Noise in dead zones

We investigate the quantum noise gained by a weak probe laser interacting with a driven two-level system in the Doppler-broadening limit in which the so-called dead zone of the absorption spectrum is formed. We find that the plot of the noise as a function of the pump-probe detuning (which we shall refer to as the noise spectrum) is hardly affected by the Doppler broadening for the case of a resonant pump. It consists of a large central peak flanked by two smaller peaks at the edges of the dead zone, which are at the Rabi sideband frequencies. Thus the dead zone, which is produced when absorption and gain regions of the absorption spectrum are averaged by Doppler broadening, is a rather noisy region, indicating the occurrence of many competing absorption and emission processes. The probe noise spectrum for a detuned pump is quite different in the presence and absence of Doppler broadening as is the absorption spectrum. On Doppler broadening the absorption spectrum consists of a dead zone centered at the Rayleigh resonance frequency with asymmetric absorption peaks on either side. The noise spectrum has a peak at the center with two sidebands at the edges of the dead zone. The sidebands are of almost the same intensity for short path lengths, but the peak on the side of the three-photon scattering becomes larger than the other peak as the path length increases.