Anisotropic electron-nuclear interactions in a rotating quantum spin bath

A. A. Wood, R. M. Goldblatt, R. P. Anderson, L. C. L. Hollenberg, R. E. Scholten, and A. M. Martin

Phys. Rev. B 104, 085419 – Published 13 August 2021

Abstract

The interaction between a central qubit spin and a surrounding bath of spins is critical to spin-based solid-state quantum sensing and quantum information processing. Spin-bath interactions are typically strongly anisotropic, and rapid physical rotation has long been used in solid-state nuclear magnetic resonance to simulate motional averaging of anisotropic interactions, such as dipolar coupling between nuclear spins. Here, we show that the interaction between electron spins of nitrogen-vacancy centers and a bath of ${}^{13}C$ nuclear spins in a diamond rotated at up to 300 000 rpm introduces decoherence into the system via frequency modulation of the nuclear spin Larmor precession. The presence of an off-axis magnetic field necessary for averaging of the dipolar coupling leads to a rotational dependence of the electron-nuclear hyperfine interaction, which cannot be averaged out with experimentally achievable rotation speeds. Our findings offer new insights into the use of physical rotation for quantum control with implications for quantum systems having motional and rotational degrees of freedom that are not fixed.

Received 19 May 2021
Revised 27 July 2021
Accepted 2 August 2021

DOI:https://doi.org/10.1103/PhysRevB.104.085419

Physics Subject Headings (PhySH)

Quantum sensing

Nitrogen vacancy centers in diamond

Nuclear magnetic resonance

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

A. A. Wood ^1,*, R. M. Goldblatt¹, R. P. Anderson², L. C. L. Hollenberg^1,3, R. E. Scholten¹, and A. M. Martin¹

¹School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
²La Trobe Institute of Molecular Science, La Trobe University, Bendigo, Victoria 3550, Australia
³Centre for Quantum Computation and Communication Technology, University of Melbourne, Parkville, Victoria 3010, Australia

^*alexander.wood@unimelb.edu.au

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Issue

Vol. 104, Iss. 8 — 15 August 2021

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Images

Figure 1
(a) A diamond is mounted on an electric motor such that the $〈 111 〉$ crystallographic direction is approximately parallel to the rotation axis. An ensemble of NV centers are optically prepared and read out by a confocal microscope, and magnetic fields are applied to tilt the total field $B$ away from the rotation axis by an angle $θ_{B}$ (inset). (b) NV electron spin (red) interacting with a bath of 20 ${}^{13}C$ nuclear spins within a diamond physically rotating around the $z$ axis at $ω_{rot}$ . The dashed circles depict radii in units of lattice constant $a_{0} = 0.154$ nm. (c) Nuclear spin precession frequencies at $t = 0$ for $| B | = 30$ G and varying tilt angles for the NV electron spin in the $m_{S} = 0$ state (top) and $m_{S} = - 1$ state (bottom). Note the shift from the bare precession frequency of 32.1 kHz due to the rotation at 3.33 kHz. The curve color corresponds to the colored vector in (b). (d) Nuclear precession frequencies of the spin ensemble for $m_{S} = 0, ω_{rot} = 3.33$ kHz as a function of time for different tilt angles $θ_{B}$ . Rotation of the diamond modulates the precession frequency of the nuclear spins due to anisotropic, nonsecular terms in the NV- ${}^{13}C$ hyperfine interaction.
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Figure 2
Measuring the coherence of a rapidly rotating NV–nuclear spin ensemble. (a) Rotating the diamond with the NV axis tilted slightly away from the rotation axis up-converts magnetic field components orthogonal to the rotation axis to fields oscillating at the rotation frequency. This modulated field can then be measured by a spin-echo pulse sequence applied synchronous with the rotation of the diamond. An additional sequence with a $3 π / 2$ -readout pulse facilitates computation of a normalized echo signal. Tilting the magnetic field further from the rotation axis increases the amplitude of the up-converted field, and results in fringes in the spin-echo signal. (b) Illustrative time-domain spin-echo signals for $B = 20$ G (top) and $B = 40$ G (bottom) for $θ_{B} = 0$ showing rotationally induced shifting of the ${}^{13}C$ contrast revivals. Adding a transverse field to change $θ_{B}$ increases the total field, which also shifts the revival. We adjust the interpulse time $τ_{R}$ so that the final $π / 2$ pulse of the spin-echo sequence occurs at the same time as first (20 G) or second (40 G) contrast revival maximum for a given magnetic field configuration. (c) Spin-echo signal at fixed $τ_{R}$ vs $θ_{B}$ for different rotation speeds. An exponentially damped sinusoid (solid line) is fitted to the experimental data (points), and a fully constrained theoretical model of the envelope is overlaid (dashed line). We observe a rapid reduction of contrast with $θ_{B}$ as the rotation speed is increased that matches well with theory; the discrepancy is attributed primarily due to imperfect magnetic field calibration. Our observations are consistent with dephasing introduced by NV- ${}^{13}C$ hyperfine modulation arising from rotation in the presence of an off-axis magnetic field.
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Figure 3
Simulated effective electron spin coherence time $T_{2}^{eff}$ as a function of magnetic field tilt angle $θ_{B}$ and rotation speed $ω_{rot}$ for $B = 20$ G (left) and 40 G (right). Each value of $T_{2}$ derives from an exponential fit to the spin-echo signal envelope, evaluated at the rotationally shifted ${}^{13}C$ revival positions and averaged over 10 distinct bath configurations, each with approximately 125 ${}^{13}C$ nuclei at random lattice sites. A decay envelope with time constant $T_{2}^{phenom}$ limits the maximum coherence time to $150 μ s$ to simulate the effects of other defects within the diamond sample used in this work.
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Figure 4
Simulating the onset of spin-echo envelope modulation due to rapid rotation with a tilted magnetic field. (a) For small $θ_{B}$ the spin-echo signal collapses as the rotation speed is increased, before contrast revivals at twice the rotation period become evident. The dashed traces depict the ${}^{13}C$ dipole-dipole limited coherence envelope for the relevant rotation speed and $θ_{B} = 15^{\circ}$ . (b) For fixed rotation speeds of 200 krpm (3.33 kHz, top) and 500 krpm (8.33 kHz, bottom), increasing the tilt angle causes the rotational revivals to decay. At larger angles, small, intermittent revivals reappear at integer multiples of the rotation period. Each simulated spin-echo trace derives from the average of at least 20 different bath configurations of up to 300 ${}^{13}C$ nuclear spins.
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