Entanglement in degenerate two-photon Tavis-Cummings model E. K. Bashkirov, E.Yu.Sochkova, E.S.Tarelnik Departments of General and Theoretical Physics, Samara State University, 443011, Samara, 1 Academican Pavlov Str., Russia bash@ssu.samara.ru Abstract Introduction An exact solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with one-mode coherent radiation field is presented. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent fields. The atom-field entanglement is investigated on the basis of the reduced atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process for model considered is shown. Conditions and times of disentanglement are derived. Entanglement is a key resource which distinguishes quantum information theory from classical one. It plays a central role in quantum information, quantum computation and communication, and quantum cryptography [1]. In recent years, there has been a considerable effort to characterize entanglement properties qualitatively and quantitatively and to apply them in quantum information. A lot of schemes are proposed for many-particle entanglement generation. The simplest scheme to investigate the atom-field entanglement is the Jaynes- Cummings model (JCM) [2] describing an interaction of a two-level atom with a single-mode quantized radiation field. This model is of fundamental importance for quantum optics [3,4] and is realizable to a very good approximation in experiments with Rydberg atoms in high-Q superconducting cavities [5,6]. The model predicts a variety of interesting phenomena. The quantum collapse and revival [7] and atom-field entanglement [6] are among them. Recently, the generalizations of the JCM for the two-atom case have also attracted a considerable interest [4]. Such a generalizations of JCM is bellow referred to as two-atom Tavis-Cummings model (TCM). The atom-field entanglement has been studied in this model for coherent initial states of a cavity mode in [8],[9]. Two-photon processes are known to play a very important role in atomic systems due to high degree of correlation between emitted photons. An interest for investigation of the two- photon JCM is stimulated by the experimental realization of a two-photon one-atom micromaser on Rydberg transitions in a microwave cavity [10]. Last years the JCM with degenerate and nondegenerate two-photon transitions as well as with two-photon Raman transitions have attracted a great deal of attention. The foregoing models have been considered in terms of atomic population dynamics research, field statistics research, field and atom squeezing analysis, atom and field entropy and entanglement examining [11]. The dynamics of two-atom two-photon JCM for initial two-mode coherent cavity field has been considered for degenerate two-photon transitions in [12,13], Raman type transitions in [14] and for nondegenerate two-photon transitions in [15]. An investigation of the atom-field entanglement for JCM has been initiated by Phoenix and Knight [16] and Gea-Banacloche [17]. Gea-Banacloche has derived an asymptotic result for the JCM state vector which is valid when the field is initially in a coherent state with a large mean photon number [18]. It is shown that the atom prepared in arbitrary initial pure atomic state is to a good approximation in a pure state in the middle of the collapse region. This has been first noticed by Phoenix and Knight by using the entropy concepts. An appreciable disentanglement between atom and field is found at the half-revival time, otherwise the atom and field are strongly entangled. Moreover, at the half-revival time, the cavity field represents a coherent superposition of the two macroscopically distinct states with opposite phases or so-called Schr o && edinger cat state. The interaction splits the initial coherent state into two parts in the phase PDF created with FinePrint pdfFactory Pro trial version www.pdffactory.com