Violation of detailed balance in microwave circuits: theory and experiment

TL;DR

This paper introduces a new theoretical framework using scattering matrix formalism to analyze detailed balance violations in microwave circuits, validated through experiments in the 4-8 GHz range, with implications for quantum circuit analysis at ultra-low temperatures.

Contribution

It presents a novel approach incorporating retardation effects into detailed balance analysis in microwave circuits, validated by experimental measurements.

Findings

Spectral densities serve as criteria for detailed balance violation

Experimental validation on various two-port circuits

Framework applicable to quantum circuits at ultra-low temperatures

Abstract

We propose a new approach to detailed balance violation in electrical circuits by relying on the scattering matrix formalism commonly used in microwave electronics. This allows to include retardation effects which are paramount at high frequencies. We define the spectral densities of phase space angular momentum, heat transfer and cross power, which can serve as criteria for detailed balance violation. We confirm our theory with measurements in the 4-8 GHz frequency range on several two port circuits of varying symmetries, in space and time. This validates our approach, which will allow to treat quantum circuits at ultra-low temperature.