Basic cell for a quantum microwave router

TL;DR

This work demonstrates a scalable basic cell for a quantum router in waveguide quantum electrodynamics, realized with a transmon qubit coherently coupled to two open microwave waveguides. The authors develop and validate a non-Hermitian Hamiltonian/ S-matrix framework to model four-port photon transmission, extract key parameters such as $Γ_A$, $Γ_B$, and $ω_{ge}$, and show robust operation at the single-photon level. Time-domain measurements corroborate steady-state results, confirming coherent qubit–waveguide dynamics and yielding $T_1$ on the order of tens of nanoseconds. The study also maps the device’s limits under flux bias, temperature, and photon number, and demonstrates photon dressing effects in the high-photon regime, establishing the basic cell as a versatile platform for open quantum system experiments and scalable quantum networking.

Abstract

We report the first experimental realization of a scalable basic cell for quantum routing, enabling coherent control and exchange of microwave photons between two spatially separated superconducting waveguides coupled via a single transmon qubit. The cell was characterized at 10 mK with an average input signal of approximately 1 photon at approximately 6 GHz, and with the qubit biased to its optimal point to minimize sensitivity to external magnetic fluctuations. By combining steady-state and time-domain measurements, we reconstructed the key parameters of the system, including qubit relaxation and dephasing, waveguide-qubit couplings, and cross-waveguide photon transfer efficiency. The observed performance is consistent with a non-Hermitian Hamiltonian formalism and demonstrates clear limits set by flux bias, temperature, and photon number, in agreement with flux- and temperature-induced dephasing models. Crucially, the cell operates reliably at the single-photon level, and in the high-photon regime we directly observe photon dressing induced by the qubit. These results establish a versatile platform for studying open quantum system phenomena and pave the way for scalable implementations of quantum routing and network nodes.

Figures (12)

• Figure 1: Conceptual sketch of the router basic cell.
• Figure 2: Sketch of the measurement setup.
• Figure 3: Measured transmission coefficients of the basic cell in comparison with the theory: a) measured transmission coefficients in a wide frequency bandwidth demonstrate the qubit response at the sweet spot. Black solid and dashed lines correspond to references curves (see details in the main text); b) transmission magnitude of the qubit response in a narrow frequency bandwidth ($t_{B B^{\prime}}^{\text{meas}}$, $t_{B A^{\prime}}^{\text{meas}}$) and comparison with the theoretical coefficients (Eq. \ref{["eq:tBB'"]}, Eq. \ref{["eq:tBA'"]}); c) transmission magnitude of the qubit response in a narrow frequency bandwidth ($t_{A A^{\prime}}^{\text{meas}}$, $t_{A B^{\prime}}^{\text{meas}}$) and comparison with the theoretical coefficients (Eq. \ref{["eq:tAA'"]}, Eq. \ref{["eq:tAB'"]}).
• Figure 4: Equivalent multiport network circuit for the basic cell with input and output lines. Here, $a_i$ are the incoming waves to the $i$-th network, and $b_i$ are the outgoing waves. $S_{A/B}$ denotes the S-matrix of the input lines, $G_{A/B}$ that of the output lines, and $S$ is the S-matrix of the basic cell.
• Figure 5: Calibrated transmission coefficients with fits. $\Gamma_A=2\pi \cdot 1.82~\text{MHz},\Gamma_B=2\pi \cdot 2.31~\text{MHz},\omega_{ge}=2\pi \cdot 6.163~\text{GHz},\varphi_A=-0.06\pi,\varphi_B=0.05\pi$.