Interacting Electrodynamics of Short Coherent Conductors in Quantum Circuits

When combining lumped mesoscopic electronic components to form a circuit, quantum fluctuations of electrical quantities lead to a nonlinear electromagnetic interaction between the components, which is generally not understood. The Landauer-Büttiker formalism that is frequently used to describe noninteracting 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-Büttiker 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 nonlinear 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 quantitatively account 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