Intermodal microwave-to-optical transduction using silicon-on-sapphire optomechanical ring resonator

Abstract

Optomechanical and electro-optomechanical systems have emerged as one of the most promising approaches for quantum microwave-to-optical transduction to interconnect distributed quantum modalities for scaling the quantum systems. These systems use suspended structures to increase mode overlap and mitigate loss to achieve high efficiency. However, the suspended design’s poor heat dissipation under strong drive limits the ultimate efficiency. Here, we demonstrate an unsuspended optomechanical ring resonator (OMR) based on the silicon-on-sapphire (SOS) platform for microwave-to-optical frequency conversion. The OMR achieves a triply resonant optical-to-optical conversion with an enhanced coupling rate G_b = 3.6 gigahertz per square-root milliwatt at a peak conversion efficiency of 1.2% with 3.6-milliwatt microwave drive power and a microwave-to-optical conversion efficiency of 1.5 × 10⁻⁵ at 10-milliwatt optical drive power. Our results show that the unsuspended SOS platform, which mitigates the thermal effect and is compatible with superconducting qubits, is a promising platform for optomechanical circuitry and quantum transduction.

A silicon-on-sapphire optomechanical ring resonator with unsuspended design boosts microwave-to-optical conversion efficiency.

INTRODUCTION

Bidirectional microwave-to-optical transduction plays a crucial role in both classical and quantum applications by converting microwave signals to optical signals, and vice versa, for long-distance communication between network nodes. In the classical regime, silicon photonics-based microwave-optical transceivers have been manufactured with standardized foundry processes and successfully deployed for optical interconnects at scales from data centers to in-package optics (1–4). Thanks to silicon’s low optical loss in the near-infrared, silicon photonics afford various types of photonic cavities such as microrings, microdisks, and photonic crystal cavities, with optical quality factors Q higher than 10⁶ (5–8). For quantum applications, thanks to silicon’s low mechanical loss, silicon-based optomechanical quantum transducers have demonstrated superior performance (9–11), promising to enable quantum optical interconnects to link distributed quantum processors to form large-scale computing clusters (12–14). To reduce mechanical loss and achieve high mechanical and optical Q factors, however, those optomechanical quantum transducers all include delicate, free-standing structures fabricated on the silicon–on–silicon dioxide (Si-on-SiO₂) substrates. These suspended structures face the difficulty of excessive thermal effect (10, 15, 16) due to poor heat dissipation when strong electrical or optical drives are used to achieve efficient transduction. Besides, superconducting qubits integrated on a Si-on-SiO₂ suffer from considerably reduced coherence time (9, 17) compared with other substrates such as crystalline silicon (18, 19) and sapphire (20). Therefore, it is highly desirable to explore alternative platforms for optomechanical transduction that afford efficient heat dissipation and retain qubit coherence while still using silicon’s exceptional optical and mechanical attributes.

Here, we report an unsuspended optomechanical microwave-to-optical transducer based on the silicon-on-sapphire (SOS) platform. SOS is the very first silicon-on-insulator material platform developed by growing crystalline silicon on sapphire to fabricate high-performance transistors for microwave applications (21, 22). The SOS platform can mitigate many of the aforementioned problems of Si-on-SiO₂. First, superconducting qubits integrated on sapphire have achieved record-long coherence time, thanks to sapphire’s very low microwave loss tangent (17, 23–27). Second, SOS is ideal for optomechanical circuits because silicon to sapphire has high contrasts in both their optical indices ( $n_{\text{silicon}}=3.5$ versus $n_{\text{sapphire}}=1.72$ ) and acoustic speeds [ $v_{\text{si}}\sim 5000\mathrm{m}/\mathrm{s}$ , Rayleigh wave (28, 29) versus $v_{\text{sapphire}}\sim \mathrm{10,000}\mathrm{m}/\mathrm{s}$ , longitudinal wave (30)]. Such high contrasts enable fabricating photonic and phononic waveguiding structures in silicon without the need for freestanding structures, thereby enjoying the sapphire substrate as an efficient heat sink to mitigate the heat management challenge. Silicon also has a high acousto-optic figure-of-merit ${\mathcal{M}}_2=36.1(\times {10}^{-15}{\mathrm{s}}^3{\text{kg}}^{-1})$ (31–33), which facilitates efficient acousto-optic coupling. In this work, we demonstrate an optomechanical ring resonator (OMR) architecture on the SOS platform, which exploits resonantly enhanced acousto-optic Brillouin scattering to achieve microwave-to-optical conversion (34). The transducer uses an integrated piezoelectric zinc oxide (ZnO) layer to generate acoustic waves from the microwave signals for electromechanical conversion. The SOS OMR is designed to have triple resonances of two photonic modes and one phononic mode, simultaneously traveling within the ring, to achieve an enhanced optomechanical coupling rate of $G_b=3.6\text{GHz}{\left(\text{mW}\right)}^{-1/2}$ . Using the OMR’s multiple photonic resonances across a broad bandwidth, the device supports multiple optical drive channels, enabling wavelength-division multiplexed (WDM) operation toward scalable systems. Our result shows that the SOS substrate is a promising platform for realizing optomechanical microwave-to-optical transduction for quantum applications.

RESULTS

Triple resonant traveling-wave cavity

Figure 1 (A and B) illustrates the OMR architecture, including photonic and phononic bus waveguides. In contrast to standing wave resonators, such as photonic crystal cavities, the OMR supports two traveling photonic modes with frequency ${\mathrm{\omega }}_{0,1}$ and wave vector ${\mathbf{\beta }}_{0,1}$ , respectively. Along with a resonant phononic mode (frequency $\mathrm{\Omega }$ and wave vector $\mathbf{q}$ ), efficient three-wave mixing can occur when phase-matching conditions, ${\mathbf{\beta }}_0+\mathbf{q}={\mathbf{\beta }}_1$ and ${\mathrm{\omega }}_0\pm \mathrm{\Omega }={\mathrm{\omega }}_1$ , are satisfied (note S1B). This multiresonant three-wave mixing enables microwave-to-optical conversion through intermodal Brillouin scattering when driven by the phononic mode or optical-to-microwave conversion through stimulated Brillouin emission when driven by one of the photonic modes. Such processes under the above phase-matching conditions are described by the interaction Hamiltonian

$${\widehat{H}}_I=\mathrm{\hslash }{g}_0({\widehat{a}}_0{\widehat{a}}_1^{†}\widehat{b}+{\widehat{a}}_0^{†}{\widehat{a}}_1{\widehat{b}}^{†})$$ (1)

where ${\widehat{a}}_i$ $\left({\widehat{a}}_i^{†}\right)$ and $\widehat{b}$ $\left({\widehat{b}}^{†}\right)$ are the annihilation (creation) operators of the ith photonic and phononic modes. The vacuum optomechanical coupling rate $g_0$ is determined by the overlap integral of the three participating modes $a_0$ , $a_1$ , and $b$ (note S1B). While the OMR supports a large number of resonant modes, for a given design, phase matching is only achieved for one set of three photonic and phononic modes so our analysis focuses on such a subspace.

Fig. 1. An SOS OMR.

(A and B) Illustrations of bidirectional microwave-optical transduction in OMR on the SOS material platform. (A) Microwave signal being up-converted to the optical signal via Brillouin scattering. (B) Optical signal being down-converted to a microwave signal via stimulated Brillouin emission. (C) The cross-sectional profile of the OMR waveguide. The silicon waveguide has a height $h=330$ nm, a width at the base $w=800$ nm, a sidewall angle θ = 82°, and a bending radius $r=50$ μm. (D and E) The cross-sectional photonic mode profiles ( $\mid E_x\mid$ ) of the TE₀ and TE₁ modes. (F and G) The phononic Love mode (L₀)’s displacement profiles ( $\mid u\mid$ ) in y and x directions. (H and I) The photonic dispersion curves of TE₀ and TE₁ modes in OMR. The phase-matching conditions in (H) and (I) correspond to the configurations in (A) and (B). The solid circles on the dispersion curves represent the OMR’s photonic resonances. The dashed lines represent the output optical (H) and microwave (I) signals. (J) The phononic dispersion curve of the L₀ mode. The solid circles on the dispersion curve represent the OMR’s phononic resonances. The inset shows an enlarged phononic dispersion curve with the resonances.

If the system is driven with a coherent microwave signal, $H_I$ can be linearized by taking $\widehat{b}\to \langle \widehat{b}\rangle$ , resulting in an effective interaction Hamiltonian

$${\widehat{H}}_I^{\text{eff}}=\mathrm{\hslash }{G}_b({\widehat{a}}_0{\widehat{a}}_1^{†}+{\widehat{a}}_0^{†}{\widehat{a}}_1)$$ (2)

which describes intermodal Brillouin scattering (Fig. 1H) (35–40). Here, $G_{\mathrm{b}}=g_0\langle \widehat{b}\rangle$ is the enhanced intermodal coupling rate. The interaction Hamiltonian in Eq. 2 is of the beam-splitter type to facilitate conversion between the two optical modes $a_{0,1}$ . Moreover, this traveling-wave optomechanical architecture mitigates the parasitic down-conversion effect typically observed in multimodal cavity systems (41). Likewise, when the system is driven by the ${\widehat{a}}_0$ mode, ${\widehat{H}}_I$ becomes

$${\widehat{H}}_I^{\text{eff}}=\mathrm{\hslash }{G}_0({\widehat{a}}_1^{†}\widehat{b}+{\widehat{a}}_1{\widehat{b}}^{†})$$ (3)

where $G_0=g_0\langle {\widehat{a}}_0\rangle$ is the enhanced optomechanical coupling rate. This Hamiltonian describes the bidirectional microwave-to-optical conversion process relating to the stimulated Brillouin scattering (Fig. 1I) (42–44). In contrast, driving the system with the ${\widehat{a}}_1$ mode produces a two-mode squeezing Hamiltonian

$${\widehat{H}}_I^{\text{eff}}=\mathrm{\hslash }{G}_1({\widehat{a}}_0\widehat{b}+{\widehat{a}}_0^{†}{\widehat{b}}^{†})$$ (4)

where $G_1=g_1\langle {\widehat{a}}_1\rangle$ . This Hamiltonian generates entanglement between microwave and optical photons (45). Such an ability to reconfigure effective interactions for either microwave-to-optical transduction or two-mode squeezing operations by choosing the drive is a key feature of the OMR system.

SOS OMIC design

The optomechanical integrated circuit (OMIC) is fabricated on an SOS wafer with a 330-nm-thick epitaxial silicon layer on a c-plane sapphire substrate (see Methods and note S2 for the fabrication process). Figure 1C shows the cross section of the waveguide design. The silicon ridge waveguide has a base width $w=800$ nm, a sidewall angle θ = 82°, and a bending radius $r=50$ μm. The waveguide supports both TE₀ and TE₁ modes in the telecommunication band, as shown in Fig. 1 (D and E). Notably, the silicon waveguide on the sapphire substrate supports a confined acoustic Love mode (L₀) without the need to suspend the waveguide (Fig. 1, F and G). Figure 1 (H to J) shows the simulated dispersion relations of the waveguide’s photonic and phononic modes and the resonant phase-matching conditions in the OMR where the microwave-optical conversion process is enhanced.

The fabricated OMIC (Fig. 2A) also consists of optical and microwave input/output (I/O) ports. For optical I/O, five grating couplers are fabricated: four for TE₀ and TE₁ I/O and one for alignment with the optical fiber array (see note S3 for the fiber array setup). The photonic circuit consists of two waveguide designs: a multimode waveguide ( $w_0=800$ nm) and a single-mode waveguide ( $w_1=450$ nm). The multimode waveguide supports both TE₀ and TE₁ modes, whereas the narrower single-mode waveguide only supports the TE₀ mode with an effective mode index $n_{\text{eff}}$ matching that of the TE₁ mode in the multimode waveguide. Both types of waveguide connect to the OMR with a separate add-drop configuration, allowing selective coupling and filtering of the TE₀ and TE₁ modes (Fig. 2B) (34). In addition, the drop ports are terminated with a waveguide taper to eliminate back-reflections (see note S4 for full photonic design parameters). At each end of the phononic waveguide, an interdigital transducer (IDT) is fabricated on a piezoelectric ZnO film (280 nm) to generate and detect acoustic waves (Fig. 2C). The IDT’s period is $\mathrm{\Lambda }=2.85$ μm to generate the L₀ mode at a frequency of $\mathrm{\Omega }=2.2$ GHz. The phononic waveguides are linearly tapered over a length of 150 μm from a width of $w_{\text{IDT}}=15$ μm at the excitation region to the OMR waveguide width, preserving the generated L₀ mode.

Fig. 2. A multimodal ring resonator with photonic and phononic resonances.

(A) An optical microscope image of the OMR on the SOS substrate. The TE₀ (TE₁) photonic mode propagation direction is indicated by the blue (green) arrows. The L₀ phononic mode propagation direction is represented by the red arrows. (B) An enlarged optical image of the OMR. Two pairs of bus waveguides are coupled to the OMR with add-drop configurations, and they correspond to the TE₀ (blue arrows) and TE₁ mode (green arrows) couplings, respectively. (C) A zoomed-in optical image of an aluminum IDT on a zinc oxide (ZnO) layer deposited on the silicon phononic waveguide. The IDT pitch is $\mathrm{\Lambda }=2.85$ μm. (D) Normalized optical transmission spectra through the TE₀ and TE₁ mode waveguides. (E) Lorentzian fitting of the normalized TE₀ mode resonance of the OMR at 1555.1 nm, yielding a $Q=1.03\times {10}^5$ . (F) Normalized microwave reflection coefficient spectrum (S₁₁) of an IDT at room temperature (RT; black line) and 4 K (red line). (G) Normalized microwave transmission coefficient spectrum (S₂₁) between the two IDTs at RT (black line) and 4 K (red line). The inset shows a zoom-in of the S₂₁ around the main transmission window of the IDT at 2.22 GHz showing multiple OMR resonance dips.

OMIC characterizations

We characterize the photonic and phononic components of the OMIC separately. We first verify the coupling of the TE₀ and TE₁ modes to the OMR through the designated drop ports, as illustrated in Fig. 2B. We couple a tunable laser source into the TE₀ (TE₁) input port, which couples to the OMR, and monitor the output power via the respective drop port. The measured free spectral ranges (FSR) of the OMR resonances from the TE₀ and TE₁ ports are used to discern the mode types (Fig. 2D). The measured FSR for the TE₀ mode is ${\mathrm{\Delta \lambda }}_0=1.86$ nm and for the TE₁ mode is ${\mathrm{\Delta \lambda }}_1=1.53$ nm. The experimental values agree well with the simulated values ( ${\mathrm{\Delta \lambda }}_{0-\text{sim}}=1.85$ nm and ${\mathrm{\Delta \lambda }}_{1-\text{sim}}=1.57$ nm), confirming that the desired modes are circulating in the OMR. The highest intrinsic photonic quality factor for the TE₀ (TE₁) mode is $Q_0=1.03\times {10}^5(Q_1=8000)$ (Fig. 2E).

To characterize the phononic components, we measure the spectrum of the microwave reflection coefficient S₁₁ at the IDT at room temperature (RT) and 4 K (Fig. 2F) using a cryogenic probe station (see Methods for the measurement setup). On the basis of simulation results, we identify the resonance near 2.21 GHz corresponding to the desired L₀ mode. The L₀ mode has a dominant shear displacement field with an antisymmetric profile (Fig. 1F), which enables optomechanical coupling between the symmetric TE₀ mode and the antisymmetric TE₁ mode. The resonance is stronger at 4 K than at RT, indicating a higher electromechanical conversion efficiency ${\mathrm{\eta }}_{\text{em}}$ due to the improved IDT impedance matching at 4 K. Applying the modified Butterworth Van Dyke model (46) to the measured S₁₁ spectrum yields ${\mathrm{\eta }}_{\text{em}}=70\%$ at 4 K (see note S5 for the definition and calculation of ${\mathrm{\eta }}_{\text{em}}$).

The OMR’s phononic resonances are investigated by measuring the spectrum of the phononic bus waveguide’s transmission coefficient S₂₁ between two IDTs. When the microwave frequency is tuned to the resonance of the OMR, the phononic mode is coupled into the OMR, and the S₂₁ spectrum shows corresponding dips. Considering the acoustic propagation time between the two IDTs is ~650 ns (with a propagation distance of 900 μm and a simulated L₀ mode velocity of 1400 m/s), a time-gating window of 175 to 750 ns is applied (47) to filter parasitic coupling between the two IDTs. We observe a stronger cross-talk signal at 4 K than at RT when the IDT efficiency is higher, which we attribute to the free space coupling in the cryogenic chamber. Figure 2G shows the measured transmission spectrum in the IDT’s passband centered at 2.22 GHz with a −3-dB bandwidth of 23 MHz and using an input power of 0 dBm. The measured S₂₁ also shows several evenly spaced resonance dips corresponding to the phononic resonances of the OMR, and the measured phononic FSR, FSR_exp = 4.1 MHz, agrees well with the simulated value of FSR_sim = 4.4 MHz. The signal intensity at 4 K is ~3 times stronger than that at RT, which is attributed to the reduced thermal phonon scattering loss (48) and the increased ${\mathrm{\eta }}_{\text{em}}$ of the IDT. The highest phononic quality factor at 4 K (RT) is $Q_a=3000$ (1000). Temperature-dependent phonon loss measurement shows that the loss is dominated by thermal phonon scattering in the material (see note S7 for temperature-dependent material loss characterization).

Multichannel microwave-to-optical conversion

We now demonstrate microwave-to-optical conversion through the intermodal Brillouin scattering between the TE₀ and TE₁ modes facilitated by the phononic mode in the OMR, as in the case of Eq. 2. In our experiment, the TE₀ mode is used as the optical drive, which is counter-propagating with the phononic L₀ mode and converted to the TE₁ mode. The generated TE₁ mode couples out of the OMR to the TE₁ waveguide and is measured with a high-speed photodetector (HPD) (Fig. 3B). To tune to triple resonances of the OMR, the TE₀ drive is first fixed at 1555.1 nm, where TE₀ and TE₁ resonances overlap (Fig. 2D), with a drive power 5 dBm. The frequency of the microwave signal is swept across the IDT passband with 0-dBm power. The spectrum measured at the HPD (optical S₂₁) at 4 K (Fig. 3B) shows multiple evenly spaced resonance peaks from 2.20 to 2.24 GHz. The average peak spacing is $\mathrm{\delta }{f}_{\text{avg}}=4.1$ MHz, which matches the OMR’s phononic FSR. From the measured FSR, we extract the phononic group velocity to be $v_{\mathrm{L}-\text{eff}}=1300$ m/s, which also agrees well with the simulated results (Fig. 1J) of $v_{\mathrm{L}-\text{sim}}=1400$ m/s. While the model suggests that only a particular pair of TE₀-TE₁ modes are phase-matched to a given L₀ mode, the finite resonance bandwidth relaxes this condition, enabling a multimode phase matching with a reduced coupling rate (49). This explains the presence of multiple peaks measured in the experimental result. For instance, the full width half maximum bandwidth of the OMR’s photonic resonance at 1550 nm is $\mathrm{\delta }f=35$ GHz (Q₀ ~ 46,500), which is much larger is the phononic FSR. Therefore, as illustrated in the inset of Fig. 3B, a single TE₀ mode can be phase-matched, although nonideal, with multiple phononic L₀ modes in the OMR to be converted to a TE₁ mode.

Fig. 3. Multiresonance microwave-to-optical conversion.

(A) Schematic diagram of the setup to characterize the TE₀-to-TE₁ intermodal conversion through the optical S₂₁ measurement. The TE₀ (L₀) mode’s propagation direction is marked with the blue (red) arrows. The TE₁ mode (green arrows) is generated via Brillouin scattering inside the OMR and coupled out through the TE₁ output port to the VNA. EDFA, erbium-doped fiber amplifier; VNA, vector network analyzer. (B) The optical S₂₁ spectrum of TE₀-to-TE₁ conversion at 4 K around the central microwave frequency of 2.22 GHz. The spectrum features multiple resonances with spacing matching the phononic FSR of the OMR. The green translucent background indicates the TE₁ mode resonance. The inset illustrates that multiple phononic resonances can phase-match the TE₀-to-TE₁ conversion within the bandwidth of one photonic resonance. The red circles indicate the phononic resonances. The blue (green) translucent area indicates the TE₀ (TE₁) spread on the dispersion diagram. (C) The optical S₂₁ measured at various photonic resonance wavelengths. The microwave signal is scanned over the same frequency range, while the optical drive is tuned to different photonic resonant wavelengths. The bandwidth of the optical S₂₁ is limited by the IDT bandwidth. (D) A two-dimensional (2D) map of the measured optical S₂₁. The microwave signal frequency is swept from 2.20 to 2.25 GHz, the same as in (C), while the drive laser is swept in steps of 0.25 nm. The data are acquired with VNA and averaged 50 times at each laser sweep step.

To further explore the capability of our system, the drive laser is tuned to seven different optical resonances of the OMR between 1537.55 and 1555.14 nm. The measured optical S₂₁ is shown in Fig. 3C, with intensity variation attributed to the different phase-matching conditions at different optical drive wavelengths. The demonstration of microwave-to-optical conversion across such a broad band of drive wavelengths shows that the OMR can support WDM operation, potentially helping scale up the system. We further construct a two-dimensional (2D) map of the system’s response when simultaneously sweeping the optical drive wavelength from 1555.5 to 1561 nm at a fixed power of 5 dBm and a microwave frequency from 2.20 to 2.25 GHz at a fixed power of 10 dBm. The resulting optical S₂₁ map (Fig. 3D) shows characteristics similar to single-frequency drive situations. We also observe a 10-dB signal-to-noise ratio between the on- and off-resonance photonic drive (horizontal bright and dark streaks). In addition, we also observe fringe-like features on the 2D map. The bright vertical fringes correspond to the case where both photonic and phononic resonant conditions are met, while the dark fringes represent only the photonic resonance conditions are met.

Determine optomechanical coupling rate

To determine the optomechanical coupling rate in the OMR, we use a heterodyne measurement scheme (Fig. 4A and Methods) to spectrally resolve the different frequency components involved in the microwave-to-optical conversion process. The tunable laser is first separated into a drive and a reference, which is shifted up in frequency by $\mathrm{\delta }/\text{2π}=102.9$ MHz with an acousto-optic frequency shifter (AOFS). The signal transmitted through the device beat with the reference signal at the HPD and analyzed with a real-time spectrum analyzer. The measured spectrum of the beating signal is shown in Fig. 4B for a microwave input frequency of $\mathrm{\Omega }/\text{2π}=2.22$ GHz. Four distinct beating tones are relevant to optomechanical coupling: (i) $P_{\mathrm{r}}$ , the beating between the unscattered drive, and the reference signal at $\mathrm{\delta }/\text{2π}=102.9$ MHz; (ii) $P_{\text{AS}}$ , the anti-Stokes (phonon absorption) signal at $(\mathrm{\Omega }-\mathrm{\delta })/\text{2π}=2.107$ GHz; (iii) $P\mathrm{s}$ , the Stokes (phonon emission) signal at $(\mathrm{\Omega }-\mathrm{\delta })/\text{2π}=2.312$ GHz; and (iv) $P_0$ , the beating between the unscattered optical drive and Stokes/anti-Stokes signal at $\mathrm{\Omega }/\text{2π}=2.22$ GHz. The 8-dB asymmetry between $P_{\text{AS}}$ and $P_S$ verifies that the counter-propagating phononic mode dominates the scattering process, consistent with the theoretical expectation.

Fig. 4. Microwave-to-optical frequency conversion efficiency characterization.

(A) Simplified schematic diagram of the heterodyne measurement setup. RSA, real-time spectrum analyzer. DUT, device-under-test. The reference optical signal is generated by shifting the drive laser frequency by $\mathrm{\delta }/\text{2π}=102.9$ MHz using an AOFS. (B) A broadband spectrum of the heterodyne response. The red and yellow peaks correspond to the anti-Stokes $P_{\text{AS}}(\mathrm{\Omega }-\mathrm{\delta })$ and Stokes $P_{\mathrm{S}}(\mathrm{\Omega }+\mathrm{\delta })$ signals of the OMR, respectively. The purple peak is the self-interference signal $P\mathrm{r}\left(\mathrm{\delta }\right)$ generated by the beating of the unscattered TE₀ mode with $P_{\text{AS}}$ and $P_{\mathrm{S}}$ . Inset: Zoom-in of the signals $P_{\text{AS}}$ , $P_{\mathrm{r}}$ , and $P_{\mathrm{S}}$ . (C) Waterfall plot of $P_{\text{AS}}$ and $P_{\mathrm{S}}$ signals at different power levels of the microwave signal $P_{\text{MW}}$ . The curves in the waterfall plot are artificially offset vertically (intensity) and horizontally (frequency) for clarity to show the oscillatory feature of the heterodyne beating signal. The gray diagonal dashed lines make the equal-frequency lines for visual assistance. (D) The intensity of $P_{\text{AS}}$ and $P_{\mathrm{S}}$ signals as a function of the microwave signal amplitude and fitted with the scattering matrix model (black curves).

To assess the transduction efficiency and the enhanced optomechanical coupling coefficient $G_b$ , we measure $P_{\text{AS}}$ and $P_{\mathrm{S}}$ with increasing microwave signal power (Fig. 4C). The drive laser is fixed on resonance at 1555.1 nm with 10-dBm power. We observe that both $P_{\text{AS}}$ and $P_{\mathrm{S}}$ increase initially with the microwave signal power (Fig. 4D). However, $P_{\text{AS}}$ shows a distinct oscillatory behavior with increasing signal power (Fig. 4D, right). To better understand this, we model our system using scattering matrix analysis (see note S1D), which gives the expression of $G_b$ as

$$G_b=g_0\frac{\sqrt{{\mathrm{\kappa }}_b}{S}_{b+}}{i\left({\mathrm{\Delta }}_{\mathrm{\Omega }}\right)+({\mathrm{\gamma }}_b+{\mathrm{\kappa }}_b)/2}$$ (5)

where ${\mathrm{\kappa }}_b\left({\mathrm{\gamma }}_b\right)$ is the extrinsic (intrinsic) coupling rate of the phononic mode of the OMR, $S_{b+}$ is the phononic signal amplitude, and ${\mathrm{\Delta }}_{\mathrm{\Omega }}$ is the microwave frequency detuning. We extracted a $G_b=3.655\text{GHz}{\left(\text{mW}\right)}^{-1/2}$ at 4 K by fitting the Stokes and anti-Stokes signal (Fig. 4D) with the device model (note S1D). The TE₀-to-TE₁ mode conversion efficiency of 1.2% is also extracted from the model at 3.6 mW microwave signal power. We then calculate the single-phonon coupling rate $g_0$ by normalizing $G_b$ to the number of input signal phonons, with a single phonon energy $E=\mathrm{\hslash }\mathrm{\Omega }$ and an electromechanical efficiency ${\mathrm{\eta }}_{\text{em}}\approx 0.70$ . We find $g_0=G_b/\langle \widehat{b}\rangle \approx 350$ Hz. Last, a microwave-to-optical transduction efficiency is also calculated to be $1.5\times {10}^{-5}$ with a 10-dBm optical drive power (see note S1E for transduction efficiency calculation and definition).

DISCUSSION

In summary, we demonstrate an OMIC on the SOS platform featuring unsuspended device structures—an important advancement over our previous work (34). This platform offers improved heat dissipation, enabling higher power handling, and is compatible with both superconducting quantum circuits (18, 20) and complementary metal-oxide semiconductor processes. In addition, we demonstrate multichannel optomechanical interactions, opening the possibility for wavelength-multiplexed quantum transduction. SOS is an ideal platform for unsuspended optomechanical transducers with the sapphire substrate providing efficient heat dissipation (50), mitigating the excessive thermal effects in previous device systems (10). The sapphire substrate’s compatibility with superconducting devices, such as high-quality-factor superconducting resonators (51), and superconducting qubits, also makes it a desirable monolithic platform for realizing quantum transduction. Using the coresonance of photonic and phononic modes in the OMR, we achieve a single phonon optomechanical coupling rate $g_0=350$ Hz, exceeding similar triply resonant electro-optic systems (16) by a factor of 10. However, our result is three orders of magnitude lower than the state-of-the-art piezo-optomechanical quantum transducer (52) ( $g_0=919$ kHz) and two orders of magnitude lower than our theoretical value of $g_0\simeq 15$ kHz, based on finite element analysis (FEA) estimates for an OMR with a radius $r=20$ μm. On the other hand, the pump-enhanced coupling rate $G_b$ and the total microwave-to-optical conversion efficiency are the practically important metrics of quantum transducers (53). The gigahertz-level $G_b$ achieved in an unsuspended device structure makes SOS a promising platform for integrating optomechanical transduction with superconducting quantum circuits. (see note S1D for the FEA simulation detail). We attriSbute this discrepancy to the nonideal triple resonance phase matching and the nonideal guided phononic mode and the excessive loss of the photonic and phononic modes. Several improvements can be engineered to increase $g_0$ : Instead of using four different photonic waveguides to couple to the OMR, as presented in the current design, a single photonic multimode waveguide can be used to reduce the photonic loss channels. Furthermore, optimizing the mode overlap by using a tuning mechanism applicable at cryogenic temperatures (54) can enable further improvement. The optical quality factor of the OMR can also be improved by optimizing the phononic waveguide coupling gap (currently 50 nm) and reducing the number of phononic waveguides to minimize the optical extrinsic loss. The efficient heat dissipation through the sapphire substrate also allows using much higher optical drive power to further enhance the coupling rate. Besides quantum applications (55), the OMR on the SOS is also promising for a plethora of classical applications, such as optical mode converters (40), frequency shifters (56), and nonmagnetic optical isolators (57).

METHODS

Device fabrication

The SOS (350 nm) substrate is purchased from Nova Electronic Materials and used as it is. The silicon photonic and phononic waveguides are patterned with electron beam lithography (EBL) (JEOL-JBX6300FS) using ZEP-520A resist. The pattern is transferred into SOS by plasma etching using chlorine-based chemistry. The 280-nm-thick ZnO film is deposited using a microwave magnetron sputtering system and lifted off in a sonicated acetone bath. The IDT pattern is written using the EBL and lift-off after depositing 220-nm aluminum film using an E-beam evaporator. See note S2 and fig. S2 for fabrication process flow.

Device measurement

The microwave transmission spectrum (S₂₁) shown in Figs. 2 and 3 is measured with a vector network analyzer (VNA; Keysight N5230C PNA-L) connected to a cryogenic probe station (Lakeshore CRX-4 K). Before the S₂₁ measurements, the VNA was calibrated at RT and to the tips of the microwave probes using a calibration substrate (GGB Inc., CS-15).

A detailed optical measurement scheme used in Figs. 3 and 4 is shown in fig. S5. The sample is measured in the cryogenic probe station using a fiber array with four ports. A tunable laser (Santec, TSL-570) is used as the laser source. The heterodyne measurement setup shown in Fig. 4 is used to resolve the anti-Stokes and the Stokes signal of the Brillouin scattering process. An AOFS (Brimrose model AMF-100-1550-2FP) is used to generate a reference signal with a frequency shift of 102.9 MHz. An erbium-doped fiber amplifier (PriTel LNHP-PMFA-23) is used to amplify the signal before a photodetector (Thorlabs, RXM25AF). The photodetector output is analyzed with a real-time spectrum analyzer (Tektronix, RSA5100B).

Supplementary Materials

This PDF file includes:

Suppplementary Notes S1 to S7

Figs. S1 to S8

Table S1

References