Electro-optic conversion of itinerant Fock states

TL;DR

This work addresses the bottleneck of connecting millikelvin superconducting qubits to long-range quantum networks by achieving on-demand generation and optical upconversion of itinerant microwave Fock states. It introduces a three-mode electro-optic transducer integrated with a superconducting qubit-cavity, enabling conversion of non-Gaussian microwave states to the telecom band with a low input-referred added noise of $N^{\text{up}}_{\text{add}}$ as low as $0.012$ quanta and an optical SNR up to $5.1\pm1.1$. The study demonstrates high-fidelity tomographic reconstruction of HP and SP microwave states, and shows a load-and-convert scheme that preserves qubit-state correlations in the optical domain, with potential for heralded entanglement distribution and gate teleportation. The results establish a viable path toward heterogeneous quantum networks, where superconducting processors can interface with photonic networks, and outline concrete routes to boost throughput and reduce noise toward quantum-limited performance in future devices.

Abstract

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.

Figures (11)

• Figure 1: Schematic view of the experimental setup.a, The blue shaded area shows a transmon qubit (teal) in a microwave cavity and the dispersively coupled system's energy level diagram. The cavity has a weakly coupled input port used to feed a two-photon drive to the transmon, and a stronger coupled output port used to collect the generated single photon (blue). A coaxial cable connects the cavity and the EO transducer (light blue disk). The optical pump (black arrow) couples out of an optical fiber and enters the transducer. The generated single infrared photon (red) propagates towards a series of filter cavities. Those are represented by two mirrors which prevent the reflected pump (black arrow) from reaching the single photon detector (grey). b, Sketch of the spectrum depicting the four electromagnetic modes involved in the upconversion process. The blue, grey, black, and red modes represent the microwave $\omega_e$, the hybridized Stokes $\hat{a}_s$, the pump $\hat{a}_p$ with frequency $\omega_p$ and the signal (anti-Stokes) mode $\hat{a}_o$, respectively.
• Figure 2: Microwave Fock state shapes and Wigner functions.a, Time-resolved MW measurements of $\abs{\ev{\hat{a}(t)}}^2$ for a prepared half photon state. b, Time-resolved MW measurements of $\ev{\hat{a}^{\dagger} \hat{a} (t)}$ for a prepared single photon state. The light blue (dark blue) curves in both panels are for the qubit-cavity resonant (off-resonant) with the EO MW cavity. The power axes in both panels are calibrated via the measured noise offset in units of quanta in panel b and multiplied with the RBW. The grey solid lines are theory of the photon generation process and the black solid lines also take into account the resonant interaction with the EO MW cavity. c (d), Wigner functions of the HP (SP) state calculated from the off-resonant experimental data. The fidelities for HP and SP states are 99.7% and 97.6%, respectively.
• Figure 3: Optical single photon shape and single photon Rabi measurements.a, Upconverted single MW photons measured in the optical domain. The red (black) curve represents detected photons vs. detection time when there's one (no) single MW photon being sent. The data are shown as absolute number of detected photons $N \pm \sqrt{N}$ within a 40 ns wide interval. The error bars represent one standard deviation. b, Single photon Rabi measurement in the optical (red) and c, the MW (blue) domain, show detected photons as a function of the qubit rotation angle prepared by linearly sweeping the qubit drive amplitude. The data points are integrated over 200 ns for the optical and 800 ns for the MW measurement. The error bars for the MW measurement are smaller than its markers. The error bars for the optical measurements are calculated by assuming a Poissonian distribution. We fit both data sets with a squared cosine, and show the 68% confidence intervals of the fits as the shaded areas (not visible in the MW case). The dashed lines describe the minima of the respective functions and the errorbars represent one standard deviation.
• Figure 4: EO transducer's signal, noise, and SNR vs optical trigger rate.a, SNR extracted from optical photon counting measurements presented in panel b. The time-resolved data for 1 kHz trigger rate are shown in Fig. \ref{['fig:RabiMeasurements']}a. Error bars represent one standard deviation. The red line and its confidence interval (shaded region) are calculated from fitted noise (blue circles in panel b) and mean single photon detection efficiency (orange dashed line in panel b). b, Measured signal and noise counts per 1 million applied optical pulses. We show the average dissipated power on the top axis. The grey dashed line represents the optical noise measured in the absence of signal photons. The orange line represents the average detection probability for 1 million repetitions. The grey and orange shaded areas represent one standard deviation. The blue dots show the MW mode occupancy inferred from MW noise spectroscopy (right axis). The solid blue line consists of two power-law fits to the MW occupation. The first $\propto P_\textrm{diss}^{1.06}$ fits up to $\approx0.6\mu\textrm{W}$ dissipated power, the second $\propto P_\textrm{diss}^{0.43}$ from there hease2020a. The error bars represent one standard deviation of the mean. For the microwave measurements (blue circles) they are smaller than the marker size.
• Figure 5: Schematic of the dilution refrigerator setup. The blue components depict cryogenic microwave equipment. Black (red) optical fibers guide the pump (signal) inside the fridge. The EO transducer is illustrated in black. The black dashed lines represent the boundaries between the blue-shaded temperature stages. All equipment, except for the fibers, is thermally anchored to the respective temperature stage. The four ports not shown on the 1-to-6 switch are connected to an unrelated sample. A SMA antenna connects the EO transducer's MW cavity to the MW setup. Band-pass (BP), low-pass (LP) and eccosorb filters reduce the noise power outside a certain range. The HEMT provides around 40 dB of gain. We write the attenuation (coupling) of the attenuators (directional couplers) next to their symbol.