Photon echoes for a system of large negative spin and few photons

Persistent photon echoes are seen for the case of a large number of two-level molecules (TLMs) prepared initially in the all-down state (large negative spin) interacting with a photon distribution with a small mean photon number in a lossless cavity. This case is interesting since 1) it has not been significantly addressed in the past; 2) the characteristic times associated with revival are not what is seen for the more frequently addressed problem of a few TLMs interacting with a photon distribution with a large mean photon number; 3) long after the echoes die out, they re-emerge completely at a much later time; and 4) the existence of echoes is not predicated on the initial photon distribution being the coherent state or Glauber distribution. Entropy, entanglement, and the Q function are considered. It is found that disentanglement only occurs at the revival times as evidenced by the entropy going to 0 and the Q function returning to the value seen at time=0. Comparison to the more normally seen results for large mean photon number and small numbers of TLMs are discussed. Finally this paper acts as a general reference for future refereed publications.