Josephson effect in topological superconducting rings coupled to a microwave cavity

Abstract

We theoretically study a one dimensional p-wave superconducting mesoscopic ring interrupted by a weak link and coupled inductively to a microwave cavity. We establish an input-output description for the cavity field in the presence of the ring, and identify the electronic contributions to the cavity response and their dependence on various parameters, such as the magnetic flux, chemical potential, and cavity frequency. We show that the cavity response is $4\pi$ periodic as a function of the magnetic flux in the topological region, stemming from the so called fractional Josephson current carried by the Majorana fermions, while it is $2\pi$ periodic in the non-topological phase, consistent with the normal Josephson effect. We find a strong dependence of the signal on the cavity frequency, as well as on the parity of the ground state. Our model takes into account fully the interplay between the low-energy Majorana modes and the gaped bulks states, which we show is crucial for visualizing the evolution of the Josephson effect during the transition from the topological to the trivial phase.

7 pages, 4 figures, extra references added

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• Microwave detection of gliding Majorana zero modes in nanowires
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• Detection of Majorana zero modes bound to Josephson vortices in planar superconductor-topological insulator-superconductor junctions
• Physical implementations of quantum absorption refrigerators
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• Phase-dependent supercurrent and microwave dissipation of HgTe quantum well Josephson junctions
• Distinguishing Majorana bound states from accidental zero-energy modes with a microwave cavity
• Detection of persistent current correlation in cavity-QED