Dipolar phase transitions in the cavity with Majorana populated Josephson junctions

Abstract

We found that QED in the lowest eigenstate of the microwave-cavity, capacitively coupled with Majorana populated Josephson junctions array, is described with an effective $\phi^{4}$ model emerging in the finite domain of the system parameters. Strong anharmonicity of the cavity mode arises due to electric-dipole phase transition facilitated by the single-electron zero mode and Cooper pair tunneling between superconducting islands. An instantonic meandering of the electromagnetic field potential at finite temperatures is predicted.