Limits to atom-vapor-based room-temperature photon-number-resolving detection

We study the atom-vapor-based photon-number-resolving detection from first principles, including quantum-mechanical treatment of the electromagnetic field. We study a photon detector model that combines coherently controlled absorption of light and resonance fluorescence to achieve photon counting at room temperature. In particular we identify the fundamental limits to this particular scheme of photon detection. We show that there exists a time-energy uncertainty between the incident pulse strength and the time period of the incident pulse. We verify the role of a large ensemble of atoms to boost the efficiency of such a detector