Sudden Death and Rebirth of Entanglement in Classical Optics: an Analogy with Quantum Optics

In this paper, we study the possible realization of a classical system with quantum characteristics on the level of classical optics. Indeed, following Arrizon et al. [J. Opt. Soc. Am. A32, 1140 (2015)JOAOD60740-323210.1364/JOSAA.32.001140], we first use quantum optics formalism to consider the propagation of two coherent states in a Kerr medium where the interaction between the two states is described by the cross-Kerr interaction. We then draw an analogy between the dynamical process of this structure and that of a Gaussian wave propagating in a quadratic gradient index medium. We demonstrate that by using this structure, we can generate a state that oscillates between a classically entangled state and a separable one.