Radiation from anN-Atom System. II. Spontaneous Emission from a Pair of Atoms

Using the formalism developed earlier, we treat spontaneous emission from a pair of identical two-level atoms A₁, A₂, whose separation r₂₁ can be comparable to the wavelength λ. We obtain expressions for time-dependent intensities and damping rates with the initial conditions (a) both atoms inverted, (b) prior excitation by a short 1/2π pulse, and (c) only A₁ inverted. The results in (a) are compared with those obtained for a model consisting of two initially excited harmonic oscillators O₁, O₂. The atoms exhibit superradiant behavior, whereas O₁, O₂ tend to trap radiation. In (a), the intensity pattern R(θ,t) develops lobes in different directions at different times, so that the spatial distribution of photons at time t→∞ is the same as in the independent-atom case r₂₁λ. For the oscillators, the lobes of R(θ,t) do not change direction, but only become more pronounced as time increases. In (b) and (c), the lobes oscillate back and forth at frequency 2Ω₁₂ corresponding to the shifts ±Ω₁₂ of the triplet and singlet states due to the A₁-A₂ interaction. The intensity can therefore have a sinusoidal component. Field correlation functions calculated for (a) and (c) show that A₂ and A₂ radiate simultaneously around the frequencies ε±Ω₁₂, where ε is the single-atom resonant frequency. The spectrum is calculated for case (c), and shows the effects of coherent linewidth enhancement in addition to the frequency shifts.