Enhanced Strain Coupling of Nitrogen-Vacancy Spins to Nanoscale Diamond Cantilevers

Srujan Meesala, Young-Ik Sohn, Haig A. Atikian, Samuel Kim, Michael J. Burek, Jennifer T. Choy, and Marko Lončar

Phys. Rev. Applied 5, 034010 – Published 18 March 2016

Abstract

Nitrogen-vacancy (NV) centers can couple to confined phonons in diamond mechanical resonators via the effect of lattice strain on their energy levels. Access to the strong spin-phonon coupling regime with this system requires resonators with nanoscale dimensions in order to overcome the weak strain response of the NV ground-state spin sublevels. In this work, we incorporate photostable NVs in diamond cantilevers with lateral dimensions of a few hundred nanometers. Coupling of the NV ground-state spin to the mechanical mode is detected in electron spin resonance, and its temporal dynamics are measured via spin echo. Our small mechanical-mode volume leads to a $10 \times - 100 \times$ enhancement in the spin-phonon coupling strength over previous NV-strain coupling demonstrations. This is an important step towards strong spin-phonon coupling, which can enable phonon-mediated quantum-information processing and quantum metrology.

Received 6 November 2015

DOI:https://doi.org/10.1103/PhysRevApplied.5.034010

Physics Subject Headings (PhySH)

Optomechanics Phonons Quantum information processing Quantum information with solid state qubits Quantum metrology

Micromechanical & nanomechanical oscillators Nitrogen vacancy centers in diamond

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Srujan Meesala, Young-Ik Sohn, Haig A. Atikian, Samuel Kim^*, Michael J. Burek, Jennifer T. Choy^†, and Marko Lončar^‡

John A. Paulson School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138, USA

^*Present address: Research and Exploratory Development Department, Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA.
^†Present address: Draper Laboratory, 555 Technology Square, Cambridge, MA 02139, USA.
^‡loncar@seas.harvard.edu

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Vol. 5, Iss. 3 — March 2016

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Images

Figure 1
(a) Representative scanning electron microscope image of the angle-etched diamond cantilevers used. (b) Representative confocal microscope scan of a section of the cantilever showing fluorescence from NV centers. (c) Driven response of the fundamental out-of-plane flexural mode (right inset) of the triangular cross-section (left inset) cantilevers studied in this work measured by optical interferometry. For this particular device, we have $w = 580 nm$ , $t = 170 nm$ , and $l = 19 μ m$ . NV centers are situated at a depth $d = 94 nm$ . The mode frequency is 937.2 kHz, and it has a $Q$ factor of 10 000. Measurements are taken in high vacuum ( $10^{- 5} torr$ ) at room temperature. (d) Hyperfine structure of the $m_{s} = 0$ to $m_{s} = + 1$ electron spin transition in the NV ground state indicating the three allowed microwave transitions. (e) ac strain-induced broadening of the $m_{s} = 0$ to $m_{s} = + 1$ hyperfine transitions near the clamp of the cantilever with gradually increasing mechanical amplitude. The mechanical mode is inertially driven at its resonance frequency with a piezostack in all measurements. Open circles indicate measured data, and smoothed solid lines serve as a guide to the eye. The legend shows values of piezodrive power for each measurement. 0 dBm of drive power corresponds to an amplitude of $559 \pm 2 nm$ at the tip of the cantilever.
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Figure 2
(a) Driven response of the cantilever measured by optical interferometry at a piezodrive power of $- 12 dBm$ . The drive frequencies used for frequency-dependent broadening measurements are indicated with numbers 1–5. (b) ESR spectra at the same location in the cantilever at mechanical drive frequencies 1–5 indicated in (a). (c) ESR spectra at the tip and clamp of the cantilever for $- 6 dBm$ of drive power. The strain profile of the mechanical mode from a FEM simulation for the corresponding displacement amplitude is also shown. Open circles in each ESR spectrum are measured data, and smoothed lines serve as a guide to the eye
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Figure 3
(a) Experimental pulse sequence for spin-echo measurement of dispersive spin-cantilever interaction due to axial strain. (b) Spin-echo signal from NVs in the cantilever at a piezodrive power of 0 dBm (tip amplitude of $559 \pm 2 nm$ ) for the mode at $ω_{m} = 923.4 kHz$ , showing two periods of the modulation due to axial strain coupling. The solid line is a fit to Eq. (6). Vertical error bars correspond to photon shot noise in the measurement. The inset shows a schematic of the dispersive interaction between the qubit and mechanical mode due to axial strain.
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Figure 4
(a) Spin echo at the same location in the cantilever for varying piezodrive powers, offset along the $y$ axis. One period of the signal is plotted in each case. Solid lines are fits to the zero-order Bessel function form indicated in the text, and vertical error bars correspond to photon shot noise. The scale bar on the side is a guide for the $y$ axis indicating the maximum (1.0) and minimum (0.3) possible population in $m_{s} = 0$ as dictated by Eq. (6). The legend on the right side indicates the piezodrive powers used for each measurement. (b) Variation of the driven spin-phonon coupling rate due to axial strain ( $G$ ) with the calibrated displacement amplitude of the mechanical mode. The five data points correspond to the piezodrive powers used in (a) in increasing order. Vertical error bars correspond to the error in each $G$ estimate from fitting to the spin-echo function given by Eq. (6). The solid line is a linear fit, which yields $d G / d x = 4.02 \pm 0.40 kHz / nm$ .
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