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Abstract
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The parity-deformations of the quantum harmonic oscillator are used to describe the generalized
Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly
that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous
external classical field. The dynamical characters of the system is explored under the influence of the
external field. In particular, we analytically study the generation of robust and maximally entangled
states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal
field. We investigate the influence of deformation and detuning parameters on the degree of the
quantum entanglement and the atomic population inversion. Under the condition of a linear interaction
controlled by an external field, the maximally entangled states may emerge periodically along with
time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved
more with the increase of the deformation parameter, i.e. the stronger external field induces better
degree of entanglement.
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