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Acta Physica Sinica

FEATURES OF EVOLUTION FOR STATISTICAL DISTRIBU-TION OF PHOTON IN TWO-PHOTON JAYNES-CUMMINGS MODEL

Lin-sheng He, JIANG HAI-HE, 中国科学院安徽光学精密机械研究所,合肥,230031

Published Jan 1, 1991• 0 citations
Publisher

Abstract

The general expression of the statistical distribution function of photons in two-photon Jaynes-Cummings model (JCM) is derived. The expression can be applied to the cases of any initial light field and any initial atomic state. Under exact two-photon resonance, the features of evolution for the statistical distribution of photons in JCM with the initial coherent state field and the initial squeeze state field are studied in detail. These two cases show striking difference.

DOI
10.7498/aps.40.393

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The general expression of the statistical distribution function of photons in two-photon Jaynes-Cummings model (JCM) is derived. The expression can be applied to the cases of any initial light field and any initial atomic state. Under exact two-photon resonance, the features of evolution for the statistical distribution of photons in JCM with the initial coherent state field and the initial squeeze state field are studied in detail. These two cases show striking difference.
The quatum statistical properties of two-photon radiation from two-level atomic system are investigated by using complete set in the nth subspace of generalized Jaynes-Cummings hamiltonian, and the general expression for field variance is obtained. The conditions for optimum squeezing as well as the optimum squeezed quantity are found out for an arbitrary initial state, and the time evolution of the optimum squeezed state is then analysed. As an example, the squeezing in an initial state with bare atomic system in thermal equilibrium is discussed, which demonstrates the dependence of squeezing on several parameters, such as, temperature, detuning, coupling strength. The conditions for squeezing are given analytically and numerically. Finally, the physical picture of the squeezing is pointed out.
The Jaynes-Cummings (JC) model is one of the most fundamental models for the interaction between light and matter. In this paper, we first derive the explicit expression for the time evolution operator of the JC model when the light field resonates with a two-level atom. Based on this, we calculate the analytical expressions for the system state and the population of each atomic energy level as a function of time when the two-level atom is initially in a superposition of two energy eigenstates and the light field is in a superposition of three photon number states and a coherent state, respectively. Finally, this paper introduces QuTiP, a useful extension library in Python for quantum mechanics simulation and numerical solution, and uses it to numerically solve the time evolution of this model, obtaining results consistent with the analytical solutions. These computational processes are of great significance in scientific research and university physics teaching.
We investigate the influence of superposition of coherent states of light on population inversion and the evolution of the field entropy for two-level atoms in the framework of the Jaynes–Cummings model. We compare the behavior of the system in the case of having a coherent superposition state and a statistical mixture of coherent states as an initial field. Our results show that the superposition of coherent states plays an important role in the evolution of the field entropy in the intensity-dependent Jaynes–Cummings model (JCM).