High-resolution microwave frequency identification via bias-tuned superconducting transmission lines

We develop a microwave frequency counter based on the complex conductivity modulation of a DC-biased superconducting transmission line while maintaining the bias below the critical current. A resonator-free platform is proposed for microwave frequency estimation. It utilizes a bias-controlled phase delay in a superconducting coplanar waveguide structure, which imprints frequency-dependent signatures on the transmitted microwave tone. Instead of relying on intentionally designed resonators, our method leverages the complex transmission spectra arising from numerous weak resonance structures due to subtle fabrication imperfections. However, even in the absence of such features, the method remains effective because the DC bias induces frequency-dependent phase shifts that modulate the microwave signal’s propagation velocity. Mixed signals are externally generated via in-phase-quadrature mixing with a reference signal, which manifests as interference-like patterns enabling high-resolution spectral identification. We measure the frequency-dependent changes in the interference-like patterns under this bias to catalog characteristic transmission loss profiles across a wide frequency range (2–8 GHz). These profiles serve as supervised training data for a machine learning algorithm that identifies unknown input microwave frequencies with high-resolution and accuracy. Our method achieves a frequency resolution (F/ΔF) of over 200 000 and a relative error in identification of below 0.01%. This scalable approach to distributed microwave sensing may be useful for quantum measurement and signal classification and is particularly well-suited for dark matter searches, such as hidden-photon detection, where broadband frequency identification without prior tuning is essential. The measured frequency range is primarily limited by the bandwidth of external microwave components, such as low-noise amplifiers and bias-tees. The superconducting device itself may be used up to its superconducting gap frequency (∼280 GHz for TiN at 3.8 K).