General formalism of interaction of a two-level atom with cavity field in arbitrary forms of nonlinearities (original) (raw)
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Laser Physics, 2014
Entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of detuning parameter and Stark effect. It is assumed that atom-field coupling and third-order susceptibility of the Kerr medium depend on the intensity of light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom-field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in standard coherent state). Then, in order to evaluate the degree of entanglement between subsystems, we investigate the dynamics of entanglement through the well-known criteria such as von Neumann reduced entropy, entanglement of formation and negativity. Finally, we analyze the influences of Stark shift, deformed Kerr medium, intensity-dependent coupling and also detuning parameter on the above-mentioned measures, in detail. Numerical results show that the amount of entanglement between different subsystems can be controlled by choosing the evolved parameters, appropriately.
Journal of the Optical Society of America B, 2013
In this paper, the interaction between a Λ-type three-level atom and two-mode cavity field is discussed. The detuning parameters and cross-Kerr nonlinearity are taken into account and it is assumed that atom-field coupling and Kerr medium to be f-deformed. Even though the system seems to be complicated, the analytical form of the state vector of the entire system for considered model is exactly obtained. The time evolution of nonclassical properties such as quantum entanglement and position-momentum entropic uncertainty relation (entropy squeezing) of the field are investigated. In each case, the influences of the detuning parameters, generalized Kerr medium and intensity-dependent coupling on the latter nonclassicality signs are analyzed, in detail.
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
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.
Laser Physics, 2013
The degree of entanglement in the time development of a three-level atom in the Ξ-configuration interacting with two-mode fields under the mechanism of multi-photon transition is investigated. The atom is prepared in its upper most excited state and the fields are prepared in the binomial states. Analytical expressions for the time evolution and the reduced density operators are derived in the framework of the dressed states. Effects of mean photon numbers, detuning and the Kerr-like parameters are investigated within various forms of the intensity coupling functionals. General conclusions reached are illustrated by numerical results.
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.
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.
Some entanglement features of a three-atom Tavis–Cummings model: a cooperative case
Journal of Physics B: Atomic, Molecular and Optical Physics, 2010
In this paper we consider a system of identical three two-level atoms interacting at resonance with a single-mode of the quantized field in a lossless cavity. The initial cavity field is prepared in the coherent state while the atoms are taken initially to be either in the uppermost excited state "|eee " or The GHZ-state or the W-state. For this system we investigate different kinds of atomic inversion and entanglement, which arise between the different parts of the system due to the interaction. Also the relationship, between entanglement and some other nonclassical effects in the statistical properties, such as collapses and revivals in the atomic inversion where superharmonic effects appear, is discussed. The Q-functions for different cases are discussed. Most remarkably it is found that the GHZ-state is more robust against energy losses, showing almost coherent trapping and Schrödinger-cat states can not be produced from such state. Also the entanglement of GHZ-state is more robust than the W-state. Therefore we conjecture that, also this sate will shows similar robustness against dissipation in the open systems. Another interesting feature found is that the state which has no pairwise entanglement initially will have a much improvement of such pairwise entanglement through the evolution. Sudden death and sudden revival of atoms-pairwise entanglement are produced with the W-state.
Atom-field entanglement in cavity QED: Nonlinearity and saturation
Physical Review A
We investigate the degree of entanglement between an atom and a driven cavity mode in the presence of dissipation. Previous work has shown that in the limit of weak driving fields, the steady state entanglement is proportional to the square of the driving intensity. This quadratic dependence is due to the generation of entanglement by the creation of pairs of photons/excitations. In this work we investigate the entanglement between an atom and a cavity in the presence of multiple photons. Nonlinearity of the atomic response is needed to generate entanglement, but as that nonlinearity saturates the entanglement vanishes. We posit that this is due to spontaneous emission, which puts the atom in the ground state and the atom-field state into a direct product state. An intermediate value of the driving field, near the field that saturates the atomic response, optimizes the atomfield entanglement. In a parameter regime for which multiphoton resonances occur, we find that entanglement recurs at those resonances. In this regime, we find that the entanglement decreases with increaing photon number. We also investigate, in the bimodal regime, the entanglement as a function of atom and/or cavity detuning. Here we find that there is evidence of a phase transition in the entanglement, which occurs at 2 /g ≥ 1.