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Communications in Theoretical Physics

An Alternative Approach to Jaynes–Cummings Model with Dissipation at Finite Temperature

Kuang Le-Man, Chen Guanghong, Mo‐Lin Ge

Published Sep 15, 1997• 0 citations
Publisher

Abstract

An alternative approach to the Jaynes–Cummings model (JCM) with dissipation at a finite environmental temperature is presented in terms of a new master equation under Born–Markovian approximation. An analytic solution of the dissipation JCM is obtained. A variety of physical quantities of interest are calculated analytically. Dynamical properties of the atom and the field are investigated in some detail. It is shown that both cavity damping and environmental temperature strongly affect nonclassical effects in JCM, such as collapse and revivals of the atomic inversion, oscillations of the photon-number distribution, quadrature squeezing of the field and sub-Poissonian photon statistics.

DOI
10.1088/0253-6102/28/2/139

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An alternative approach to the Jaynes–Cummings model (JCM) with dissipation at a finite environmental temperature is presented in terms of a new master equation under Born–Markovian approximation. An analytic solution of the dissipation JCM is obtained. A variety of physical quantities of interest are calculated analytically. Dynamical properties of the atom and the field are investigated in some detail. It is shown that both cavity damping and environmental temperature strongly affect nonclassical effects in JCM, such as collapse and revivals of the atomic inversion, oscillations of the photon-number distribution, quadrature squeezing of the field and sub-Poissonian photon statistics.
An alternative approach to the Jaynes-Cummings model (JCM) with dissipation at a finite enviromental temperature is presented in terms of a new master equation under Born-Markovian approximations. An analytic solution of the dissipation JCM is obtained. A variety of physical quantities of interest are calculated analytically. Dynamical properties of the atom and the field are investigated in some detail. It is shown that both cavity damping and environmental temperature strongly affect nonclassical effects in the JCM, such as collapse and revivals of the atomic inversion, oscillations of the photon-number distribution, quadrature squeezing of the field and sub-Poissonian photon statistics.
In this paper, we study a Jaynes-Cummings model (JCM) with phase damping, by introducing a master equation describing phase damping under the Markovian approximation. With the help of the superoperator technique, we find an analytic solution of the master equation for a nonresonant multiphoton JCM with phase damping. We investigate the influence of phase damping on nonclassical effects in the JCM, such as revivals of the atomic inversion, oscillations of the photon-number distribution, the quadrature squeezing of the cavity field, and sub-Poissonian photon statistics. It is shown that phase damping suppresses the revivals of the atomic inversion and nonclassical effects of the cavity field in the JCM.
We study the effect of phase damping in the two-mode Jaynes–Cummings model (JCM) using a master equation describing phase damping under the Markovian approximation. An analytic solution of the master equation for the nondegenerate bimodal multiquanta JCM with phase damping is obtained. We show that phase damping has a less detrimental effect on nonclassical properties of the field than energy damping. In contrast to energy damping the strong nonclassical coherences of a Schrödinger's cat superposition state of two well separated coherent states decay with a similar time constant, independent of the separation of the two states.
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.
We have shown that the Jaynes-Cummings model (JCM) with an environment-induced pure decoherence is an exactly solvable problem. Rabi oscillation of atomic population inversion and oscillation in the field population get trapped due to decoherence. But the decay of the coherence properties of the atom as well as of the field is comparatively slower than that of the population terms. It is also shown that although the fast oscillation in nonclassical properties are suppressed due to decoherence but an initial Poissonian field acquires a sub-Poissonian character in the steady state. So unlike the ordinary spontaneous emission all the nonclassical properties of the system are not erased.
In this paper, we investigate thermal effects of the Jaynes–Cummings model (JCM) at finite temperature with a perturbative approach. We assume a single two-level atom and a single cavity mode to be initially in the thermal equilibrium state and the thermal coherent state, respectively, at a certain finite low temperature. Describing this system with Thermo Field Dynamics formalism, we obtain a low-temperature expansion of the atomic population inversion in a systematic manner. Letting the system evolve in time with the JCM Hamiltonian, we examine thermal effects of the collapse and the revival of the Rabi oscillations by means of the third-order perturbation theory under the low-temperature limit, that is to say, using the low-temperature expansion up to the third-order terms. From an intuitive discussion, we can expect that the period of the revival of the Rabi oscillations becomes longer as the temperature rises. Numerical results obtained with the perturbation theory reproduce well this temperature dependence of the period.