Cold-Electron Bolometer as a 1-cm-Wavelength Photon Counter

We investigate theoretically the possibility of using the cold-electron bolometer (CEB) as a counter for 1-cm-wavelength (30-GHz) photons. To reduce the flux of photons from the environment that interact with the detector, the bath temperature is assumed to be below 50 mK. At such temperatures, the time interval between two subsequent photons of 30 GHz that hit the detector is more than 100 h, on average, for a frequency window of 1 MHz. Such temperatures allow the observation of the physically significant photons produced in rare events, such as axion conversion (or Primakoff conversion) in a magnetic field. We present the general formalism for the detector's response and noise, together with numerical calculations for proper experimental setups. We observe that the current-biased regime is favorable due to lower noise and allows for photon counting at least below 50 mK. For the experimental setups investigated here, the voltage-biased CEBs may also work as photon counters but with less accuracy and, eventually, may require smaller volumes of the normal-metal island.