Interacting electrodynamics of short coherent conductors in quantum circuits

TL;DR

This paper extends the Landauer-Büttiker formalism to include quantum voltage fluctuations in short coherent conductors, revealing their impact on conductance and internal states, and enabling improved quantum circuit design.

Contribution

It introduces a method to incorporate quantum voltage fluctuations into the Landauer-Büttiker formalism for short coherent conductors, advancing understanding of non-linear electrodynamics in quantum circuits.

Findings

Quantum voltage fluctuations reduce conductance via dynamical Coulomb blockade.

Fluctuations modify the internal density of states and transmission.

Quantitative agreement with conductance measurements on quantum point contacts.

Abstract

When combining lumped mesoscopic electronic components to form a circuit, quantum fluctuations of electrical quantities lead to a non-linear electromagnetic interaction between the components that is not generally understood. The Landauer-B\"uttiker formalism that is frequently used to describe non-interacting coherent mesoscopic components is not directly suited to describe such circuits since it assumes perfect voltage bias, i.e. the absence of fluctuations. Here, we show that for short coherent conductors of arbitrary transmission, the Landauer-B\"uttiker formalism can be extended to take into account quantum voltage fluctuations similarly to what is done for tunnel junctions. The electrodynamics of the whole circuit is then formally worked out disregarding the non-Gaussianity of fluctuations. This reveals how the aforementioned non-linear interaction operates in short coherent conductors: voltage fluctuations induce a reduction of conductance through the phenomenon of dynamical Coulomb blockade but they also modify their internal density of states leading to an additional electrostatic modification of the transmission. Using this approach we can account quantitatively for conductance measurements performed on Quantum Point Contacts in series with impedances of the order of $R_K = h / e^2$. Our work should enable a better engineering of quantum circuits with targeted properties.