A frequency-agile microwave-optical interface for superconducting qubits

1. Problem Statement

Superconducting quantum processors operate at microwave frequencies (4–8 GHz) in millikelvin environments. Interconnecting distant nodes for quantum networks using conventional microwave wiring is impractical due to thermal load, crosstalk, and physical constraints. Microwave-to-Optical (M2O) transduction offers a solution by converting microwave photons to optical photons for transmission via low-loss fiber.

However, a critical bottleneck exists:

• Bandwidth Mismatch: State-of-the-art M2O transducers typically operate efficiently only over a narrow frequency span (often $\sim$10–100 MHz) determined by their resonant mode linewidths.
• Heterogeneity: Superconducting qubits and their readout resonators are often fabricated with specific frequencies that can differ by gigahertz-scale offsets from the fixed resonance of an M2O transducer.
• Rigidity: Existing solutions (e.g., Josephson Parametric Converters or fixed-frequency transducers) lack the flexibility to bridge these large frequency gaps without requiring specialized, custom-tuned superconducting circuits for every specific transducer.

2. Methodology

The authors propose and demonstrate a cascaded, frequency-agile architecture that combines two distinct conversion stages to overcome the bandwidth limitation:

1. Stage 1: Multimode Microwave-to-Microwave (M2M) Frequency Converter

   • Device: An NbN (Niobium Nitride) kinetic-inductance multimode ring resonator fabricated on a silicon substrate.
   • Mechanism: It supports a dense set of resonant modes with a Free Spectral Range (FSR) of 76 MHz.
   • Tunability: The resonator features asymmetric loop sections that allow flux tuning via an external magnetic field. This enables the selection of specific signal-idler mode pairs to bridge large frequency gaps.
   • Function: It translates an input microwave signal from a target qubit frequency (e.g., 7.3 GHz) to a specific "idler" frequency that matches the operating band of the M2O stage.

2. Stage 2: Electro-Optic Microwave-to-Optical (M2O) Transducer

   • Device: A hybrid device integrating an AlN (Aluminum Nitride) double-ring optical resonator with an NbN microwave resonator on a sapphire substrate.
   • Mechanism: Utilizes the electro-optic effect (Pockels effect) to convert microwave photons to optical sidebands.
   • Tunability: The microwave resonance of this stage is also flux-tunable, providing an additional 90 MHz of in-situ tuning range to align with the M2M idler.

3. System Integration

   • The M2M stage is mounted on a higher-temperature stage (cold plate) to minimize heat load on the mixing chamber, while the M2O stage remains at the mixing chamber (50 mK).
   • Protocol:
     1. Flux-tune the M2M signal mode to resonate with the fixed-frequency qubit readout tone.
     2. Flux-tune the M2M idler mode to align with the M2O microwave resonance.
     3. Apply an M2M pump to coherently convert the signal to the idler.
     4. Apply an optical pump to the M2O stage to convert the idler to the optical domain.

3. Key Contributions

• Frequency Agility: The system achieves continuous frequency coverage from 5.0 to 8.5 GHz within a single reconfigurable system, bridging a 3.5 GHz span.
• Deterministic Frequency Matching: The authors demonstrate a protocol to deterministically align a fixed-frequency qubit (detuned by 1.7 GHz from the native M2O resonance) to the optical interface without retuning the qubit itself.
• Scalable Architecture: By placing the M2M converter on a higher temperature stage, the system reduces the thermal load and wiring complexity at the mixing chamber, addressing a key scalability challenge for optical readout.
• Dual-Mode Operation (Conversion + Amplification): The M2M stage was operated in a combined conversion and parametric amplification mode, providing 30 dB of gain to compensate for the relatively low efficiency of the M2O stage.

4. Key Results

• Conversion Efficiency:
  • The standalone M2O stage demonstrated a bidirectional conversion efficiency of $\sim 10^{-3}$ (0.1%) with a tuning range of 90 MHz.
  • The cascaded M2M–M2O system achieved high translation efficiency ($\eta_{MM} > 50\%$) across the 5.0–8.5 GHz range.
• Qubit Readout Demonstration:
  • The system successfully optically read out a superconducting qubit with a readout resonator at 7.339 GHz, which was 1.7 GHz detuned from the M2O device's native resonance (5.669 GHz).
  • Coherence Metrics: The optical readout reproduced standard qubit characterization results with high fidelity:
    • Rabi Oscillations: Matched microwave readout dynamics.
    • $T_1$ (Relaxation): $T_1^{opt} = 28.7 \pm 3.1$ $\mu$s vs. $T_1^{mw} = 30.9 \pm 0.3$ $\mu$s.
    • $T_2$ (Dephasing): $T_2^{opt} = 2.6 \pm 0.3$ $\mu$s vs. $T_2^{mw} = 3.1 \pm 0.1$ $\mu$s.
  • The slight degradation in $T_2$ was attributed to thermal noise from the elevated operating temperature of the mixing chamber, not the transduction process itself.
• Noise Performance:
  • The M2M stage added noise was estimated to be $< 1.3$ quanta.
  • The M2O microwave mode occupancy was calibrated at $3.1 \pm 0.2$ quanta.

5. Significance and Outlook

• Enabling Quantum Networks: This work solves the "frequency mismatch" problem, allowing heterogeneous superconducting qubits (which naturally vary in frequency) to be connected via optical fibers without requiring custom fabrication of the transducer for every specific qubit.
• Scalability: The architecture supports frequency multiplexing. Multiple qubits can be read out simultaneously by assigning each to a different M2M signal mode within the resonator's FSR, bridging them to a single M2O transducer.
• Bidirectional Control: The system is inherently bidirectional. It can function as an Optical-to-Microwave (O2M) link for qubit control, where optical signals are converted to microwaves and then frequency-translated by the M2M stage to control specific qubits.
• Future Impact: This frequency-agile interface provides a unified route toward scalable, fiber-linked superconducting quantum processors, essential for distributed quantum computing and the quantum internet.