Electro-optic conversion of itinerant Fock states

Superconducting qubits are a leading candidate for utility-scale quantum computing due to their fast gate speeds and steadily decreasing error rates. The requirement for millikelvin operating temperatures, however, creates a significant scaling bottleneck. Modular architectures using optical fiber links could bridge separate cryogenic nodes, but superconducting circuits do not have coherent optical transitions and microwave-to-optical conversion has not been shown for any non-classical photon state. In this work, we demonstrate the on-demand generation and tomographic reconstruction of itinerant single microwave photons at 8.9 GHz from a superconducting qubit. We upconvert this non-Gaussian state with a transducer added noise below 0.012 quanta and count the converted telecom photons at 193.4 THz with a signal-to-noise ratio of up to 5.1$\pm$1.1. We characterize the trade-offs between throughput and noise, and establish a viable path toward heralded entanglement distribution and gate teleportation. Looking ahead, these results empower existing superconducting devices to take a key role in distributed quantum technologies and heterogeneous quantum systems.

💡 Research Summary

The authors present the first demonstration of on‑demand generation, up‑conversion, and detection of a non‑Gaussian microwave quantum state—specifically, itinerant single‑photon Fock states—using a superconducting transmon qubit and an electro‑optic (EO) transducer. A transmon embedded in a three‑dimensional aluminum cavity is prepared in the excited state via a blue‑sideband (BSB) pulse that swaps the qubit excitation into a single photon in the cavity mode at 8.9 GHz. The photon leaks out through a strongly coupled output port, travels via a coaxial line, and enters a cryogenic EO transducer.

The EO device consists of a thin‑film‑electroded lithium‑niobate (LiNbO₃) whispering‑gallery mode resonator coupled to a microwave cavity. A strong optical pump (1.22 mW, 200 ns) at 1550 nm drives the Pockels effect, creating a beam‑splitter interaction between the microwave mode and an anti‑Stokes optical mode. The interaction Hamiltonian reduces to H≈ℏ√nₚ g₀(aₑaₒ†+aₑ†aₒ) with a vacuum coupling rate g₀/2π≈4.2 Hz. Operating in the low‑cooperativity regime (C≈4.1×10⁻⁴) yields an internal conversion efficiency η_int≈1.6×10⁻³ and an overall (including input‑output coupling) efficiency η_ext≈2.2×10⁻⁴. Crucially, the added input‑referred noise is ≤0.012 quanta, essentially at the quantum limit.

After conversion, the up‑converted telecom photon (193.4 THz) co‑propagates with the residual pump. A cascade of four Fabry‑Perot filter cavities (55 MHz bandwidth, 43.7 % transmission) provides >170 dB pump suppression while passing the signal. The filtered photons are detected with a superconducting nanowire single‑photon detector (SNSPD) of ≈85 % efficiency. The measured signal‑to‑noise ratio (SNR) reaches 5.1 ± 1.1, confirming that the non‑classical microwave state survives the conversion with sufficient fidelity for practical use.

Microwave‑domain quantum state tomography is performed using heterodyne detection amplified by a Josephson parametric amplifier. By preparing half‑photon (|0⟩+|1⟩)/√2 and pure single‑photon states, the authors reconstruct Wigner functions showing clear negativity. The half‑photon state exhibits |⟨a⟩|=0.51, ⟨a†a⟩=0.49 and 99.7 % fidelity; the single‑photon state shows ⟨a†a⟩=0.95 and 97.6 % fidelity. These results demonstrate that the EO transducer does not appreciably degrade the quantum state.

A “load‑and‑convert” protocol is employed: the itinerant microwave photon first populates the EO microwave mode; only when the occupation is high is the optical pump switched on, ensuring that conversion occurs only when the signal dominates over the residual thermal population of the microwave mode. Because the transducer bandwidth (1.3 MHz) matches the source linewidth (1.4 MHz), the conversion is efficient despite the low cooperativity. Numerical simulations based on QuTiP match the measured temporal profiles, confirming a thorough understanding of the dynamics.

The paper quantifies the trade‑off between conversion efficiency and added noise. Increasing pump power raises cooperativity and efficiency but also amplifies thermal and Brillouin scattering noise. The current operating point balances a modest external efficiency with quantum‑limited noise, suitable for heralded entanglement distribution and gate teleportation across distant cryogenic nodes.

In summary, this work establishes a viable quantum‑coherent microwave‑to‑optical interface: (1) deterministic generation of microwave Fock states from a superconducting qubit, (2) low‑noise electro‑optic up‑conversion preserving non‑Gaussian features, (3) high‑SNR single‑photon detection at telecom wavelengths, and (4) comprehensive modeling and experimental validation. These achievements pave the way for modular, distributed quantum computing architectures that integrate superconducting processors with existing fiber‑optic networks.