The device's working principle, illustrated in Fig. 1, involves controlling strain within a suspended silicon waveguide to modulate the emission wavelength of embedded G-centers (Fig. 1a). The MEMS consists of a mechanical cantilever capacitively actuated by a voltage difference between the silicon device layer and the silicon handle (Fig. 1b). The applied voltage induces strain along the waveguide, which affects the energy levels of the G-centers (Fig. 1c), resulting in a shift in their emission wavelength (Fig. 1d).
An above-bandgap laser excites the G-centers via a confocal microscope focused on the cantilever. Emission from the color centers is collected through the waveguide, which is suspended by mechanical tethers. A photonic Bragg reflector at the end of the waveguide reflects the emission along the cantilever, increasing the collection efficiency. A linear inverse taper then couples the emitted light out, which is collected by an ultra-high numerical aperture (UHNA) fiber and detected by a superconducting nanowire single-photon detector (SNSPD). The photonic components were optimized for the fundamental quasi-TE waveguide mode using finite-difference time-domain (FDTD) simulations. Further details on the design and experimental setup can be found in Supplementary Notes 1 and 2.
The fabrication process consists of three main phases: preprocessing, commercial fabrication, and post-processing.
During preprocessing, we start with a 100-oriented silicon-on-insulator (SOI) wafer. The SOI device layer is 220 nm thick, and the bottom oxide is 2 μm thick. Carbon ion implantation into the device layer is followed by rapid thermal annealing (RTA) to form G-centers.
In the commercial fabrication phase, the wafer is sent to a photonics foundry for electron beam lithography patterning and reactive ion etching (RIE) of the device layer. A 2 μm silicon dioxide cladding is deposited via plasma-enhanced chemical vapor deposition (PECVD).
Post-processing involves releasing the MEMS structures by wet etching in hydrofluoric acid (HF), removing the oxide cladding, and undercutting the structures. Critical point drying (CPD) is used to prevent collapse during drying. Chromium-gold electrical contact pads are patterned through electron beam evaporation with a shadow mask to avoid any liftoff or etching step that could damage the suspended structures (see Supplementary Note 3). Finally, the chip is wire-bonded to a printed circuit board for electrical connection. The details of the fabrication process are provided in the "Methods" section.
Schematics of the fabrication process and final device are shown in Fig. 2a, b. Scanning electron micrographs of the key photonic components after fabrication are shown in Fig. 2c, d. Figure 2c displays the MEMS cantilever waveguide, including the Bragg reflector and tethers. Figure 2d shows the linear inverse taper edge coupler. The Bragg reflector is designed with a reflectance of 95%. The tether transmission, measured experimentally, is 94%, and the coupling efficiency of the edge coupler to the UHNA fiber is calculated to be above 12%. Further details on the efficiency of the device's components are provided in Supplementary Note 4.
After packaging, the device is mounted in a closed-cycle cryostat and cooled down to cryogenic temperatures (T = 7 K) to investigate photoemission from waveguide-coupled G-centers. An above-band continuous-wave laser (λ = 532 nm, see Supplementary Note 5 for additional above-band spectroscopy) is scanned around the suspended cantilever region, and emission from G-centers is collected into UHNA fibers through the tapered edge coupler. The UHNA fibers are then spliced to SMF28 fibers for further routing (see Supplementary Note 6). The color center photoluminescence (PL) is then coupled to a free-space bandpass filter (1250-1300 nm) to suppress the excitation laser and unwanted background emission before detection on the SNSPDs (see "Methods"). The PL raster scan shown in Fig. 3a reveals two bright locations (A and B) in the cantilever part of the device (see inset of Fig. 3a). The unfiltered emission from the two locations is then sent to a spectrometer with a resolution of 40 pm (see "Methods") and reveals several zero-phonon lines (ZPLs), as shown in Fig. 3b. On each excitation position, we record the spectra of the ZPLs as a function of the applied voltage between the cantilever and the substrate. As the voltage is increased from 0 V up to 35 V, the central wavelength of the ZPL shifts, with a sign and magnitude analyzed in the theoretical model introduced in the next section. A maximum tuning of δ = 130 pm is observed, with an electrical power dissipated as low as ≈10 nW (see Supplementary Note 5), and we ensure that the process is reversible by recording spectra from 35 V back to 0 V, as shown in Supplementary Note 5. This actuation results in a spectral tuning rate of 680 MHz/V, and other devices investigated, as shown in Supplementary Note 7, demonstrate that rates up to 5.8 GHz/V are achievable. This latter result, obtained by applying a strain with a combination of lateral and vertical displacement, is sufficient to bring two emitters in resonance (see Supplementary Note 7).
To verify the two-level system nature of the tunable ZPLs, we first investigate the saturation of the single ZPL on position B by increasing the excitation laser power and recording individual spectra on the spectrometer. The integrated intensity of each peak as a function of excitation power is fitted to the saturation of a two-level system (see "Methods") from which we extract a saturation power of P = (13.6 ± 0.5) μW measured before the objective, as shown in Fig. 3c. Saturation curves from other emitters are provided in Supplementary Note 5, all demonstrating agreement with a model of saturation of a two-level system.
We then verify the single-photon nature of the collected PL by performing a Hanbury-Brown-Twiss experiment on the narrow-filtered ZPL (see "Methods") from position B at saturation. Figure 3d shows the time correlation between two SNSPDs, measured after the ZPL emission is split using a 50:50 fiber beam splitter, with a bin size of 700 ps. We measure a second-order correlation function of g(0) = 0.09 ± 0.04 without background subtraction and after normalization by long-time delay correlation (200 μs), a clear signature of emission from a single emitter. Deviation from the ideal second-order correlation of a pure single-photon source g(0) = 0 is attributed to residual background emission or emission from other G-centers. The error bars on each correlation, and thus on the raw measured g(0), are given by Poissonian statistics. The raw correlations are fitted to a second-order correlation function, which includes a bunching term due to blinking to phenomenological dark states or to the dark metastable triplet state identified in G-centers. We extract an antibunching time constant of τ = 2.7 ± 0.5 ns while the bunching time constant reads τ = 6.0 ± 0.8 ns. We measure the color center's lifetime by time-resolved measurement of PL from the ZPL excited at position A with an above-band pulsed laser (λ = 532 nm) while filtering the A2 line. The result is shown in Fig. 3e and is fitted to a mono-exponential decay, giving a lifetime of τ = 6.61 ± 0.09 ns. A similar result, shown in Supplementary Note 5, is obtained for ZPL on position B, indicating a lifetime of τ = 6.4 ± 0.1 ns. We highlight that previous works demonstrated that the lifetime is independent of the pulsed excitation power. The lifetime value confirms that the color centers employed in this work are the genuine G-centers, which is guaranteed by following a similar implantation process as in refs. . Additional spectroscopy results for each investigated ZPL are available in Supplementary Note 5.
The spectral response of the emitters to the mechanical actuation depends on two microscopic characteristics: the color centers' position inside the waveguide and their orientation within the crystalline lattice. The position influences the magnitude of strain applied to them, while the orientation of the defect determines how sensitive they are to the applied strain. Additionally, both characteristics affect the coupling efficiency of the emitter to the waveguide mode. By modeling these factors, we can extract the color centers' defect orientation and vertical position with nanometric resolution.
To estimate the position and orientation of the emitters, we express the joint probability conditioned on the orientations of the emitters. The variables Z represent the emitters' vertical positions relative to the waveguide's center, while O denotes the equivalence classes of their orientations. The equivalence classes of orientations, O, group together orientations that exhibit identical behaviors for strain, such as having the same piezospectroscopic coefficients, and dipole orientation, meaning they couple with the same efficiency into the fundamental quasi-TE waveguide mode. To collectively represent all emitters, we define E = {A, A, A, B}, with Z = {Z: i ∈ E} as their positions and O = {O: i ∈ E} as their orientations. The joint probability of emitter positions and orientations is
assuming the marginal independence of emitter positions given their orientations allows us to factorize the joint probability of all vertical positions. Substituting this factorization into the original expression gives
Here, P(O) represents the joint probability distribution of the emitters' orientation equivalence classes, which cannot be factorized due to the model's interdependence between the estimated emitter orientations. The intensities of the observed emitters provide information about their coupling efficiencies, which, in turn, influence the estimation of the other emitters' coupling efficiencies and dipolar orientations.
The model used to determine each scenario's probability is shown in Fig. 4a, with the probability distribution of the emitters' vertical position presented in the right plot of Fig. 4b. We estimate the probability by evaluating the likelihood of all emitter orientation and vertical position combinations, starting with the product of conditional probabilities for each emitter's position given its dipole orientation. The coordinate system used for the model is illustrated in Fig. 4c. The origin of the coordinate system is defined at the center of the waveguide cross-section for x and z and at the center of the last tether along the cantilever's y-axis. A three-dimensional finite element method (FEM) simulation calculates the strain versus voltage along the cantilever, with the result at 35 V displayed in Fig. 4d. This simulation reveals the longitudinal strain distribution, which transitions from compressive to tensile along the vertical axis. To determine the positions of the emitters along the cantilever, we use their y-coordinates extracted from the PL scan in Fig. 3a. Different positions along the cantilever exhibit specific strain profiles, as depicted in the heatmap of Fig. 4d. By fitting the simulated strain curves, evaluated at the PL spot locations along the cantilever, to the emission wavelength shifts (Fig. 4e), we determine the vertical positions of the emitters associated with each equivalence class of dipole orientations.
We assign probabilities to the positions based on normalized carbon concentration data from secondary ion mass spectroscopy (SIMS), shown in the left plot of Fig. 4b (More details in Supplementary Note 8). Since two carbon atoms and an interstitial silicon are required to form a G-center, assuming a uniform interstitial silicon distribution, the G-center density is quadratic with the carbon concentration. The shaded area in the plot represents this distribution. Consequently, we assign a probability proportional to the square of the normalized carbon concentration at each vertical position. The probabilities for the vertical positions of the color centers, P(Z ∣ O), are normalized across all possible orientations for each emitter.
The second term of the probability function describes the likelihood of each possible combination of the emitters' dipole orientations, represented by the joint probability of the emitters being aligned along specific directions. To evaluate this probability, we consider the intensity of the color centers' emission and the coupling related to their dipole orientations. The right diagram of Fig. 4a illustrates the corresponding model structure. The measured intensity depends on the excitation power, emitter generation rate, and collection efficiency, which has two components: η, the coupling efficiency between the emitter's dipole emission and the waveguide mode, and η, the coupling efficiency from the waveguide mode to detection. For the four emitters analyzed, excitation power and η are constant, so the main factors influencing intensity are dipole orientations and generation rates. The generation rate, as reported in ref. , is assumed to follow a normal distribution. To isolate the impact of the generation rate on the emitters' intensities, the intensity is scaled by dividing it by η for each potential scenario. Coupling is averaged across the cantilever's x-direction to account for uniform emitters' distribution. η is computed for all dipole orientations and vertical positions via FDTD simulations (Fig. 4f and more details in Supplementary Note 9). Since the dipole coupling to the quasi-TM mode is significantly lower than to the quasi-TE mode (Supplementary Note 9), we only consider the latter one in our model. Once the relative generation rates are obtained, a maximum likelihood estimation determines the most likely Gaussian distribution for these rates. The likelihood of the four-generation rate samples from each distribution is computed, yielding the overall likelihood for each orientation scenario, which corresponds to P(O).
We combine the two components of the model to compute the probability for each scenario, evaluating the probability P(Z ∩ O) for all the possible emitter positions and orientations. The distributions, detailed in Supplementary Note 10, show that the most likely scenario (67.0%) corresponds to the case with all emitters aligned along the [110] or [] direction. Marginal probabilities for these orientations show likelihoods of 98.6%, 96.0%, 93.4%, and 68.2% for emitters B, A, A, and A, respectively. The outcome aligns with our expectation, as the brightest emitters are typically aligned along the [110] direction, making them more likely to be observed during the measurements. Based on these dipole orientations, the vertical positions of the emitters are estimated (right plot of Fig. 4b). Monte Carlo simulations (detailed in Supplementary Note 10) are used to estimate the error in the vertical localization, accounting for uncertainties in FEM simulation, piezospectroscopic coefficients, and y-coordinate positioning. The vertical localization estimate achieves nanometric resolution with error margins below 3 nm.