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.
Highlights
INTERACTIONS IN QUANTUM CIRCUITSAt small scales and low temperatures, electronic components become quantum: Their state is not described by classical currents and voltages anymore but by operators that have quantum fluctuations
We work out how the fluctuation-mediated interaction occurs in a somewhat general dissipative circuit consisting of a short coherent component (SCC) that can be described in the LB formalism and an arbitrary external circuit with substantial quantum fluctuations
We show and discuss how quantum fluctuations qualitatively modify the current noise and the admittance of the SCC predicted in the LB formalism
Summary
At small scales and low temperatures, electronic components become quantum: Their state is not described by classical currents and voltages anymore but by operators that have quantum fluctuations. When considering several of these components interconnected at a scale larger than the electronic coherence length (so that electronic interferences between components vanish), one recovers the familiar lumped-element description of the whole circuit, just like taught in high school for classical electrical circuits [Fig. 1(a)] In such a circuit, the Kirchhoff laws apply to the operator-valued currents and voltages, including their quantum fluctuations, at all frequencies for which the lumped description applies. The junction becomes nonlinear in the presence of voltage fluctuations, with its conductance at low voltages that can be strongly reduced This phenomenon is known as the dynamical Coulomb blockade (DCB) and is quantitatively explained by the PðEÞ theory [4,5,6]. There are no theories readily applicable for nonohmic environments such as high impedance resonant structures that were recently used in experiments probing the radiative signatures of DCB [20,21,22]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
