Probing Surface Noise with Depth-Calibrated Spins in Diamond

B. A. Myers, A. Das, M. C. Dartiailh, K. Ohno, D. D. Awschalom, and A. C. Bleszynski Jayich

Phys. Rev. Lett. 113, 027602 – Published 9 July 2014

Abstract

Sensitive nanoscale magnetic resonance imaging of target spins using nitrogen-vacancy (NV) centers in diamond requires a quantitative understanding of dominant noise at the surface. We probe this noise by applying dynamical decoupling to shallow NVs at calibrated depths. Results support a model of NV dephasing by a surface bath of electronic spins having a correlation rate of 200 kHz, much faster than that of the bulk N spin bath. Our method of combining nitrogen delta-doping growth and nanoscale depth imaging paves a way for studying spin noise present in diverse material surfaces.

Received 20 February 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.027602

Authors & Affiliations

B. A. Myers¹, A. Das¹, M. C. Dartiailh¹, K. Ohno¹, D. D. Awschalom^1,2, and A. C. Bleszynski Jayich¹

¹Department of Physics, University of California, Santa Barbara, California 93106, USA
²Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA

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Issue

Vol. 113, Iss. 2 — 11 July 2014

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Images

Figure 1
(a) Schematic of a CVD-grown diamond film with three nitrogen delta-doped layers (orange) that contain nitrogen-vacancy (NV) spins at nanoscale separations. A 532 nm laser is focused onto NVs via an inverted confocal microscope giving a diffraction-limited depth of field. To achieve nanoscale depth discrimination between NVs, a scanning magnetic tip and microwave field form a resonance slice. Colored red is a NV that intersects this slice. (b) Confocal image showing individual NVs. (c) Optically detected ESR images recorded as a function of the magnetic tip position over a single NV. Dark rings mark reduced fluorescence when the ESR slice crosses the NV.
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Figure 2
(a) ESR slice photoluminescence contrast images in a lateral-height plane ( $Y Z$ ) measured for four NVs of identical orientation. Relative depths were extracted via image registration (see the Supplemental Material [24]), and dashed curves are polynomial fits as guides to the eye. (b) Hahn echo coherence data (markers) with shot noise-limited error bars and fits (lines) for the four NVs in (a). (c) Coherence times ( $T_{2, echo}$ and $T_{2, X Y 4}$ ) and relaxation times ( $T_{1}$ ) versus NV depth, showing strong suppression of coherence near the surface. The lower panel shows $T_{2, X Y 4} / T_{2, echo} = N^{λ}$ is reduced with decreased depth, indicating that dynamical decoupling with $N = 4$ pulses is less efficient for shallower NVs. The dashed line ( $λ = 2 / 3$ ) is expected for NV dephasing by a slow bulk nitrogen spin bath.
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Figure 3
(a) Depth dependence of NVs’ coupling frequency to the surface (blue diamonds) and bulk (orange squares) noise baths as extracted by fitting coherence decay data to a two-bath dephasing model (see inset schematic). Horizontal error bars on data points denote relative depth errors from the magnetic resonance imaging registration. The solid blue curve is a fit to a 2D electronic spin bath model. The fit gives a surface spin density $σ_{surf} = 0.0 4 {nm}^{- 2}$ and absolute NV depths (shallowest 8.2 nm). (b) Total rms magnetic field of the two spin baths. The solid line is a fit to the two-bath model.
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Figure 4
The effect of the number of dynamical decoupling pulses $N$ on coherence of a 12.4 nm deep NV. (a) $T_{2}$ measured using CPMG- $N (N < 8)$ and $X Y 8 − N$ (orange circles) and numerical calculations (blue squares) based on the dephasing due to surface and bulk spin baths. The model parameters are $b_{surf} = 71 (4) kHz$ and $τ_{surf} = 5 (1) μ s$ , based on fits to the echo and CPMG-4 data. $T_{2, N}$ error bars ( $δ T_{2, N}$ ) are coherence fit parameter standard deviations, and the dashed line indicates the measured $T_{1}$ . (b) Plotted is the decoupling efficiency $λ$ , which relates each $T_{2, N}$ to $T_{2, N = 1}$ . Error bars are propagated from $δ T_{2, 1}$ and each $δ T_{2, N}$ . The dotted line indicates the measured value of $2 / 3$ for bulk NVs. The model and data exhibit excellent agreement through $N = 24$ .
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