Dipolar phase transitions in the cavity with Majorana populated   Josephson junctions
  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. 
S. I. Mukhin, N.V. Gnezdilov, Seid ali Seidov
cond-mat.str-el cond-mat.mes-hall