  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.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics