We have calculated the spectrum of resonance fluorescence and the second-order correlation function for a system of two two-level atoms interacting via the dipole-dipole interaction and via radiative coupling. The method employed is the "master equation" for the reduced atomic density operator. The scattered spectrum is symmetric about the resonant frequency and is altered significantly by the presence of the dipole-dipole term. For large incident field strengths pairs of sidebands are displaced from resonance by (+OR-)(omega)(,R) and (+OR-)2(omega)(,R), where (omega)(,R) is the Rabi frequency. Additional peaks arise when the dipole-dipole interaction is of the same order as the atom-field interaction. For weak incident fields the spectrum consists of a central peak and two peaks displaced symmetrically by (omega)(,d), the strength of the dipole-dipole interaction. The spectrum when averaged over the atomic separation and orientation consists of the central peak and two pairs of sidebands displaced by (+OR-)(omega)(,R) and (+OR-)2(omega)(,R). The central and first pair of sidebands become weaker and broader as the number density increases, whereas the second pair of sidebands is enhanced and broadened. The first effect is probably observable for suitable atomic number densities. Perhaps the second pair of sidebands could also be observed in a careful experiment. The second-order correlation function of this system predicts incomplete antibunching for strong incident field strengths. At weak field strengths the antibunching depends strongly on the dipole-dipole energy.
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.
We experimentally demonstrate the resonance fluorescence of a two-level artificial atom strongly coupled to a single-mode cavity field. The effect was theoretically predicted thirty years ago by Savage [Phys. Rev. Lett. 63, 1376 (1989)]. The system consists of a superconducting qubit circuit and a one-dimensional transmission line resonator. In addition, a one-dimensional transmission line strongly coupled to the atom serves as an open space. The effect takes place, when a microwave field is applied to the cavity, which in turn is resonantly coupled to the atom. The fluorescence spectrum is measured via the emission into the transmission line. We find that the central peak is determined by the atom spontaneous emission to the open space and the widths of side peaks are largely determined by the coherent interaction between the atom and the cavity, that is, the fluorescence spectrum here is very different from that of the Mollow triplet. We also derive analytical form for the spectrum. Our experimental results agree well with theoretical calculations.
The exact steady-state solution is presented for the reduced atomic density operator describing the cooperative resonance fluorescence from a system of two atoms separated by an arbitrary distance in an off-resonance laser field, with the dipole-dipole near-field interaction between the atoms included. It is shown that the destructive effect of the dipole-dipole interaction on the formation of squeezing in two-atom resonance fluorescence found recently by Ficek et al. can be compensated to a very large extent by an appropriate choice of the detuning between the laser frequency and the single-atom transition frequency.