Nanoelectromechanical Control of Spin–Photon Interfaces in a Hybrid Quantum System on Chip

Abstract

Color centers (CCs) in nanostructured diamond are promising for optically linked quantum technologies. Scaling to useful applications motivates architectures meeting the following criteria: C1 individual optical addressing of spin qubits; C2 frequency tuning of spin-dependent optical transitions; C3 coherent spin control; C4 active photon routing; C5 scalable manufacturability; and C6 low on-chip power dissipation for cryogenic operations. Here, we introduce an architecture that simultaneously achieves C1–C6. We realize piezoelectric strain control of diamond waveguide-coupled tin vacancy centers with ultralow power dissipation necessary. The DC response of our device allows emitter transition tuning by over 20 GHz, combined with low-power AC control. We show acoustic spin resonance of integrated tin vacancy spins and estimate single-phonon coupling rates over 1 kHz in the resolved sideband regime. Combined with high-speed optical routing, our work opens a path to scalable single-qubit control with optically mediated entangling gates.

To reach practical utility, quantum information processors in proposed quantum repeater networks¹⁻⁷ and modular quantum computers^2,8,9 require thousands of logical qubits,⁹ motivating the development of architectures that can scale beyond millions of physical qubits. Solid-state atom-like defects are well suited for scalability due to their potential for high-density integration in nanophotonic devices, enabling proximity with very large-scale integrated circuit (VLSI) and photonic integrated circuit (PIC) semiconductor technologies. Color centers (CCs) in diamond moreover have long-lived spin ground states^8,10,11 and coherent optical transitions;^3,12−15 and group-IV-vacancy CCs such as the negatively charged silicon and tin divacancies in particular have stable optical transitions even in nanostructured diamond.^12,16,17 Their “symmetry-protected” resilience to electric field fluctuations has enabled a number of recent advances, including coherent optical transitions in nanophotonic waveguides^13,18−20 and cavities,^21,22 memory-enhanced quantum communication,²³ and a 2-qubit quantum network.^24,25

A central challenge now lies in scaling to large numbers of individually controllable color centers.² Recent developments have shown individual optical addressing and capacitive frequency tuning for large numbers of waveguide-coupled color centers,²⁰ but this architecture lacked methods for scalable, low-power-dissipation optical routing and coherent spin control. Conventional spin control methods using electromagnetic fields and microwave striplines suffer from high energy consumption and crosstalk.^26,27 Researchers recently showed promising alternatives that rely on the coupling of CC ground state levels to driven acoustic phonons in the host crystal.²⁸⁻³¹ However, methods reported to date rely on propagating acoustic modes excited in bulk samples via piezoelectric transducers,²⁸ which present bottlenecks in component density and power dissipation under cryogenic conditions.

Here, we introduce an alternative device based on piezoelectrically driven nanoelectromechanical strain tuning of CCs in diamond nanophotonic waveguide arrays or quantum microchiplets (QMCs). By driving localized acoustic modes in the diamond nanostructure, our “Strain-Transduction by Resonantly Actuated Integrated Nanoelectromechanical Systems” (STRAINEMS) device meets six essential criteria for scalability in terms of optical access and individual color-center control: (C1) individual optical addressing of spin qubits; (C2) strain-based frequency tuning of CC optical transitions; (C3) capability for coherent ground state control by exciting high-frequency acoustic modes; (C5) low device footprint to ∼100 μm²; and (C6) low power consumption due to localized resonance.

As shown in Figure 1, the STRAINEMS module completes the essential components of an architecture that can now satisfy all criteria C1–C6. We achieve this by hybrid integration of diamond nanophotonic waveguides with a cryogenically compatible system on chip (SoC) that combines the STRAINEMS device with scalable optical addressing (C1) as well as high-speed electro-optic modulation and optical waveguide routing (C4).^32,33 Based on full-wafer runs in a CMOS-compatible, 200 mm Si process,^33,34 our platform satisfies the scalable manufacturability requirement (C5). We term the full device a hybrid quantum system on chip (HQ-SoC). While we focus on diamond color centers in this work, our architecture is widely applicable to heterogeneous integration of other solid-state emitters such as quantum dots and defects in layered materials, limited by their sensitivity to strain.

Figure 1.

(a) Hybrid quantum system on a chip with components for quantum memory and control connected to active photonic modulators by optical waveguides (blue). (b) Structure of the STRAINEMS component of the HQ-SoC integrating SnVs in a QMC with a piezoelectric cantilever and SiN waveguides for mechanical and optical coupling, respectively. (c) Vertical deflection of the cantilever by an amount d induces uniaxial strain in the attached QMC along the X axis (⟨110⟩ crystal direction), XX. (d) SnV coordinate system (primed coordinates) relative to device coordinates and orientations within the diamond lattice. SnV dipole axes are aligned along the ⟨111⟩ crystal directions, with two distinct orientations relative to the uniaxial strain. Axial SnV dipole axes (purple, Z′_a) lie along [111] or [1], while transverse SnV dipole axes (green, Z′_t) along [111] or [111]. (e) (i) SnV orbital states are split by the spin–orbit interaction, leading to four optical transitions (labeled “a” through “d”) under zero external magnetic field. A laser field at frequency v detuned from v₀ by an amount probes the c transition. (ii) Under acoustic driving by the cantilever, red and blue detuned sidebands are visible in the PLE spectrum surrounding v₀ at integer multiples of the drive frequency due to coupling with acoustic phonons. (iii) An external magnetic field splits the spin-degenerate orbital states, allowing acoustic driving of the spin transition at with optical readout using the spin-flipping B1 transition.

In our approach, piezoelectric cantilevers utilizing the aluminum nitride active layer in our photonics platform mechanically couple to a heterogeneously integrated QMC hosting implanted Sn vacancy defects (SnVs, Figure 1b). On-chip silicon nitride (SiN) waveguides optically couple to the QMC via inverse tapering,^20,27 providing a scalable interface between SnV fluorescence and an active PIC. We excite the SnVs through free space, perpendicular to the QMC, where a spatial light modulator enables simultaneous excitation of multiple color centers. The NEMS actuators in our chip share the same layer-stack as photonic modulators already demonstrated in our platform,^32,34 allowing seamless integration of tunable quantum memories with large-scale photonics in the HQ-SoC. Trenches defining the undercut region of the cantilever confine the mechanical displacement, limiting crosstalk between actuators.

Under an applied voltage V(t) = V_DC + V_AC sin(ω_dt) the cantilever deflects along Z̃ (Figure 1c) introducing primarily uniaxial strain in the QMC along X̃, ε(t) ≈ ε_XX(t) = ε_XX,DC + ε_XX,AC) sin(ω_dt) (Supplemental Section 1). This leads to a strain Hamiltonian with static and time varying components in the form of H_Strain = H_static + H_AC(t), where H_AC(t) describes strain varying at a time scale faster than the CC radiative lifetime. Static strain shifts the optical transition energies of SnVs in the QMC by an amount Δ_n (where n refers to a particular transition), while dynamic strain leads to sideband transitions at multiples of ω_d.

The anisotropic ε(t) breaks the orientational degeneracy of SnVs in the QMC (Figure 1d), with axial SnVs ([111], [1] dipole axes, purple) and transverse SnVs ([111], [111] dipole axes, green) experiencing a distinct strain tensor (Supplemental Figure 2) and correspondingly different deformation of their orbital states in response to ε(t). Axial SnVs experience primarily a common mode shift in their optical transition energies due to strain along their dipole axis, while transverse SnVs experience relative shifts and state mixing due to off-axis strain.^16,35,36 The magnitude of the shift depends on the corresponding strain susceptibility parameter.

We probe the strain-dependence of SnV optical transitions using near-resonant laser excitation at frequency ν while monitoring the red-shifted phonon sideband (PSB). Figure 1e illustrates this photoluminescence excitation (PLE) spectroscopy for probing shift Δ_c of SnV transition c.

We first characterize Δ_c under static strain (referred to as Δ_DC) with V_AC = 0. Figure 2a shows a PLE spectrum for a SnV at the location marked by the red dot in Figure 2a inset when ε(t) = 0. We observe a line width (Γ_opt) of 120 ± 18 MHz for this SnV extracted from a Lorentzian fit to the data (black curve), consistent with other SnVs in this device after integration and postprocessing. When V_DC ≠ 0, Δ_DC increases or decreases linearly depending on the sign of ε (Figure 2b, v₀ is obtained from Lorentzian fits to PLE data). Results from an SnV at a different location within the same QMC (SnV 3) and from the same location in a second STRAINEMS module with a different QMC (SnV 2) are also shown in Figure 2b. We consistently measure over 20 GHz frequency tuning for SnVs located in the region of the QMC under high DC strain (Supplemental Figure 2), while the hold power dissipated on-chip for our device remains below 1 nW even at 60 V (Supplemental Section 3) satisfying requirement C6.

Figure 2.

(a) Photoluminescence excitation data for an SnV at the location marked by the red dot in the inset SEM image (SnV 3), taken at ε(t) = 0. Inset: Location of SnVs 1–3 within the QMC. (Scale bar: 10 μm.) (b) Δ_DC vs V_DC for SnV 1–3, with V_AC = 0. (c) Displacement measured at the front edge of the cantilever vs V_DC. (d) Calibrated finite-element model showing displacement consistent with measured values in panel c. (e) ε_z′a extracted from finite-element simulations at the location of SnV1 at a depth of 75 ± 5 nm (based on SRIM calculations) in the nanobeam cross-section, in the coordinate frame of an axial SnV. The uncertainty is due to implantation straggle estimated from SRIM calculations. (f) Δ_DC vs ε_z′a for SnV 1, fit using linear regression to extract t_||,u–t_||,g of −0.490 ± 0.075 PHz/strain. The error bars in parts e and f are due to uncertainty in the SnV depth within the diamond nanobeam due to implantation straggle.

We next calibrate our finite-element model to accurately determine the strain in the diamond nanobeam and extract values for strain susceptibility t_||,u–t_||,g for the SnV (we conjecture SnVs 1 and 2 are oriented axially based on the direction of their frequency shift vs strain, see Supplemental Section 2 for a derivation of the strain susceptibility parameters). We adjusted the adhesion between the QMC and the cantilever in our model until the simulated cantilever displacement (Figure 2d) matches profilometer measurements of vertical deflection as a function of V_DC (Figure 2c). After extracting ε_Z’a in the coordinate frame of an axially oriented SnV (Figure 2c), we fit Δ vs ε_Z’a (Figure 2d) and obtain an estimate of −0.46 ± 0.051 PHz/strain for t_||,u–t_||,g. We note that for an axial SnV (ε_X′X′ + ε_Y′Y′) ≪ ε_Z′Z′ (Figure 1c) and ignore the contribution from t_⊥ similar to the procedure used for SiVs and GeVs.^35,36 We find good agreement between the fits for SnVs located in high strain areas of the device (SnV 1 and SnV 2), yielding values of −0.490 ± 0.075 and −0.436 ± 0.071 PHz/strain respectively for t_||,u–t_||,g. While our estimated susceptibility values are slightly lower than those reported for the SiV and GeV (−1.7 PHz/strain), our estimate could be subject to additional errors arising from the deviation of our finite-element model from the real device and variations in the depth of SnVs within the nanobeam cross-section.

We now apply a voltage V_AC sin(ω_dt) to the cantilever and characterize the frequency-dependent behavior of the device. Confocal displacement measurements of the cantilever (Figure 3a, 3a inset, gray curves) and coupled QMC (Figure 3a inset, red curve) as a function of excitation frequency reveal mechanical resonances extending to GHz frequencies (see Supplemental Section 4 for details of measurement setup). For we observe ε(t) under AC driving in the PLE spectrum of SnVs, with a width equivalent to 2Δ_AC, where Δ_AC is the energy shift of the SnV transition at V_AC (Figure 3b).

Figure 3.

(a) Frequency response of the device measured on the cantilever (gray curve) and QMC (red curve). (i) Higher resolution frequency sweep of frequencies below 35 MHz. (b) Phonon sideband fluorescence as a function of δ_ν for V_AC of 0.5, 1.5, and 2.5 V showing Δ_AC with = 1 MHz. (c) Δ_AC measured at V_AC = 0.125 V at values from 9.8 to 10.4 MHz, showing the effect of a mechanical resonance at 10 MHz on Δ_AC. Inset: Finite-element simulation of the mechanical mode responsible for the resonance at 10 MHz. d) Δ_AC measured for both on resonance (10 MHz), and off resonance (DC, 5 kHz, 1 MHz).

This provides a tool to explore the enhanced strain response of SnVs when the cantilever is driven by its mechanical resonances. Figure 3c plots Δ_AC measured with V_AC = 0.125 V for SnV 2, as we increase through the mechanical resonance at 10 MHz in Figure 3a. Voltage dependence reveals Δ_AC ∼ 0.1 GHz for values far from mechanical resonances (1 MHz, 5 kHz, and DC with V_AC = 0.25V) vs 1.9 GHz under resonant driving at 10 MHz with the same V_AC, an almost 20-fold increase (Figure 3d). This amplified resonant response allows fast frequency tuning of integrated quantum memories with ultralow on-chip power dissipation. For the conditions in Figure 3, we estimate less than 4 × 10^–18 J switching energy (defined as the energy required to switch the device from −V_AC to +V_AC) at 0.25 V_AC, or 0.4 nW at 10 MHz with a measured device capacitance of ∼1 pF (Supplemental Section 3). Using the extracted susceptibility coefficient from DC measurements, we determine a switching energy of <5 pJ/strain.

The large frequency range of our device also allows engineered coupling between acoustic vibrations and SnVs in the diamond nanostructure. We first investigate coupling between SnV orbital states and quantized strain in the vibrating nanobeam in the resolved-sideband regime, where and the response of the SnV to ε(t) is described by H_AC(t). The rapidly oscillating ε(t) leads to coupling with virtual states visible as red- and blue-detuned sidebands in the PLE spectrum (Figure 4a, Snv 2) at integer multiples of the drive frequency Figure 4ai shows a finite-element simulation of the mechanical mode responsible for the sideband occurring at 1 GHz (Figure 4a, V_AC = 0.5 V) arising from coupling with 1 GHz phonons. With V_AC maintained at 0.5 V, we observe sidebands up to = 2.5 GHz (Figure 4b), reflecting the large operational bandwidth of our device. The relative amplitudes of the sidebands and main peak fit to Bessel functions of the first kind (Figure 4c), with the population of the kth sideband given by³⁷

1

where ⟨n⟩ is the phonon occupation number of the mechanical mode driven at V_AC, and g_orb is the single-phonon coupling rate for the SnV orbital states, arising from strain due to zero-point fluctuations in the diamond nanobeam. Finite-element simulations of g_orb yield ∼2 kHz at the location of SnV 1 (Supplemental Section 5 and Figure 8) with a maximum of ∼8 kHz for an axially oriented SnV and ∼10 kHz for transversely oriented SnVs. Using eq 1, we extract ⟨n⟩ as a function of V_AC (Supplemental Figure 10) and estimate ⟨n⟩ ∼ 10⁵ for V_AC < 0.5 V.

Figure 4.

(a) Phonon sideband fluorescence as a function of δ_ν measured for = 1 GHz, in the resolved sideband regime. Inset: FEM simulations of the mechanical deformation at 1 GHz. (b) Fluorescence as a function of δ_νfor of 1, 2, and 2.5 GHz. (c) Carrier peak and first sideband amplitudes as a function of V_AC, with error bars denoting 95% confidence intervals, derived from fits to the data. Dashed lines show a fit to Bessel functions of the first kind. (d) Fluorescence as a function of excitation frequency in an external magnetic field, showing four distinct transitions due to Zeeman splitting of the spin states in the external magnetic field. (e) Phonon sideband fluorescence as a function of measured by exciting the spin flipping transition B1. Inset: Pulse sequence used for acoustic spin resonance measurements in the main figure.

In order to investigate coupling between the SnV electron spin and phonons generated by the driven cantilever, we split the spin-degenerate orbital ground states of the SnV by using a permanent magnet. We adjust the proximity and orientation of the magnet until the spin transition frequency extracted from the PLE spectrum (Figure 4d) roughly aligns with the ∼600 MHz mechanical resonance observed in our devices (Supplemental Section 6). We initialize the SnV spin to |2↓⟩ by optically pumping the spin-flipping B1 transition and probe the spin population in the |1↑⟩ state following the application of a 150 ns acoustic pulse from the cantilever. Figure 4e shows the phonon sideband fluorescence under an optical readout pulse resonant with the B1 transition as is swept from 350 MHz to 1.05 GHz, following the pulse sequence shown in Figure 4e inset. When ∼ 550 MHz, at the frequency separation of the spin ground states (Supplemental Figure 11), we observe an increase in counts due to transfer of spin population from |2↓⟩ back to |1↑⟩ by the resonant acoustic pulse, suggesting successful measurement of acoustic spin resonance from the SnV electron spin.

An important metric for acoustic manipulation of CC spins is the spin-phonon coupling rate, g_sm, dictating the efficiency of acoustic spin manipulation and potential for coherent coupling between spin states and single phonons.³⁹⁻⁴² For SnVs g_sm depends on the degree of spin–orbit mixing as well as the prestrain present in the sample (Supplemental Figure 12); prestrain can counteract the effects of transverse magnetic field, quenching g_sm. Using a model¹² taking into account magnetic field, prestrain, and Jahn–Teller effects, we fit the peak locations in the PLE spectra for the SnV shown in Figure 4d (Supplemental Figure 11a) and estimate a transverse magnetic field of 0.022 ∓ 0.005 T at the sample, with a ground state prestrain of 865 GHz. Under these conditions, we narrow our estimate of g_sm to ∼500 Hz. Applying even modest transverse fields of 0.05–0.1 T where the frequency of the SnV spin transition is still within the frequency range of our device (Supplemental Figure 12, Figure 5d) could increase g_sm to kHz frequencies without the need for complex mechanical resonator structures, allowing us to reach effective spin-phonon coupling rates near the orbital limit.

Figure 5.

(a) Optical microscope image of an HQ-SoC comprising an 8-channel STRAINEMS module connected to two 4 × 1 multiplexing switches. (b) The dCPS-MZI module allows for high extinction switching of SnV fluorescence between the two output ports. (ii) Normalized SnV fluorescence collected from the bar (blue) and cross (orange) ports of a dCPS-MZI with integrated QMC as a function of V_θ, while V_φ is maintained at −7 V. (iii, iv) Fluorescence spectra measured at the bar and cross ports of the dCPS at V_θ = −5 V and 11 V. (c) Operation of a 4-channel switch within the HQ-SoC shown in panel a. (i) A fiber array collects light from the HQ-SoC and directs it out of the cryostat to single photon detectors labeled 1–4. A zoom-in to the STRAINEMS module shows two actuators (“a” and “b”) controlling CCs in channels 1–4 of the QMC. (ii) PLE spectra for CC’s in channels 1–4, collected at the output indicated in each plot. (iii) Δ_DC for each emitter shown in (ii) as V_DC is applied to the indicated actuator. (iv) Autocorrelation measurements for the CCs in channels 2 and 3 using the CPS-MZI to split the single photon output to detectors 2 and 3. (v) PLE as a function of detuning with = 1 GHz for V_AC = 0.75 V (top) and 1.125 V (bottom). (d) (i) Spin–phonon and orbital–phonon coupling rate as a function of transverse magnetic field, for an SnV with no prestrain. (ii) Engineering strain concentrating structures can increase the coupling to phonons.

Application of our STRAINEMS module in future quantum networks and quantum processors motivates systems capable of both controlling integrated CCs and routing their emitted photons. Figure 5a shows an optical microscope image of an example device connecting an 8-channel STRAINEMS module to two 4 × 1 photonic switches. Each switch multiplexes four adjacent channels of the QMC to a single output (input) port and allows interference between photons emitted from the color centers in arbitrary combinations of the four input channels. The switches are composed of double and single cantilever phase shifter MZIs (cps-MZIs) previously demonstrated in this platform,³² for switching and beam splitting, respectively.

Figure 5b shows high contrast routing of SnV ZPL fluorescence under off-resonant excitation at 532 nm, using a dCPS-MZI connected to a single channel of an integrated QMC (Supplemental Figure 13). Control of both θ and φ in the dCPS-MZI (Figure 5bi) compensates for variations in nontunable directional coupler splitting ratio³⁸ and allows >25 dB extinction of fluorescence from CCs (Figure 5bii, Supplemental Figure 13). We observe negligible SnV ZPL fluorescence from ports in the “off” state (Figure 5biii,iv) using control of both θ and φ to achieve maximum extinction.

Figure 5c demonstrates the operation of the HQ-SoC shown in Figure 5a. Independent piezoactuators within the STRAINEMS component each apply strain to two adjacent channels of the integrated QMC. We consider CCs 1–4 marked in Figure 5ci, controlled by piezoactuators “a” and “b”. All CCs show frequency tuning upon actuation of their cantilever (Figure 5cii,iii), with Δ_DC proportional to the simulated strain at their location within the QMC (see Supplemental Section 2), up to a maximum of ∼18 GHz for the high-strain region (CC 4). Importantly, we still observe a significant response at acoustic drive frequencies (Figure 5cv). Finally, we use the cps-MZI at the output of the 4 × 1 switch as a 50:50 beam splitter to direct single photon emission to outputs 2 and 3. In this configuration, we perform an autocorrelation measurement for emitters 2 and 3 and observe an antibunching dip at τ = 0 ns between signals collected from the two outputs (Figure 5civ).

This prototype device demonstrates the potential of the HQ-SoC architecture to combine active optical routing with photon frequency tuning and spin control within a manufacturable integrated platform. While we focused on color centers within a diamond host matrix in this work, our method is, in principle, widely applicable to other solid state quantum emitters and quantum materials, limited by their sensitivity to strain. Further refinement of our design (Figure 5dii) can increase g_orb, raising the limiting constraint on the spin-phonon coupling rate to enable further improvement of the efficiency of acoustic spin control and optical frequency tuning. Combined with operation in an optimized magnetic field (Figure 5di), this could enable efficient acoustic spin control, completing a scalable and integrated platform for quantum information processing and networking.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.3c04301.

• FEM simulation of strain in diamond QMC, on-chip power dissipation under piezoelectric driving, simulation of phonon–orbital and spin–phonon coupling rates (PDF)

Author Contributions

G.C. built the cryo-optical setup, performed the optomechanical measurements, and designed the PICs. H.R. carried out FEM simulations of orbital–phonon and spin–phonon coupling rates. M.K. assisted with cantilever displacement measurements. K.C. and L.L. fabricated the diamond microchiplets. M.Z. and M.D. assisted with on-chip power dissipation measurement and calculations. Y.H.W. performed frequency response measurements. A.L. and D.D. fabricated the photonic chips. M.T. provided the model of SnV optical transitions and cosupervised H.R. D.E. provided theory analysis. M.E., G.G., and D.E. supervised the work. G.C. and D.E. wrote the manuscript with input from all authors.

The authors declare no competing financial interest.