Exact Duality at Low Energy in a Josephson Tunnel Junction Coupled to a Transmission Line

Luca Giacomelli; Michel H. Devoret; Cristiano Ciuti

doi:10.1103/1k3s-m3b9

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Exact Duality at Low Energy in a Josephson Tunnel Junction Coupled to a Transmission Line

Luca Giacomelli, Michel H. Devoret, Cristiano Ciuti

DOI 10.1103/1k3s-m3b9 · Physical Review Letters

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Abstract

We theoretically explore the low-energy behavior of a Josephson tunnel junction coupled to a finite-length, charge-biased transmission line and compare it to its flux-biased counterpart. For transmission lines of increasing length, we show that the low-energy charge-dependent energy bands of the charge-biased configuration can be exactly mapped onto those of the flux-biased system via a well-defined duality transformation of circuit parameters. In the limit of an infinitely long transmission line, the influence of boundary conditions vanishes, and both circuits reduce to a resistively shunted Josephson junction. This convergence reveals the system’s intrinsic self-duality and critical behavior. Our exact formulation of charge-flux duality provides a foundation for generalizations to more complex superconductor-insulator phase transitions.