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Journal of Optics B Quantum and Semiclassical Optics

Entanglement degree of a nonlinear multiphoton Jaynes-Cummings model

Mahmoud Abdel‐Aty, Shigeru Furuichi, A.‐S. F. Obada

Published Jan 14, 2002• 38 citations
Publisher

Abstract

We extend our earlier investigations ( Furuichi S and Abdel-Aty M 2001 J. Phys. A: Math. Gen. 34 6851 ) on the entanglement degree of a two-level atom to include any forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. We present a derivation of the unitary operator within the frame of the dressed state approach, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. The influences of the nonlinearity, Stark shifts and detuning on the degree of entanglement are examined. It is shown that features of the degree of entanglement are influenced significantly by the kinds of nonlinearity of the single-mode field. The model presented in this paper can be regarded as a generalization of the Jaynes-Cummings model.

DOI
10.1088/1464-4266/4/1/306

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We extend our earlier investigations ( Furuichi S and Abdel-Aty M 2001 J. Phys. A: Math. Gen. 34 6851 ) on the entanglement degree of a two-level atom to include any forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. We present a derivation of the unitary operator within the frame of the dressed state approach, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. The influences of the nonlinearity, Stark shifts and detuning on the degree of entanglement are examined. It is shown that features of the degree of entanglement are influenced significantly by the kinds of nonlinearity of the single-mode field. The model presented in this paper can be regarded as a generalization of the Jaynes-Cummings model.
An 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 a detuning parameter and Stark effect. It is assumed that the atom–field coupling and third-order susceptibility of the Kerr medium depend on the intensity of the 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 a standard coherent state). Then, in order to evaluate the degree of entanglement between the subsystems, we investigate the dynamics of the entanglement by employing the entanglement of formation. Finally, we analyze in detail the influences of the Stark shift, the deformed Kerr medium, the intensity-dependent coupling, and also the detuning parameter on the behavior of this measure for different subsystems. The numerical results show that the amount of entanglement between the different subsystems can be controlled by choosing the evolved parameters appropriately.
In this communication, the entanglement degree due to quasi-mutual entropy of a three-level atom interacting with a single cavity field is investigated. We consider the situation for which the three-level system is initially in a mixed state, whereas the field may start from either a coherent or a squeezed state. We present a derivation of the unitary evolution operator on the basis of the dressed-state formalism taking into account an arbitrary form of nonlinearity of the intensity-dependent coupling, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Most interestingly, it is shown that features of the degree of entanglement are influenced significantly by different forms of the nonlinearity. The atom and radiation subsystems exhibit alternating sets of collapses and revivals due to the initially mixed states of the atom and radiation employed here.
In this paper, a model in which two moving atoms interact with a two-mode field with nondegenerate two-photon transitions is studied in the presence of intensity-dependent coupling. To discuss the entanglement dynamics between subsystems as well as nonclassicality of the system, the time-dependent form of the state vector of the system is exactly obtained. The dynamics of entanglement between the atoms and the field is evaluated by the von Neumann entropy. To examine the degree of entanglement between the atoms, concurrence and negativity are obtained. Then, in order to understand the nonclassicality feature of the state vector of the system, the two-mode Wigner–Weyl quasi-probability distribution function is precisely derived. It is deduced from the numerical results that the domain and the maximum amount of the degree of entanglement and nonclassicality of the system can be appropriately tuned by suitably adopting the nonlinearity function and the field-mode structure parameters.
We have studied the influences of the Stark shifts and a Kerr-like medium on the degree of entanglement and the spectrum, for a system in which a two-level atom interaction occurs with a single mode of an electromagnetic field two-photon processes. The analytical expression for the spectrum is obtained from the finite double-Fourier transform of the two-time field correlation function. It is shown that the Stark shift effect changes the quasiperiod of the field entropy and, hence, the entanglement between the particle and the field.
Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.
The emission spectrum of a single atom in a two-mode Jaynes-Cummings model including any form of nonlinearity of both the two-mode fields and the intensity-dependent atom-field coupling is studied. A general expression for the emission spectrum is given as an explicit function of any nonlinear terms presented in the model. The effects of the nonlinearities on the spectrum are demonstrated for several important examples. It is shown that features of the emission spectrum are influenced significantly by the kinds of intensity-dependent atom-field coupling and the nonlinearities of the two-mode fields. It is also found in an analytic way that the effects on the emission spectrum of both the specific intensity-dependent nonlinear medium and the initial two-mode field photon statistics can be counterbalanced in some special cases.