The exponential laws for emission and decaying of entangled atoms

The first photon emission and the disentanglement of a pair of identical bosonic atoms in excited entangled states follow an exponential law. We extend the theory to distinguishable and identical fermionic two-atom systems. As a byproduct of the analysis we determine the symmetries of the fermionic wave function. We also derive the emission distributions of excited atoms in product states, which must take into account the presence of simultaneous detections. Comparing both distributions reveals a direct manifestation of the modifications induced by entanglement on the atomic emission properties.