Josephson radiation patterns in underdamped topological Josephson junctions

Abstract

Majorana zero mode is a unique quasiparticle state on the edge of topological superconductors. For Josephson junctions with Majorana zero modes, there will be 4π-periodic current components in the current-phase relation. Within the quantum resistively and capacitively shunted junction model, we study the dynamics of the Josephson phase which is correlated with the Majorana twolevel system through the 4π-periodic Josephson effect, and show that the feedback of the quantum oscillation of the Majorana two-level system induces a oscillatory pattern in the Josephson radiation spectra. We numerically studies this radiation spectra and find that the unique oscillatory patterns universally exists in the underdamped junction regime. We solve the model analytically for typical junction parameters and find solutions of the Bessel function form which explains the main features of the oscillation patterns in the Josephson radiation.