Coherent effects on two-photon correlation and directional emission of two two-level atoms

Sub- and superradiant dynamics of spontaneously decaying atoms are manifestations of collective many-body systems. We study the internal dynamics and the radiation properties of two atoms in free space. Interesting results are obtained when the atoms are separated by less than half a wavelength of the atomic transition, where the dipole-dipole interaction gives rise to new coherent effects, such as (a) coherence between two intermediate collective states, (b) oscillations in the two-photon correlation G((2)), (c) emission of two photons by one atom, and (d) the loss of directional correlation. We compare the population dynamics during the two-photon emission process with the dynamics of single-photon emission in the cases of a Lambda and a V scheme. We compute the temporal correlation and angular correlation of two successively emitted photons using the G((2)) for different values of atomic separation. We find antibunching when the atomic separation is a quarter wavelength lambda/4. Oscillations in the temporal correlation provide a useful feature for measuring subwavelength atomic separation. Strong directional correlation between two emitted photons is found for atomic separation larger than a wavelength. We also compare the directionality of a photon spontaneously emitted by the two atoms prepared in phased-symmetric and phased-antisymmetric entangled states parallel to +/->(k0)=e(0)(ik)center dot r(1)parallel to a(1),b(2)>+/- e(0)(ik)center dot r(2)parallel to b(1),a(2)> by a laser pulse with wave vector k(0). Photon emission is directionally suppressed along k(0) for the phased-antisymmetric state. The directionality ceases for interatomic distances less than lambda/2.