Anticrossing Spin Dynamics of Diamond Nitrogen-Vacancy Centers and All-Optical Low-Frequency Magnetometry

David A. Broadway, James D. A. Wood, Liam T. Hall, Alastair Stacey, Matthew Markham, David A. Simpson, Jean-Philippe Tetienne, and Lloyd C. L. Hollenberg

Phys. Rev. Applied 6, 064001 – Published 2 December 2016

Abstract

We investigate the photoinduced spin dynamics of single nitrogen-vacancy ( $N − V$ ) centers in diamond near the electronic ground-state level anticrossing (GSLAC), which occurs at an axial magnetic field around 1024 G. Using optically detected magnetic resonance spectroscopy, we first find that the electron-spin transition frequency can be tuned down to 100 kHz for the ${}^{14}N − V$ center, while, for the ${}^{15}N − V$ center, the transition strength vanishes for frequencies below about 2 MHz owing to the GSLAC structure. Using optical pulses to prepare and read out the spin state, we observe coherent spin oscillations at 1024 G for the ${}^{14}N − V$ center which originate from spin mixing induced by residual transverse magnetic fields. This effect is responsible for limiting the smallest observable transition frequency, which can span 2 orders of magnitude ranging from 100 kHz to tens of megahertz, depending on the local magnetic noise. A similar feature is observed for the ${}^{15}N − V$ center at 1024 G. As an application of these findings, we demonstrate all-optical detection and spectroscopy of externally generated fluctuating magnetic fields at frequencies ranging from 8 MHz down to 500 kHz using a ${}^{14}N − V$ center. Since the Larmor frequency of most nuclear-spin species lies within this frequency range near the GSLAC, these results pave the way towards all-optical, nanoscale nuclear magnetic resonance spectroscopy, using longitudinal spin cross-relaxation.

Received 14 July 2016

DOI:https://doi.org/10.1103/PhysRevApplied.6.064001

Physics Subject Headings (PhySH)

Spin relaxation

Nitrogen vacancy centers in diamond

Nuclear magnetic resonance Optically detected magnetic resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

David A. Broadway¹, James D. A. Wood¹, Liam T. Hall², Alastair Stacey^1,3, Matthew Markham³, David A. Simpson², Jean-Philippe Tetienne^1,*, and Lloyd C. L. Hollenberg^1,2

¹Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Melbourne, Victoria 3010, Australia
²School of Physics, The University of Melbourne, Melbourne, Victoria 3010, Australia
³Element Six Innovation, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX110QR, United Kingdom

^*jtetienne@unimelb.edu.au

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Vol. 6, Iss. 6 — December 2016

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Images

Figure 1
(a) Schematic view of the system under study. The $N − V$ center in diamond comprises a nuclear spin and an electron spin, which can be initialized and read out optically using a confocal microscope equipped with an avalanche photodiode (APD); it is surrounded by target spins located within the diamond or external to it. A magnetic field of strength $B_{z}$ is applied along the $N − V$ –quantization axis. (b) Schematic diagram showing the transition frequencies of the $N − V$ electron spin (the black lines) and of a target nuclear spin (the orange line) as $B_{z}$ is varied, with the resonance points shown as dots. The spin states are labeled by their spin projection, $| m_{e} = 0, \pm 1 ⟩$ for the $N − V$ electron, $| m_{t} = ↑, ↓ ⟩$ for the target spin. (c),(d) Calculated hyperfine structure for the (c) ${}^{14}N − V$ and (d) ${}^{15}N − V$ centers, plotted near the GSLAC where the two branches $m_{e} = 0$ and $m_{e} = - 1$ cross. The different states are labeled as $| m_{e}, m_{n} ⟩$ , where $m_{e}$ ( $m_{n}$ ) is the electronic- (nuclear-) spin projection of the unperturbed states (away from the GSLAC). Owing to hyperfine interaction, some of the energy levels exhibit an avoided crossing at the GSLAC.
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Figure 2
ODMR spectra of (left panels) a ${}^{14}N − V$ and (right panels) a ${}^{15}N − V$ center, measured as a function of the axial-magnetic field strength near the GSLAC. The top panels show the electron spin transitions $| 0_{e} ⟩ \to | + 1_{e} ⟩$ , while the bottom panels show $| 0_{e} ⟩ \to | - 1_{e} ⟩$ . Overlaid on the graph are the theoretical frequencies of all allowed or partly allowed (via spin mixing) transitions. However, dynamic nuclear-spin polarization makes some of the transitions dominant (shown as solid lines), with the other transitions having comparatively small or vanishing contrast (the dashed lines).
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Figure 3
(a) Depiction of the laser-pulse sequence used to measure the spontaneous spin dynamics, containing an initialization pulse and a readout pulse after a wait time $t$ . (b) Time trace measured for a single ${}^{14}N − V$ center at a field $B_{z} = 1000 G$ . Here, a decay with a characteristic time $T_{1} \approx 5 ms$ , associated with phonon relaxation, is observed. (c) Set of PL scans as a function $B_{z}$ for various evolution times $t$ , under a small residual transverse field $B_{⊥}$ , showing a narrow feature at $B_{z} \approx 1024 G$ . The evolution times $t = 2 μ s$ (gray), $10 μ s$ (light blue), and 1 ms (purple) are indicated as dashed lines in (b), with exaggerated positions for ease of viewing. (d) Time traces recorded at $B_{z} \approx 1024 G$ . The top curve is measured with a detuning $δ B_{z} = 0.2 G$ , showing no variation in the range $t = 0 - 15 μ s$ . The other curves are recorded with no detuning, but with a transverse magnetic field $B_{⊥}$ increasing from about 0 to approximately 0.5 G (top down). The curves are vertically offset from each other for clarity. (Inset) Averaged time traces $⟨ P_{0} (t) ⟩$ computed from Eq. (6) where $δ B_{z}$ and $B_{⊥}$ are normally distributed, with mean values $⟨ δ B_{z} ⟩ = 0$ and $⟨ B_{⊥} ⟩ = 0 G$ (the orange curve) or 0.2 G (the green curve) and variances $σ_{B_{z}} = 1.3 μ T$ and $σ_{B_{⊥}} = \sqrt{3 / 4} σ_{B_{z}}$ . The dashed blue line is the approximate envelope $e^{- (t / T_{\times})^{2}}$ , with $T_{\times} = (γ_{e} σ_{B_{⊥}})^{- 1} = 5 μ s$ .
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Figure 4
(a) PL scan across the GSLAC for a shallow ${}^{14}N − V$ center in a CVD diamond, with evolution times $t = 2 μ s$ , $10 μ s$ , and 1 ms. Here, no oscillation is detected, but an overall decrease in spin population is observed at $B_{z} \approx 1024 G$ . (b) Time traces recorded at the crossing feature ( $B_{z} \approx 1024 G$ , the blue dots) and away from it ( $B_{z} \approx 1020 G$ , the gray dots). (c) PL scans across the GSLAC recorded with ${}^{14}N − V$ centers in various diamond samples. (i) Deep $N − V$ center in isotopically purified CVD diamond, as in Fig. 3. (ii) Deep $N − V$ center in natural-isotopic-content CVD diamond. (iii) Shallow $N − V$ center in CVD diamond as in (a) and (b). (iv) Deep $N − V$ center in type-Ib diamond. The curves are vertically offset from each other for clarity.
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Figure 5
(a) PL scan across the GSLAC for a shallow ${}^{15}N − V$ center in a CVD diamond, with evolution times $t = 2 μ s$ , $10 μ s$ , and 3 ms. A feature at $B_{z} \approx 1024 G$ is observed, attributed to spin mixing induced by transverse magnetic fields. (b),(c) Time traces recorded at the crossing feature ( $B_{z} \approx 1024 G$ , the orange dots) and away from it ( $B_{z} \approx 1020 G$ , the blue dots). The long and short time scales are shown in (b) and (c), respectively. (d) Energy-level structure of the ${}^{15}N − V$ center in the presence of a transverse magnetic field $B_{⊥} = 0.3 G$ , showing an induced avoided crossing (indicated by the arrow).
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Figure 6
PL scans across the GSLAC recorded with an evolution time $t = 10 μ s$ on the same ${}^{14}N − V$ center as in Fig. 3. For each scan, a magnetic noise is generated at central frequencies of 8 MHz, 4 MHz, 1 MHz, and 500 kHz, respectively (from the top down). The root-mean-square amplitude of the applied field is $1 μ T$ . The curves are offset from each other for clarity.
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