Microwave radiometry of a quantum-critical, hybrid Josephson array

Arrays of Josephson junctions can be tuned through anomalous metallic, quantum-critical, and insulating regimes. We introduce a new experimental probe, capturing microwave radiation across all three regimes, using a two-dimensional array of superconductor-semiconductor hybrid Josephson junctions as a model system. Our approach allows in-situ calibration of the sample’s circuit parameters and provides isolation from measurement back-action effects. We measure the radiation temperature of the anomalous metal, and find that it is hotter than both the quantum-critical and insulating regimes. We further show that the anomalous-metallic regime is more susceptible to additional heating than other regimes, explaining its emergence in otherwise thermalized systems. Turning to the quantum-critical regime, we discover nonlinear scaling of radiative noise with applied bias, consistent with theoretical predictions of universal non-equilibrium behavior at quantum critical points.

💡 Research Summary

In this work the authors introduce a microwave radiometry technique to probe the thermal and non‑equilibrium properties of a two‑dimensional array of superconductor‑semiconductor hybrid Josephson junctions. By applying a top‑gate voltage they continuously tune the array across the superconductor‑insulator transition (SIT), accessing three distinct regimes: a conventional superconducting state, an anomalous metallic (AM) phase with saturated low‑temperature resistance, and an insulating phase. The key experimental advance is the integration of a cryogenic circulator, a quantum‑limited low‑noise amplifier, and on‑chip capacitive coupling that allow the sample’s emitted microwave power in the 1.4 GHz band to be measured without back‑action. Simultaneously, the reflection coefficient S₁₁ is recorded, providing a real‑time calibration of the impedance match and the loss factor α of the measurement chain.

At high cryostat temperatures the detected power follows the equilibrium relation P = k_B T_cryo, confirming that the setup correctly measures thermal radiation. As the temperature is lowered, the power saturates to a gate‑dependent value P_sat, indicating that the sample is no longer in thermal equilibrium with the bath. By fitting the data to the phenomenological model P² = (k_B T_cryo)² + P_sat², the authors extract the saturation power for each gate voltage. The largest P_sat occurs when the array is tuned near the critical sheet resistance (~60 kΩ), i.e., at the center of the AM regime.

To translate the measured microwave power into an effective sample temperature T_s, the authors develop a linear relation:

 P/k_B = −α |S₁₁|² (T_s − T_cryo) + T_s,

where α accounts for losses in the input lines and the measurement chain. By deliberately heating the sample with a far‑detuned 547 MHz tone of varying power, they demonstrate that P and |S₁₁|² remain linearly related, and the slope and intercept scale with the drive power. From these fits they obtain α ≈ 64 dB and an effective cryostat temperature T_cryo ≈ 50 mK, consistent with independent calibrations. Applying the calibrated model to the undriven AM data yields T_s ≈ 150 mK, far above the base temperature of the dilution refrigerator. This elevated temperature coincides with the onset of resistance saturation, supporting the interpretation that the anomalous metallic state is a manifestation of the system falling out of equilibrium.

Having established a reliable thermometry, the authors turn to the quantum‑critical regime. By applying a small DC bias current I while the array is tuned to the critical point, they measure the excess microwave noise temperature T_noise. Remarkably, T_noise scales as √I over more than an order of magnitude in current, exactly as predicted by theories of universal non‑equilibrium dynamics at quantum critical points (based on critical field theory and gauge‑gravity duality). The √I scaling is observed for multiple gate voltages, indicating a broad regime of universal behavior around the SIT.

Additional observations include a strong negative correlation between excess noise and the reflection coefficient: the noise is maximal when the sample is impedance‑matched (|S₁₁| ≈ 0), confirming that the measured power truly originates from the sample rather than from the 50 Ω termination of the circulator. A sharp isolated noise spike at a specific gate voltage is attributed to a collective plasma mode of the Josephson array.

Overall, the paper delivers three major contributions: (1) a non‑invasive, in‑situ calibrated microwave radiometry method suitable for delicate quantum‑critical systems; (2) direct experimental evidence that the anomalous metallic phase is a non‑equilibrium, overheated state, explaining its sensitivity to additional heating; and (3) the first experimental verification of the universal √I scaling of non‑equilibrium noise at a superconductor‑insulator quantum critical point. The methodology opens a pathway for precise thermal diagnostics in a wide class of low‑dimensional superconducting networks, strange metals, and other strongly correlated quantum materials where conventional thermometry fails.