Simulation of supersymmetric quantum mechanics in a Cooper-pair box shunted by a Josephson rhombus

Abstract

Supersymmetries in quantum mechanics offer a way to obtain degeneracies in the excitation spectrum which do not originate from selection rules. The mechanism behind the degeneracies is the same as the one that leads to the miraculous cancellations of divergences in supersymmetric field theories found in the high energy physics context. There is up to now no realistic proposal of nonintegrable systems that show level degeneracies due to a supersymmetric structure. Here, we propose an implementation of a quantum-mechanical supersymmetry in a Cooper-pair box shunted by a Josephson junction rhombus which is effectively π periodic in the superconducting phase difference. For a characteristic ratio between the strength of the 2π- and the π-periodic junction, we find a twofold degeneracy of all the energy levels all the way from the weak junction/charge qubit limit to the strong junction/transmon regime. We provide explicit experimental values for the parameters of the system and show that tuning in and out of the supersymmetric point is easily achieved by varying an external gate voltage. We furthermore discuss a microwave experiment to detect the supersymmetry and conclude that it can indeed be implemented with currently existing Josephson junction technology.

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