Quantum Entropy of a Nonlinear Two-level Atom with Atomic Motion

Abstract

The wave function of a system governed by the time-dependent nonlinear JaynesCummings (JC) model is obtained. We compute analytically the eigenvalues of the reduced field density operator by which the dynamics of the entropy of entanglement of the cavity field are analyzed. The influences of the atomic motion, the field-mode structure and the Kerr-like medium on this phenomenon are illustrated. The population dynamics of an excited atom is also discussed for the same set of parameters. The cavity field is assumed to be initially excited in either a Fock or a coherent states. The cavity excitation in a Fock state generates a class of an entanglement without death with fixed amplitude by adjusting the parameters of the atomic motion as well as the Kerr and the field-mode structure. In case of a coherent cavity, the only phenomenon to be noted is the periodical behavior of the dynamics under study when the atomic motion is considered. Although the Kerr medium affects the strength of the entanglement negatively, the entropy of entanglement loses its zeros where the Kerr is taken into consideration.

Controlling the non-classical properties of a hybrid Cooper pair box system and an intensity dependent nanomechanical resonator

“…Recently, several authors have employed various methods to investigate the dynamics of entanglement [12,[66][67][68]. Here the name "entanglement" means "mixing of states", whose degree can be measured by the entropy.…”

Entanglement Dynamics and Spin-Squeezing of the Nonlinear Tavis–cummings Model Mediated by a Nonlinear Binomial Field

“…The close relation between the entanglement and spin squeezing enhances the importance of spin squeezing which motivate us to explore the role of Kerr medium [38][39][40][41] and the nonlinear binomial state on the spin squeezing and entanglement.…”

“…We denote by χ the dispersive part of the third order susceptibility of the Kerr-like medium [38][39][40][41]. The parameter λ represents the atoms-field coupling constant.…”

“…Wang and Sanders [37], presented a generalization of the results of Ref.[28] to the multiqubit case, where the authors showed that spin squeezing implies pairwise entanglement for arbitrary symmetric multiqubit states. More quantitatively, for spin states with a certain parity, if a state is spin squeezed according to the definition for Kitagawa and Ueda [15], a quantitative relation is obtained between the spin squeezing parameter and the concurrence [42][43][44][45], quantifying the entanglement of two half-spin particles [28,37].The close relation between the entanglement and spin squeezing enhances the importance of spin squeezing which motivate us to explore the role of Kerr medium [38][39][40][41] and the nonlinear binomial state on the spin squeezing and entanglement.A binomial state is one of the important nonclassical states of light which has attracted much attention in the field of quantum optics in the last few decades, see for example [46][47][48]. This, in fact, is due to the importance of these states which have been experimentally produced and characterized.…”

An Investigation of a Nonlocal Entanglement of Two Uncoupled Atoms Embedded in a Coherent Cavity Field and the Associated Phase Space Distribution: One Quantum Nonlinear Process

“…where a ( a † ) is bosonic annihilation (creation) operator for the single mode field of frequency ω and λ is atoms-field coupling constant, the operators σ + = |+ −| , σ − = |− +| and σ z = |+ +| − |− −| represent, respectively, the raising, lowering and population atomic operators which obey the commutation relations [ σ + , σ − ] = σ z , while ∆ = ω 0 − ω is the detuning parameter which represents the difference between the atomic and cavity subsystems eigenfrequencies. We denote by χ the dispersive part of the third order susceptibility of the Kerr-like medium [15,16,20,[29][30][31].…”