Multilevel atomic entanglement induced by spontaneous emission infree space

We investigate two identical Λ-type atoms in free space, and focus on the entanglement between the two atoms. We derive a master equation for the atomic subspace and solve it analytically to show how the spontaneous emission from the two atoms system induces entanglement. The magnitude of the entanglement and the steady state entanglement are found to be strongly dependent on the initial states and the orientation of the dipoles of the two atoms.