Josephson radiation patterns in underdamped topological Josephson junctions

Josephson radiation is a useful signature for detecting Majorana zero modes\nin topological superconductors. We study the Josephson radiation of the\nunderdamped topological Josephson junction within the quantum resistively and\ncapacitively shunted junction model. We show that the quantum dynamics of the\nMajorana two-level system induce oscillatory patterns in the Josephson emission\nspectra. With the Floquet method, we obtain analytical results for these\noscillatory patterns and find that they are well described by Bessel functions.\nWe perform numerical simulations to verify the analytical results and\ndemonstrate that these Bessel radiation patterns exist for a wide range of\njunction parameters.\n