Sudden Death of Entanglement of Two Jaynes-Cummings Atoms

Entanglement is a defining feature of quantum mechanics that makes fundamental distinctions between quantum and classical physics. As an unambiguous and quantifiable property of sufficiently simple multi-party quantum systems, entanglement has a definite time evolution that has recently begun to be studied in several contexts [1, 2, 3, 4, 5, 6, 7, 8]. Entanglement in a quantum system may deteriorate due to interaction with background noise or with other systems usually called environments. Interest was originally concerned with the consequences for quantum measurement and the quantum-classical transition [9, 10, 11]. More recently, entanglement decoherence has been studied in connection with obstacles to realizing various quantum information processing schemes. Particularly, we have shown that entanglement can decay to zero abruptly, in a finite time, a phenomenon termed entanglement sudden death [4, 5]. The purpose of this paper is to examine two interesting time-evolving quantum systems that have no route for mutual iteraction, but whose mutual entanglement nevertheless evolves in an unusual way. We have chosen the “double Jaynes-Cummings” model consisting of two two-level atoms. Each one is in a perfect one-mode nearresonant cavity and interacts with its initially unexcited cavity mode, but each is completely isolated from the other atom and cavity. By tracing over the cavity modes at time t we are left with a mixed state of atoms A and B similar to that treated previously by us [4], but in this case the underlying intra-cavity dynamics are quite different since the cavities are here treated as lossless rather than as per-