Quantum Decoherence and Entanglement Induced by Nonlinear Dissipative Environment

Abstract

The analytical description of the dynamics of a nonlinear atom-field system described by a diagonal f -deformed Jaynes-Cummings model for a chosen initial state is obtained. The purity loss of the global system, and the atomic and field subsystems are discussed. Information on entanglement between the field and matter is studied by comparing the results for mutual entropy, which is a measure of the total correlation, and the negativity as a measure of the amount of entanglement. It is found that the nonlinearity of the dissipation tends to accelerate the decoherence of the global, field, and atomic states. In addition, we find that the so-called entanglement sudden death can occur when both of the nonlinearity couplings between the cavity field and the dissipation are combined.Subject Index: 061 §1. IntroductionThe Jaynes-Cummings (JC) model 1) is one of the oldest and paradigmatic nontrivial models in quantum optics. It has been used extensively to describe the quantum features of the interaction of a single two-level atom with a single cavity mode. One of the simplest physical realizations of the JC model is the one-atom maser or micromaser. 2) Recently, cooling techniques have allowed the trapping and manipulation of atoms by optical means. These new technologies have provided an alternative physical realization of the JC model, 3) where cold trapped ions can be excited in such a way that the effective unitary dynamics is described by a nonlinear JC model.In the above situation, the phonon field corresponding to the vibrational motion of the ion plays the role of an electromagnetic cavity field, and the electronic levels of the ion effectively act as a two-level system. By conveniently choosing the laser excitation, different coupling schemes can be realized. The resulting dynamics is a generalization of the JC model, where the effective two-level system and the vibrational modes can interchange k excitation quanta. 4) There is an increasing interest in the study of this system the main motivation comes from the field of quantum computation and information, 5) where trapped-ion systems are considered as one of the most promising resources for implementing controlled generation and manipulation of quantum states.One of the major problems to overcome in these areas is decoherence. Much work has been dedicated to the theoretical study of the dissipative JC model by considering cavity loss and atom decay with constant coupling between the cavity field and its environment, 6), 7) and with the coupling being deformed with the atom in a