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Journal of Mathematical Physics

Jaynes–Cummings model governed by the Milburn equation without diffusion approximation

Xin Chen, Le‐Man Kuang, Mo‐Lin Ge

Published Dec 1, 1995• 3 citations
Publisher

Abstract

In this paper, we study the Jaynes–Cummings model governed by the Milburn equation for quantum mechanics. We find the exact solution of the Milburn equation without diffusion approximation and apply this solution to studying nonclassical properties of Jaynes–Cummings model (JCM) in the full range of decoherence parameter γ. The influence of the decoherence on nonclassical properties of JCM for different ranges of γ is investigated in detail.

DOI
10.1063/1.531257

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In this paper, we study the Jaynes–Cummings model governed by the Milburn equation for quantum mechanics. We find the exact solution of the Milburn equation without diffusion approximation and apply this solution to studying nonclassical properties of Jaynes–Cummings model (JCM) in the full range of decoherence parameter γ. The influence of the decoherence on nonclassical properties of JCM for different ranges of γ is investigated in detail.
In this paper, we study the multiphoton Jaynes-Cummings model (JCM) governed by the Milburn equation [G. J. Milburn, Phys. Rev. A 44, 5401 (1991); 47, 2415 (1993)], which models the decoherence of a quantum system as the quantum system evolves through intrinsic mechanisms beyond conventional quantum mechanics. We give an exact solution of this equation for the multiphoton Jaynes-Cummings Hamiltonian and apply it to investigate the influence of the intrinsic decoherence on nonclassical effects (atomic inversion, oscillations of the photon-number distribution, squeezing of the cavity field, and photon antibunching) in the JCM. It is shown that during the time evolution, the intrinsic decoherence in the atom-field interaction suppresses these nonclassical behaviors in the JCM.
The Milburn equation without diffusion approximation is solved exactly for the two-photon Jaynes-Cummings model in the presence of Stark shift. This allows the study of the decoherence problem in the whole range of the decoherence parameter gamma . The influence of decoherence on atomic inversion is studied. The dynamical behaviour is adjusted in the presence of Stark shift. It is shown that even in the presence of Stark shift the revivals of atomic inversion are destroyed in the decoherence process.
In this paper, we find an analytic solution of the master equation of a non-resonant two-photon Jaynes-Cummings model (JCM) with phase damping with the help of the super-operator technique. We study the influence of phase damping on non-classical effects in the JCM, such as oscillations of the photon-number distribution, revivals of the atomic inversion, and sub-Possion photon statistics. It is demonstrated that the phase damping suppresses the revivals of the atomic inversion and non-classical effects of the cavity field in the JCM.