Effect of pairwise Dipole - Dipole interaction among three atoms Systems

We present analysis of a system of three two-level atoms interacting with each other through the dipole-dipole interaction. The interaction manifests between excited state of one of the atoms and the ground state of its nearest neighbour. Steady state populations of the density matrix elements are presented and are compared with a situation when only two atoms are present. It can be noticed that the third atom modifies the behaviour of the three atoms. Two configurations are analysed, one in which the three atoms are in a line, with no interaction between atoms at the end points and the other in which the atoms form a closed loop with each atom interacting with both its neighbours.