Demonstration of a Coherent Electronic Spin Cluster in Diamond

Helena S. Knowles, Dhiren M. Kara, and Mete Atatüre

Phys. Rev. Lett. 117, 100802 – Published 2 September 2016

Abstract

An obstacle for spin-based quantum sensors is magnetic noise due to proximal spins. However, a cluster of such spins can become an asset, if it can be controlled. Here, we polarize and readout a cluster of three nitrogen electron spins coupled to a single nitrogen-vacancy spin in diamond. We further achieve sub-nm localization of the cluster spins. Finally, we demonstrate coherent spin exchange between the species by simultaneous dressing of the nitrogen-vacancy and the nitrogen states. These results establish the feasibility of environment-assisted sensing and quantum simulations with diamond spins.

Received 13 January 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.100802

Physics Subject Headings (PhySH)

Metrology Quantum simulation

Nitrogen vacancy centers in diamond

General PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Helena S. Knowles, Dhiren M. Kara, and Mete Atatüre^*

Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom

^*ma424@cam.ac.uk

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Vol. 117, Iss. 10 — 2 September 2016

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Images

Figure 1
(a) Energy levels of the NV and N states. Spin transfer (at rate $Ω$ ) between NV ES and N spin can take place efficiently, if the energy splittings are commensurate. Bottom right: illustration of the NV and proximal Ns. (b) The calculated NV ES electronic transitions (red) and N spin transitions (blue) as a function of applied field $B_{app}$ . (c) NV ES optically detected magnetic resonance data (red circles) and a triple Lorentzian fit (red curve). Spectrum of N spins (blue circles) measured through a DEER sequence illustrated in the inset: the NV GS spin echo (SE) coherence is monitored for fixed $τ = 1 μ s$ with NV spin rotations driven at 2.105 GHz while a radio-wave $π$ pulse (synchronous with the refocusing microwave (MW) $π$ pulse on the NV) is scanned in frequency and a model of driven N transitions (blue curve) [17]. At a magnetic field of 24 mT the central transitions of the N spins ( $m_{I} = 0$ ) are commensurate with the lower, most highly populated NV hyperfine level as indicated by the gray region.
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Figure 2
(a) Illustration of NV spin on the Bloch sphere as it undergoes a DSE measurement, along with the MW sequence used to control the NV spin (red, orange pulses) and the radio-wave sequences for the N spins (blue pulses). The polarization of the N cluster (“down” green arrows and “up” blue arrows) occurs during the optical initialization step (1), the magnetic field created by the N spins is probed in (2) and (3), and the readout of the NV spin is performed after the final $π / 2$ pulse. We perform two sequences labeled $D$ and $U$ where the NV detects the field created by a cluster polarized “down” ( $D$ ) and “up” ( $U$ ). The $π$ rotation on the N spin, coincident with the echo pulse, ensures that $B_{pol}$ contributes a cumulative phase for the full DSE duration. The second pulse in $D$ returns the cluster to its original state before the next measurement cycle. (b) DSE measurement with readout about the $y$ axis, where we plot the probability of the NV state $| 0 ⟩$ , $P_{0}$ . The gap between data acquired for the sequence $D$ (green) and $U$ (blue) shows the presence of polarized spins surrounding the NV. Solid curves are fits to $\propto \frac{1}{2} \exp [- (τ / t_{DSE})^{2}] (1 + \sin ϕ)$ . (c) IDSE measurement where $α$ is scanned with an optical initialization time of $2 μ s$ (left) and $20 μ s$ (right). (d) Phase difference $δ_{pol}$ as a function of the IDSE free precession time $τ$ for $2 μ s$ (black) and $20 μ s$ initialization (red). Fits using a three N spin model (solid lines, see main text for parameters) and a single N spin model (dashed lines).
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Figure 3
Map of $N_{1}$ , $N_{2}$ , and $N_{3}$ locations with respect to the NV. The N spins lie within the red areas (red circles) with 68% probability and within the blue areas (blue circles) with 95% probability. Gray circles represent the locations of carbon atoms in the diamond lattice. The axis $r_{⊥} = \sqrt{x^{2} + y^{2}}$ shows the transverse separation between the NV and the carbon atoms. In this representation each circle occurs 6 times within the three-dimensional lattice, due to the diamond symmetry.
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Figure 4
(a) Illustration of sequences used for the double locking HH experiments. Top sequence: N spin is locked about the $y$ axis for duration $τ_{L o c k}$ after the first $π_{x} / 2$ rotation and then returned to its initial position with a $- π_{x} / 2$ pulse. Three sequences below: (i) The NV spin is locked into the $| + ⟩ = (| 0 ⟩ + i | 1 ⟩ / \sqrt{2})$ state ( $D_{+}$ ), (ii) into the $| - ⟩ = (| 0 ⟩ - i | 1 ⟩ / \sqrt{2})$ state ( $D_{-}$ ), and (iii) the lock is alternated between the $| + ⟩$ state and the $| - ⟩$ state ( $A$ ). (b) NV contrast as a function of $τ_{L ock}$ with predominantly optical polarization of the N cluster ( $20 μ s$ optical initialization) for $D_{+}$ (green circles), $D_{-}$ (blue circles), and $A$ (red circles). All signals are normalized to the NV lock decay in the absence of sequence N. The solid curves are fits to $a \cos [2 π ν τ_{L ock}] e^{- τ_{L ock} / t_{osc}} + (1 - a - C) e^{- τ_{L ock} / t_{L ock}} + C$ yielding oscillation amplitudes of $a = 0.085$ , 0.094, and 0.095 for $D_{+}$ , $A$ , and $D_{-}$ , respectively. This indicates that $N_{1}$ is coupled to the NV with $1.68 \pm 0.01 MHz$ and is only weakly polarized by the optical scheme. Inset: Spin locking experiment for mixed optical and locking frame HH polarization ( $2 μ s$ optical initialization), where $N_{1}$ is now polarized by the HH locking (amplitudes for $D_{+}$ and $D_{-}$ , and $A$ are $a = 0.033$ , 0.038 and 0.088, respectively). In the $D_{+}$ sequence, the optical and HH polarization act in the same direction and we observe a stronger polarization than in (b), while in $D_{-}$ they compete with each other and the spin transfer is suppressed compared to (b).
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