Strain Coupling of a Nitrogen-Vacancy Center Spin to a Diamond Mechanical Oscillator

We report on single electronic spins coupled to the motion of mechanical resonators by a novel mechanism based on crystal strain. Our device consists of single-crystal diamond cantilevers with embedded nitrogen-vacancy center spins. Using optically detected electron spin resonance, we determine the unknown spin-strain coupling constants and demonstrate that our system resides well within the resolved sideband regime. We realize coupling strengths exceeding 10 MHz under mechanical driving and show that our system has the potential to reach strong coupling. Our novel hybrid system forms a resource for future experiments on spin-based cantilever cooling and coherent spin-oscillator coupling.

Figure 1

(a) Schematics of the hybrid device studied in this work. Isolated electronic spins (red arrows) in the form of negatively charged nitrogen-vacancy (NV) centers (inset) are embedded in a diamond mechanical oscillator and coupled to the oscillator motion through crystal strain. (b) Confocal image of our cantilever devices showing individual, implanted NV centers scattered across the sample surface. (c) Mechanical excitation spectrum of a cantilever with typical resonance frequency and quality factor. The mechanical resonance was measured by monitoring the drop in NV fluorescence from the cantilever end, as the mechanical drive frequency ${\omega }_d$ was varied across ${\omega }_{\text{mech}}$ [21]. (d) Optically detected electron spin resonance (ESR) of a NV center in a cantilever. The schematic illustrates the NV electronic ground-state spin configuration, which consists of a spin triplet, whose sublevels can be optically read out, since the $|\pm 1⟩$ states yield less NV fluorescence than the $|0⟩$ state.

Figure 2

(a) Calculated shifts of NV ESR transition frequencies as a function of crystal strain. The effects of strain transverse (${\epsilon }_{x,y}$) and longitudinal (${\epsilon }_z$) to the NV axis are plotted separately (solid lines and dotted lines, respectively). (b) Schematic of the NV electronic spin states and the action of $H_{\text{strain}}$. For ${\epsilon }_{x,y}\ne 0$, $\widetilde{|-1⟩}$ and $\widetilde{|1}⟩$ split, while for ${\epsilon }_z\ne 0$, $\widetilde{|\pm 1⟩}$ shift with respect to $|0⟩$. (c) Strain splitting of NV ESR lines as a function of static cantilever displacement. Positive and negative values of $\delta$ correspond to two different data sets (separated by the dashed line) and represent tensile and compressive strain at the NV location, respectively (see inset).

Figure 3

(a) ESR trace of the NV in the cantilever in the absence (upper trace) and presence (lower trace) of resonant mechanical excitation. Without excitation, the ESR line exhibits a splitting into three hyperfine components. Mechanical driving induces sidebands to this central carrier at frequencies ${\omega }_0\pm {\omega }_{\text{mech}}$, where ${\omega }_0=2.796\mathrm{GHz}$ is the bare ESR frequency of the NV center. (b) Evolution of the ESR sidebands as a function of mechanical drive frequency ${\omega }_d$ at an excitation amplitude $V_{\text{piezo}}=9\mathrm{V}$. A clear resonant behavior is observed with a maximal sideband amplitude appearing when ${\omega }_d={\omega }_{\text{mech}}$. (c) Amplitude of the carrier signal (blue) and the two sidebands ($n=1,2$ in green and red, respectively) as determined by a Lorentzian fit to the observed ESR dips. A slight asymmetry in the sideband amplitudes with respect to ${\omega }_d$ is caused by the onset of a mechanical nonlinearity of the diamond mechanical oscillator.

Figure 4

(a) Amplitude of ESR sidebands for increasing excitation drive voltage $V_{\text{piezo}}$ of the mechanical oscillator. (b) Relative amplitudes of carrier signal (blue line) and sidebands as a function of excitation amplitude (dots). We determined the amplitudes by Lorentzian fit to the ESR peaks in (a) and normalized the dips in each line by the total measured ESR signal strength. Sidebands of order $n=1,2,3$ are color coded in red, green, and gray, respectively. Lines indicate squares of $n$th-order Bessel functions.