An RF Photon-Number-Resolving Detector Using Majorana Zero Mode*

RF photon-number-resolving detectors play an essential role in transmon quantum computers. Generally, thermal photon detectors absorb individual photons and then transfer the excess energy to lattice oscillations, yielding a temperature gain. In designing a detector, it is important to satisfy 3 criteria: establishing non-invasive bolometer capability such that absorbed photoelectrons are not washed out by the measurement process; ensuring that the temperature gain per photon is sufficiently large to be measurable; and guaranteeing that the electron-phonon heat transfer is much faster than parasitic electron losses. Here, we propose a system consisting of a p-wave superconducting nanowire side-coupled to a quantum dot (QD). The Majorana zero mode (MZM) at the edge facing the QD couples with the QD’s electronic mode. This interaction breaks the energy degeneracy, yielding composite QD-Majorana states separated by a finite energy gap, which we tune to be resonant with the incoming photon field. By analyzing the phase space, we derive the electron-phonon energy transfer rate, showing that it vastly exceeds the radiative decay rate. We also calculate the absorption rate, thus yielding the required detector density for deterministic photon number measurement.