Mapping generalized Jaynes–Cummings interaction into correlated finite-sized systems (original) (raw)
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International Journal of Advanced Science and Engineering, 2022
In the present paper, standard Jaynes Cummings model involving multiphoton interaction between the field and the atom has been considered. We study the variation of entanglement properties of a pair of two–level Rydberg atoms passing one after another into a lossless cavity with single mode multiphoton interaction. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the cavity field results in the final two atoms mixed entangled type state. The entanglement of formation of the joint two atom state as a function of the Rabi angle gt is calculated for Fock state field and Coherent state field. A comparative analysis is done to study the extent of atoms being entangled when they interact through a cavity mode of single frequency but via different orders of interaction.
Entanglement Criteria of Two Two-Level Atoms Interacting with Two Coupled Modes
International Journal of Theoretical Physics, 2015
In this paper, we study the interaction between two two-level atoms and two coupled modes of a quantized radiation field in the form of parametric frequency converter injecting within an optical cavity enclosed by a medium with Kerr nonlinearity. It is demonstrated that, by applying the Bogoliubov-Valatin canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Then, under particular initial conditions which may be prepared for the atoms (in a coherent superposition of its ground and upper states) and the fields (in a standard coherent state), the time evolution of state vector of the entire system is analytically evaluated. In order to understand the degree of entanglement between subsystems (atom-field and atom-atom), the dynamics of entanglement through different measures, namely, von Neumann reduced entropy, concurrence and negativity is evaluated. In each case, the effects of Kerr nonlinearity and detuning parameter on the above criteria are numerically analyzed, in detail. It is illustrated that the amount of the degree of entanglement can be tuned by choosing the evolved parameters, appropriately.
Quantum correlations between each two-level system in a pair of atoms and general coherent fields
Results in Physics, 2016
The quantitative description of the quantum correlations between each two-level system in a two-atom system and the coherent fields initially defined in a coherent state in the framework of power-law potentials (PLPCSs) is considered. Specifically, we consider two atoms locally interacting with PLPCSs and take into account the different terms of interactions, the entanglement and quantum discord are studied including the time-dependent coupling and photon transition effects. Using the monogamic relation between the entanglement of formation and quantum discord in tripartite systems, we show that the control and preservation of the different kinds of quantum correlations greatly benefit from the combination of the choice of the physical quantities. Finally, we explore the link between the dynamical behavior of quantum correlations and nonclassicality of the fields with and without atomic motion effect.
The European Physical Journal Plus, 2015
In this paper, we present a model which exhibits two identical Ξ-type three-level atoms interacting with a single-mode field with k-photon transition in an optical cavity enclosed by a Kerr medium. Considering full nonlinear formalism, it is assumed that the single-mode field, atom-field coupling and Kerr medium are all f-deformed. By using the adiabatic elimination method, it is shown that, the Hamiltonian of the considered system can be reduced to an effective Hamiltonian with two two-level atoms and f-deformed Stark shift. In spite of the fact that, the system seems to be complicated, under initial conditions which may be prepared for the atoms (coherent superposition of their ground and upper states) and the field (coherent state), the explicit form of the state vector of the entire system is analytically obtained. Then, the entanglement dynamics between different subsystems (i.e. "field-two atoms", "atom-(field+atom)" and "atom-atom") are evaluated through appropriate measures like von Neumann entropy, tangle and concurrence. In addition, the effects of intensity-dependent coupling, deformed Kerr medium, detuning parameter, deformed Stark shift and multi-photon process on the considered entanglement measures are numerically analyzed, in detail. It is shown that the degree of entanglement between subsystems can be controlled by selecting the evolved parameters, suitably. Briefly, the Kerr medium highly decreases the amount of different considered measures of entanglement, especially for two-photon transition. This destructive effect preserves even when all other parameters are present, too. Furthermore, we find that the so-called entanglement sudden death and birth can occur in the atom-atom entanglement.
Atom-field entanglement in two-atom Jaynes–Cummings model with nondegenerate two-photon transitions
Optics Communications, 2008
An exact solution of the problem of two-atom one-and two-mode Jaynes-Cummings model with intensity-dependent coupling 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 both models is shown. Conditions and times of disentanglement are derived.
Atom–Atom Entanglement in a Nonresonant Two-Photon Tavis–Cummings Model
2020
Entanglement between two identical two-level atoms (qubits) that interact nonresonantly with the thermal field of a single-mode ideal resonator via effective degenerate two-photon transitions is studied. Based on an exact solution for the time-dependent density matrix, negativity is calculated as a measure of atom entanglement. The effect detuning between the atomic frequencies and the doubled frequency of the resonator field has on the dynamics of qubit entanglement in cases of separable and entangled initial atomic states is investigated.
Entanglement in the degenerate two-photon Tavis–Cummings model
Physica Scripta, 2010
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 twophoton 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
Indian Journal of Physics, 2014
We study the entanglement between two identical two-level atoms located near an ideal model of invisibility cloaks by monitoring the time evolution of the concurrence measure. We obtain the reduced density operator of the atomic subsystem based on a canonical quantization scheme presented for the electromagnetic field interacting with atomic systems in the presence of an anisotropic, inhomogeneous, and absorbing magnetodielectric medium. It is shown that two atoms, which are prepared initially in an unentangled state, are correlated in the weak coupling regime via the spontaneous emission and the dipole-dipole interaction of two atoms mediated by the invisibility cloak. We therefore find that the invisibility cloak, independent of the hidden object, works fairly well at frequencies far from the resonance frequency of the object and the cloak, whereas near the resonance frequency the hidden object becomes detectable due to a sharp reduction of the concurrence.
European Physical Journal D, 2003
In this article a treatment of a three-level atom interacting with two modes of light in a cavity with arbitrary forms of nonlinearities of both the fields and the intensity-dependent atom-field coupling is presented. A factorization of the initial density operator is assumed, with the privileged field modes being in a pair-coherent state. We derive and illustrate an exact expression for the time evolution of the density operator, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. We show that entanglement can be significantly influenced by different kinds of nonlinearities. The nonlinear medium yields the superstructure of atomic Rabi oscillation. We propose a generation of Bell-type states having a simple initial state preparation of the present system.
Quantum dynamics of a two-atom-qubit system
Journal of Physics: Conference Series, 2009
A physical model of the quantum information exchange between two qubits is studied theoretically. The qubits are two identical two-level atoms, the physical mechanism of the quantum information exchange is the mutual dependence of the reduced density matrices of two qubits generated by their couplings with a multimode radiation field. The Lehmberg-Agarwal master equation is exactly solved. The explicit form of the mutual dependence of two reduced density matrices is established. The application to study the entanglement of two qubits is discussed.