Single $\mathrm{Si}$-$V^{-}$ Centers in Low-Strain Nanodiamonds with Bulklike Spectral Properties and Nanomanipulation Capabilities

We report on the isolation of single negatively-charged-silicon-vacancy ($\mathrm{Si}$-$V^{-}$) centers in nanodiamonds. We observe the fine structure of single $\mathrm{Si}$-$V^{-}$ centers with reduced inhomogeneous ensemble linewidth below the excited-state splitting, stable optical transitions, good polarization contrast, and excellent spectral stability under resonant excitation. On the basis of our experimental results, we develop an analytical strain model where we extract the ratio between strain coefficients of excited and ground states as well the intrinsic zero-strain spin-orbit splittings. The observed strain values are as low as the best values in low-strain bulk diamond. We achieve our results by means of $\mathrm{H}$-plasma treatment of the diamond surface and in combination with resonant and off-resonant excitation. Our work paves the way for indistinguishable, single-photon emission. Furthermore, we demonstrate controlled nanomanipulation by an atomic-force-microscope cantilever of one- and two-dimensional alignments with an accuracy of about 10 nm, as well as new tools including dipole rotation and cluster decomposition. Combined, our results show the potential to utilize $\mathrm{Si}$-$V^{-}$ centers in nanodiamonds for controlled interfacing via optical coupling of individually-well-isolated atoms for bottom-up assemblies of complex quantum systems.

Figure 1

A conceptual design for single-emitter assemblies involves bottom-up formation from preselected nanodiamonds. Hydrogen surface termination is found to improve the optical properties of $\mathrm{Si}$-$V^{-}$ centers in nanodiamonds, which could enable deterministic creation of emitter arrays for quantum applications. The optical properties of the $\mathrm{Si}$-$V^{-}$ center in diamond arise from four optical transitions between doublet ground and excited states.

Figure 2

Comparison of optical properties of untreated and $\mathrm{H}$-plasma-treated $\mathrm{Si}$-$V^{-}$ in NDs at cryogenic temperature. (a) Time-resolved spectrum of $\mathrm{Si}$-$V^{-}$ in an untreated ND sample exhibiting many lines and spectral diffusion. (b) Time-resolved spectrum of $\mathrm{Si}$-$V^{-}$ in a $\mathrm{H}$-plasma-treated ND sample, which exhibits the four-line fine structure of the $\mathrm{Si}$-$V^{-}$ ZPL, with no spectrometer-resolvable spectral diffusion. The discontinuity of time between 70 and 110 s is due to refocusing of the confocal microscope. (c) The broader, orange spectrum (15 spots) is the inhomogeneous spectrum from untreated ND samples. The narrower, blue spectrum, where doublet-like fine structures can be resolved, is the inhomogeneous spectrum of spectrally stable points from $\mathrm{H}$-plasma-treated ND samples (23 spots). (d) Comparison of the total fluorescence and maximum peak height for spots in the $\mathrm{H}$-plasma-treated (blue circles) and untreated (orange triangles) samples. The shaded regions illustrate that the $\mathrm{H}$-plasma treatment reduces the total fluorescence much more than the height of individual peaks in the spectra. Only 7% of spots from the untreated sample have total fluorescence overlapping with total fluorescence from treated-sample spots, while 47% of the points from the untreated sample have a maximum peak height in the same range as points from the $\mathrm{H}$-plasma-treated sample.

Figure 3

Strain analysis of $\mathrm{Si}$-$V^{-}$ centers in the nanodiamond environment. (a) The four optical transitions A, B, C, and D (see Fig. 1) are resolved at low temperature in the PL spectrum. Transverse strain increases the ground-state (GS) and excited-state (ES) splittings, and axial strain (along with other factors) can alter the ZPL position. (b) The four-line PL spectrum is clearly identified in 17 of the 23 spots measured, and the splittings are determined. There is no correlation between the $\mathrm{Si}$-$V^{-}$ ground-state splitting and the ZPL central frequency due to the random orientation of strain in the NDs. The shaded region (30 GHz horizontally and vertically) is interpreted as low strain and contains eight of the 17 NDs. (c) There is close correlation between ground-state splitting and excited-state splitting. The orange region represents the 95% credible region inferred from a transverse-strain model, and these data indicate that the excited-state strain-splitting coefficient is ${1.688}_{-0.008}^{+0.008}$ times larger than that of the ground state. (d) Statistical inference of the $\mathrm{Si}$-$V^{-}$ strain splitting from 18 PL spectra (a spot with an unresolved four-line pattern is suitable for this analysis). The gray lines represent the 95% credible region for the optical transition energies split by transverse strain, and provide a systematic identification of the $\mathrm{Si}$-$V^{-}$ zero-field splittings in the ground (${46.3}_{-3.4}^{+2.5}$ GHz) and excited (${252.0}_{-1.8}^{+1.3}$ GHz) states. Each spectrum is placed at its inferred transverse-strain value, with the shaded band corresponding to the 95% credible region. The spectra between 14 and 30 strain units are colored to aid visual differentiation. Thirteen of the $\mathrm{Si}$-$V^{-}$ spectra correspond to the low-transverse-strain situation, where the splitting is dominated by spin-orbit interaction (increasing the chances of spectrally identical emitters).

Figure 4

Polarization of ZPL and spectral stability under resonant excitation of $\mathrm{Si}$-$V^{-}$ in $\mathrm{H}$-plasma-treated NDs. (a) The polarization pattern of the four-line fine structure for optical transitions A, B, C, and D (from top to bottom). The expected behavior of low-strain bulk $\mathrm{Si}$-$V^{-}$ can be recovered. (b) Line position of a resonantly excited $\mathrm{Si}$-$V^{-}$ center over 600 s. Occasional blinking destroys the symmetry of some PLE scans, resulting in ill-fitted peak position (open circles). Excluding such points, the transition frequency remains inside a range of 108 MHz, as indicted by the shaded band. (c) The average PLE linewidth (blue triangles) is 842 MHz and the narrowest scan (orange circles) has a width of 549 MHz. The peak heights are normalized to 1 for better comparison.

Figure 5

Manipulation of NDs at the nanoscale. (a) One-dimensional alignment of four NDs with an accuracy of $37$ nm. From top to bottom, fluorescence image of a spin-coated ND sample on glass, fluorescence image of the same sample area after nanopositioning with the AFM in contact mode, and topography image of the aligned four-ND string with the ac mode of the AFM. The intensity of fluorescence of emitters is plotted logarithmically, and is normalized by the fluorescence intensity of the unmoving ND (far right) for better visual recognition of the spatial positions. The inset spans $0.2\times 0.2\mu {\mathrm{m}}^2$ to illustrate the AFM resolution, which has a full width at half maximum of 75 nm. (b) Two-dimensional nanopositioning with accuracy of $37$ nm. From top to bottom, fluorescence image of a spin-coated ND sample on glass, fluorescence image after nanopositioning of AFM in contact mode, and topography image of the aligned four-ND square with ac mode of the AFM. The color bars are shared between (a) and (b).

Figure 6

In situ manipulation of NDs. (a) Demonstration of nitrogen-vacancy axis rotation during one tip push with the AFM in contact mode with a pushing distance of approximately 100 nm in a constant magnetic field. Before the rotation (top) the resonant frequencies are $2834.8\pm 0.1$ MHz and $2913.8\pm 0.2$ MHz, corresponding to $39\pm 4$ G and the angle between the nitrogen-vacancy axis and the magnetic field $\theta ={69}^{\circ }\pm 2^{\circ }$. After the rotation (bottom) the resonant frequencies are $2788.3\pm 0.1$ MHz and $2954.0\pm 0.1$ MHz, corresponding to $38\pm 4$ G and an angle $\theta ={38}^{\circ }\pm 6^{\circ }$. (b) Decomposition of a ND cluster. Larger clusters of ND (top) can be decomposed by pressing the AFM cantilever into the cluster (bottom).

Figure 7

$g^2(\tau )$-autocorrelation-function measurement shows the existence of single $\mathrm{Si}$-$V^{-}$ emitters in ND. (a) PL spectrum of the measured single $\mathrm{Si}$-$V^{-}$ site. (b) Confocal-microscopy image of the measured $\mathrm{Si}$-$V^{-}$ site. (c) Normalized $g^2(\tau )$ autocorrelation function. Measurement data are shown in blue, while the 95% credible region of the Bayesian inference is plotted as red shading. The $y$ axis on the left shows normalized values without background correction, while the $y$ axis on the right shows the value of $g^2(\tau )$ after background correction.

Figure 8

MCMC-sampler chain trajectories for the fundamental $\mathrm{Si}$-$V^{-}$ Hamiltonian parameters. (a) Median (orange line) and 95% credible region (blue shading) of the distribution of MCMC walkers for the ground-state spin-orbit splitting ${\lambda }_{\mathrm{SO}}^g$. The credible region and median are calculated for blocks of 50 steps at a time. Initial guesses are distributed randomly in the neighborhood of 47 GHz. On the basis of previously reported $\mathrm{Si}$-$V^{-}$ ground-state splittings less than 50 GHz, this parameter is constrained by a prior limiting it to values less than 50 GHz. It is apparent that from about 125 000 steps the distribution is skewed by this constraint. (b) Histogram showing the final distribution of the MCMC samples, calculated for the final 5000 steps. (c),(d) Walker trajectory and final distribution of samples for the excited-state spin-orbit splitting ${\lambda }_{\mathrm{SO}}^e$. (e),(f) Walker trajectory and final distribution of samples for the ratio of transverse-strain coefficients $\delta E^e/\delta E^g$.

Figure 9

Spectrum and MCMC-sampler chain trajectories for parameters specific to $\mathrm{Si}$-$V^{-}$ spot 1. (a) The Bayesian analysis infers Hamiltonian parameters directly from the raw spectral data (green circles). The final “fit” is represented by the median (orange line) and 95% credible region (blue shading). (b) The MCMC-sampler chain trajectory for the transverse strain of this spot. This parameter provides the horizontal positioning of the spectrum in the strain-summary figure [Figs. 8 and 3]. (c) Sampler trajectory for the axial-strain term for this spot. This affects the shift of the ZPL and therefore considers all four peaks together, and so it is not surprising that this parameter reaches equilibrium in the sampler trajectory more quickly than the transverse strain. (d) Sampler trajectory for the background count. There are a lot of CCD pixels that measure almost nothing but background, and so it is unsurprising that this parameter quickly reaches equilibrium in the sampler trajectory. (e) Sampler trajectory for the linewidth. Since the linewidth is limited by the instrument or by temperature, our model takes the same width for all four peaks in the spectrum. (f)–(i) Sampler trajectories for the amplitudes $D$, $C$, $B$, and $A$ of the four peaks. Peak position matters for the strain analysis, but peak height is not important. Here it is visually apparent that sensible values are obtained.

Figure 10

Strain analysis with expanded detail. This is a reproduction of Fig. 3, with the spectra annotated by their “focal spot number.” Not all of the recorded spectra have a clear-enough “single $\mathrm{Si}$-$V^{-}$” structure to be used in this analysis. The inset shows more detail of the dense region at low strain, which contains numerous almost-overlapping spectra. The 95%-credible-region shading has been omitted from the inset for better viewing of the individual spectra.