin-echo signal, with effective $T_{2}$ time and decay exponent (see main text) allow for $> 100$ times longer interferometric interrogation. Error bars derived from uncertainty in Gaussian fits to spin-echo revivals.
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Figure 3
Rotational up-conversion magnetometry results. (a) We use an interrogation time of $τ = 124 μ s$ at a rotation speed of 3.33 kHz, at which the fourth ${}^{13}C$ revival provides the optimum signal to noise for ac magnetometry. The $π$ pulse of the echo sequence is concurrent with the zero crossing of the Zeeman modulation from the up-converted dc field, so that equal and opposite phase shifts ( $ϕ_{1} = - ϕ_{2}$ ) are accumulated on each side of the pulse sequence, yielding the maximum sensitivity for $τ$ less than one rotation period ( $300 μ s$ ). The statistical error bars are smaller than the data points. (b) Spin-echo signal at $τ = 124 μ s$ for an additional field applied along the $y$ axis, orthogonal to $z$ . Error bars are standard deviation of three repeated measurements at each $B_{y}$ consisting of $2.5 \times 10^{5}$ repetitions of an echo sequence with $π / 2$ and $3 π / 2$ readout. Lines are sinusoidal fits and shaded regions denote average error bounds.
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Figure 4
Comparison between rotational up conversion and standard dc Ramsey magnetometry. (a) Configurations of NV axis and magnetic field vectors for Ramsey- $y$ , Ramsey- $z$ , and RU- $y$ . All experiments were conducted with a $B_{0} = 5.7 mT$ magnetic bias field parallel to the rotation axis. Spin-echo magnetometry signals for (b) $y$ -Ramsey (gray circles) and $z$ -Ramsey (green circles) compared to rotational up conversion (orange squares) (c). All measurements consist of average signal from three separate acquisitions of $10^{6}$ experimental repetitions (Ramsey) and $2.5 \times 10^{5}$ repetitions (RU); error bars denote standard deviation. Lines are sinusoidal fits and shaded regions denote average error bounds. (d) Comparison of linear regions of magnetometer signal for all three techniques, with the $B$ axis scaled so that all traces intercept at $B = 0$ .
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