Converting microwave and telecom photons with a silicon photonic nanomechanical interface

Large scale quantum networks promise secure communication and distributed quantum computation but require interfaces between low-loss telecom photons and local quantum processors that often operate at gigahertz frequencies. Superconducting circuits, solid-state spins, and quantum dots process quantum information in the microwave domain, where long-distance transmission is lossy and noise-prone, limiting practical cryogenic links to tens of meters. Optical photons at telecom wavelengths can be transmitted over ~100 km in fiber with low loss, motivating coherent microwave–optical transducers. Several physical platforms can mediate such conversion (mechanical, piezoelectric, electro-optic, magneto-optic, rare-earth, Rydberg), but existing solutions often face trade-offs between efficiency, scalability, and noise characterization. This work demonstrates a fully integrated, silicon photonic nanomechanical interface operating at millikelvin temperatures that coherently converts between 10.5 GHz and 198 THz using only picowatt pump powers, minimizing cryogenic heat load. The device is CMOS-compatible, compact, and compatible with silicon photonics and superconducting qubits. The design targets strong radiation pressure coupling to achieve high internal efficiencies and provides a comprehensive experimental and theoretical noise analysis to assess prospects for future noise-free conversion.

Optomechanical approaches have achieved the highest reported photon conversion efficiency up to 47% with added noise of 38 quanta using hand-assembled Fabry–Perot cavities and low-frequency membrane modes. Piezoelectric devices have demonstrated coherent uni- and bidirectional conversion at room temperature and cryogenic temperatures with integrated platforms but so far with low efficiency or unspecified noise. Electro-optic implementations have reached promising efficiencies (up to 2% at 2 K) but generally require milliwatt-level pump powers. Prior demonstrations include coherent wavelength conversion between optical modes and mechanical mediation between microwave modes in the quantum regime. These works highlight efficiency–noise–scalability trade-offs and motivate integrated, low-power, noise-characterized transducers.

Theory: The system comprises one microwave resonator and one optical cavity, each parametrically coupled to a common mechanical mode via vacuum coupling rates g_oj (j = e, o). Optical and microwave resonators have intrinsic loss rates κ_in,o and κ_in,e and external coupling rates κ_ex,o and κ_ex,e with coupling ratios η_j = κ_ex,j/(κ_in,j+κ_ex,j). The mechanical mode has frequency ω_m and intrinsic decoherence rate γ_m. In the interaction frame, the linearized Hamiltonian under red-detuned pumping is H_int = Σ_j G_j(a_j^† b + a_j b^†) + H_CR, where a_j (b) annihilate electromagnetic (mechanical) excitations; counter-rotating terms H_CR can be neglected in the resolved-sideband regime (4ω_m > κ_j), yielding a beam-splitter interaction. Cooperativity C_j = 4G_j^2/(κ_j γ_m). Near-unity conversion η ≈ 4η_e η_o C_e C_o/(1 + C_e + C_o) is possible for C_e, C_o ≫ 1. In the non-sideband-resolved optical cavity, counter-rotating terms induce gain, characterized by an optomechanical gain G_o related to the minimum phonon occupation from quantum backaction, while the microwave side is sideband-resolved (G_m ≈ 1), giving total gain G ≈ G_o. The total (possibly amplified) conversion ζ can be expressed via susceptibilities of the microwave and mechanical modes and decomposed into gain G and pure conversion θ.

Design and fabrication: The device integrates an optomechanical photonic crystal zipper cavity with two aluminum-coated, mechanically compliant silicon nanostrings. Mechanical coupling hybridizes in-plane vibrational modes into symmetric/antisymmetric supermodes; the antisymmetric mode (180° out-of-phase motion) is used. The photonic crystal cavity supports two telecom resonances with similar optomechanical coupling; the higher-frequency, lower-loss mode is used. The microwave resonator is a lumped-element design with a planar spiral inductor and two vacuum-gap (~70 nm) compliant capacitors, inductively coupled to a shorted coplanar waveguide for in/out-coupling. Fabrication uses electron-beam lithography, silicon etching, aluminum thin-film deposition, and HF vapor etching on a 220 nm silicon-on-insulator device layer.

Characterization: Measured parameters at millikelvin temperatures: optical resonance ω_o/2π = 198.081 THz with κ_o/2π = 1.6 GHz and κ_ex,o/2π = 0.18 GHz (η_o = 0.11); microwave resonance ω_e/2π = 10.5 GHz with η_e ≈ 0.4 and κ_ex,e/2π = 1.15 MHz (optical light off); mechanical mode ω_m/2π = 11.843 MHz with γ_m/2π = 15 Hz at 150 mK. Single-photon couplings: g_oe/2π = 67 Hz (electromechanical) and g_om/2π = 0.66 MHz (optomechanical).

Measurement setup and protocol: The chip is mounted on the mixing chamber of a dilution refrigerator at T_fridge ≈ 50 mK. Coherent red-detuned microwave and optical pumps with powers P_e and P_o establish linearized interactions. A weak signal tone is applied in either domain to measure bidirectional conversion. A microwave switch feeds signals to an ESA; optical heterodyne detection is used for low powers. A self-calibrated method independent of line gains/losses is used to extract scattering parameters, focusing on upper-sideband transduction at ω_o + ω_m. S-parameters: normalized reflection S_11 and bidirectional transmission ζ = |S_21||S_12| are measured versus signal detuning δ = ω − ω_m. Pump detunings are set to Δ_e = ω_m − ω_ae and Δ_o = ω_o − ω_ao. Exemplary operating point: P_o = 601 pW, P_e = 625 pW, Δ_e = ω_m, Δ_o/2π = 126 MHz, intracavity photon numbers n_de ≈ 9×10^5 and n_do ≈ 0.2, cooperativities C_e ≈ 0.57 and C_o ≈ 0.9. Bandwidth Γ_conv/(2π) ≈ 0.37 kHz (≈ (C_e+1)γ_m in current regime). The method separates amplified total conversion from pure conversion by mapping conversion versus optical detuning at fixed intracavity photon number and computing gain from theory.

Noise measurements: Output noise spectra are recorded at both ports to quantify added noise N_add,j referenced to the device output (effective input noise N_add,j/η_j). Fits use a single effective mechanical bath occupation as the parameter. Power dependence of mechanical bath temperature is extracted versus optical and microwave pump powers and compared to theory. Changes in coupling efficiencies (κ_ex/κ) and intrinsic losses with pump powers are quantified via broadband reflection.

• Demonstrated fully integrated, coherent microwave–optical transduction between 10.5 GHz and 198 THz at millikelvin temperatures using sub-nanowatt pump powers.
• Achieved total (waveguide-to-waveguide) bidirectional photon transduction efficiency up to ≈1.2%; at a representative setting obtained ≈1.1% total corresponding to ≈96.7% internal (resonator-to-resonator) efficiency; maximum reported internal efficiency ≤135% (amplified due to nonsideband-resolved gain). Conversion bandwidth Γ_conv/(2π) ≈ 0.37 kHz.
• Coupling efficiencies: optical η_o = 0.11; microwave η_e ≈ 0.4 (without optical pump) and η_m (microwave resonator to waveguide) ranging 0.07–0.18 with pumps on; both resonators are undercoupled.
• Single-photon coupling rates: g_oe/2π = 67 Hz; g_om/2π = 0.66 MHz. Mechanical mode: ω_m/2π = 11.843 MHz; γ_m/2π = 15 Hz at 150 mK.
• Pure, noiseless (in absence of thermal noise) conversion efficiency maximized near Δ_o ≈ κ_o/2: total pure efficiency θ ≈ 0.019% (internal θ/(η_e η_o) ≈ 1.6%).
• Nonsideband-resolved optical cavity induces amplification (gain G_o), increasing apparent conversion by ≈110× at chosen detuning; minimum quantum-backaction-limited phonon occupancy ≈ κ_o/(4ω_m) ≈ 30 at optimal detuning.
• Added noise at operating point: N_add,o ≈ 224 quanta at optical output; N_add,e ≈ 145 quanta at microwave output; effective input noise scales as N_add,j/η_j. Noise is dominated by thermal population of the mechanical mode; optical pump-induced absorption heating raises the mechanical bath temperature with increasing P_o; microwave pump heating is negligible.
• Voltage for π optical phase shift as low as V_π = 16 µV, nearly 9× lower than previous record and ~10^12× more power-efficient than commercial X-band EO modulators.
• Observed degradation of κ_ex/κ and increase in intrinsic losses (κ_in,e and γ_m) at higher optical pump powers due to heating, reducing cooperativities and total efficiency.

The work addresses the need for an efficient, scalable, and low-noise interface between microwave and telecom photons for quantum networks. By leveraging silicon photonics and cavity optomechanics integrated with superconducting-compatible materials (Si, Al), the device demonstrates coherent, bidirectional conversion with picowatt pump powers, thereby minimizing cryogenic heat load. The achieved total and internal efficiencies validate strong radiation-pressure coupling in a compact platform. However, the optical cavity’s nonsideband-resolved regime introduces quantum-limited amplification that inflates apparent efficiency and necessarily adds at least vacuum noise, while optical absorption heats the mechanical bath, which dominates the measured added noise. The comprehensive gain–conversion separation and noise analysis clarify that thermal mechanical occupation, not parametric amplification alone, limits noise performance. Despite narrow bandwidth, the device’s ultra-low V_π and compatibility with superconducting circuits indicate strong potential for both quantum transduction (with improved noise) and classical RF–optical interfacing.

An integrated silicon photonic nanomechanical interface has been demonstrated for coherent conversion between microwave X-band and telecom S-band photons at millikelvin temperatures with picowatt pump powers. The transducer attains up to ≈1.2% total (≤135% internal, including gain) efficiency, and a maximum pure internal efficiency of ≈1.6% (0.019% total) at optimal detuning, with conversion bandwidth of ≈0.37 kHz and V_π = 16 µV. Noise analysis shows that thermal occupation of the mechanically shared mode, driven primarily by optical absorption heating, dominates added noise, while nonsideband-resolved amplification contributes a smaller fraction. Future improvements include: enhanced waveguide–resonator coupling and fabrication optimization to boost pure efficiency by up to nearly two orders of magnitude; improved optical sideband resolution via higher mechanical frequencies to gain up to ~25×; operation at higher cooperativities; and mitigation of optical heating through better chip thermalization, reduced absorption, and low-duty-cycle pulsed operation. These steps could enable unity efficiency and near-noiseless conversion suitable for quantum networking, while the present device already offers compelling performance for classical RF–optical applications.

• Optical cavity is nonsideband-resolved (κ_o ≫ 4ω_m), leading to parametric amplification that precludes strictly noise-free operation and complicates interpretation of conversion without gain separation.
• Significant optical absorption heating increases the effective mechanical bath temperature, degrading γ_m and κ_ex/κ, reducing cooperativity and efficiency; heating constrains pump powers and bandwidth.
• Both optical and microwave resonators are undercoupled, limiting external (waveguide-to-waveguide) efficiency despite high internal conversion.
• Narrow conversion bandwidth (~0.37 kHz) due to low γ_m and modest cooperativities in current operating regime.
• Added noise is dominated by thermally excited mechanical mode; present configuration is not quantum-limited.