We discuss a mean-field quantum-mechanical model which describes the dynamics of a homogeneously broadened system of two-level atoms contained in a pencil-shaped resonant cavity and driven by a coherent resonant field
EI. The model is treated in the semiclassical approximation. The model is justified on the basis of Maxwell-Bloch equations with two coherently coupled directions of propagation, with boundary conditions for the fields taken into account. Above a suitable critical density of atoms the system exhibits a bistable behavior including both the stationary situation and the transient, both the light transmitted in the forward direction and the fluorescent light. Bistability is shown to be a consequence of atomic cooperation. We give a simple description of optical bistability leading to new predictions for the transient behavior of the transmitted light and for the spectrum of the fluorescent light. The damping constant which characterizes the rate of appraoch to the stationary situation exhibits a hysteresis cycle. In the low-transmission regime the approach is monotonic, whereas in the highly transmitting situation the approach is oscillatory. One finds a critical slowing down in correspondence with the values
EI(+), ${{E}_{I}}^{(\ensuremath{-})}$ of the incident field where the transmitted field (as well as the total fluorescence intensity, the rate of approach to the stationary state, etc.) changes discontinuously. On the basis of the regression hypothesis we give a qualitative description of the spectrum of the fluorescent light. This is shown to undergo hysteresis and discontinuous changes at the same values
EI(+), ${E}_{I}^{(\ensuremath{-})}$ of the incident field. Below the critical density of atoms one recovers the usual picture of resonance fluorescence, with a continuous transition from a single-line spectrum to a three-peaked structure when the Rabi frequency becomes equal to the natural linewidth. Above the critical density the triplet appears only when the Rabi frequency becomes equal to the cooperative linewidth of pure super-fluorescence (i.e., for
EI=EI(+)). Moreover, it appears discontinuously: when
EI crosses the value
EI(+) the spectrum changes from a single narrow line to a triplet with well-separated sidebands.
Analytic results for the absorption spectrum in cooperative resonance fluorescence are presented. An initial broad-band absorption spectrum on the cooperative branch develops a sharp spike as the instability point is approached. The usual one-atom absorption spectrum is regained on the non-cooperative branch. The photon statistics of the scattered light are studied through a calculation of the second-order correlation function g (2) (0). On the cooperative branch the value of g (2) (0) is unity reflecting the coherent scattering from the cooperative atomic state. On the non-cooperative branch the value of g (2) (0) jumps to two, reflecting the incoherent scattering from independently scattering atoms.
We consider N two level atoms driven far from equilibrium by a coherent driving field. The atoms may decay by a cooperative (J2 preserving) mechanism or a non-cooperative (J2 non-conserving) mechanism where J is the atomic pseudo angular momentum. We adopt a mean field theory to study the J2 non-conserving interaction. This indicates that the system displays a first order phase transition in several observables, e.g., mean field, spectrum and photon statistics. The two stable branches of the hysteresis curve are shown to be regions of cooperative and non-cooperative behaviour respectively. In the case of cooperative atomic decays we find a solution to the Fokker-Planck equation in the atomic coherent state representation. This predicts a second order phase transition in atomic observables—a cooperative fluorescent critical point.
We describe the resonance fluorescence spectrum of an atomic three-level system where two of the states are coupled by a single monochromatic laser field. The influence of the third energy level, which interacts with the two laser-coupled states only via radiative decays, is studied in detail. For a suitable choice of parameters, this system gives rise to a very narrow structure at the laser frequency in the fluorescence spectrum which is not present in the spectrum of a two-level atom. We find those parameter ranges by a numerical analysis and use the results to derive analytical expressions for the additional narrow peak. We also derive an exact expression for the peak intensity under the assumption that a random telegraph model is applicable to the system. This model and a simple spring model are then used to describe the physical origins of the additional peak. Using these results, we explain the connection between our system, a three-level system in the V configuration where both transitions are laser driven, and a related experiment that was recently reported.
The fluorescence spectrum of a system of a large number of two-level atoms driven by a strong resonant field has been treated, so far, for atoms contained in a region that is small compared to a wavelength. For high laser intensities resonances displaced from the line center by twice the Rabi frequency were predicted1-3 in addition to the usual Stark sidebands.4 We show that the explicit spatial distribution of the two-level atoms affects the shape of the radiation spectra and leads to the appearance of additional sidebands.
A theoretical analysis is developed for the spectrum of the light scattered by two two-level atoms driven near resonance by an external coherent electromagnetic field. The atoms are assumed to relax to equilibrium with the driving field as a result of radiation damping. The explicit dependence of the coherent dipole-dipole interactions on the distance between the two atoms is taken into account. For the case of two two-level atoms with a fixed distance smaller than a wavelength, an analytical result for the resonance fluorescence line shape is obtained, and the result is compared to previous work.>