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Journal of Baoji University of Arts and Sciences

Nonlinear two-level atomic model in high intensity one-mode light field

Di Li

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Aim To modify the traditional JC(Jaynes-Cummings) model by considering the influence of the term A2, and a more rigorous and practical quantum optics model was obtained.Methods The model including the term A2 is rigorously derived by using second-quantization method. Results A nonlinear quantum optics model for a two-level atom interacting with light field is given. This model can be used to study the atomic behavior in the intense light field. Finally, a simple solution of this model under the condition that the two-photon process is neglected is obtained, and the difference of this solution with that of the JC model is also simply discussed.Conclusion The term of A2 is greatly modify the form of the JC model and the model presented here can provide a relative precise results if the light field is strong.

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Aim To modify the traditional JC(Jaynes-Cummings) model by considering the influence of the term A2, and a more rigorous and practical quantum optics model was obtained.Methods The model including the term A2 is rigorously derived by using second-quantization method. Results A nonlinear quantum optics model for a two-level atom interacting with light field is given. This model can be used to study the atomic behavior in the intense light field. Finally, a simple solution of this model under the condition that the two-photon process is neglected is obtained, and the difference of this solution with that of the JC model is also simply discussed.Conclusion The term of A2 is greatly modify the form of the JC model and the model presented here can provide a relative precise results if the light field is strong.
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.
The emission spectrum of a single atom in a two-mode Jaynes-Cummings model including any form of nonlinearity of both the two-mode fields and the intensity-dependent atom-field coupling is studied. A general expression for the emission spectrum is given as an explicit function of any nonlinear terms presented in the model. The effects of the nonlinearities on the spectrum are demonstrated for several important examples. It is shown that features of the emission spectrum are influenced significantly by the kinds of intensity-dependent atom-field coupling and the nonlinearities of the two-mode fields. It is also found in an analytic way that the effects on the emission spectrum of both the specific intensity-dependent nonlinear medium and the initial two-mode field photon statistics can be counterbalanced in some special cases.
An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.
Multiphoton interaction of single-mode squeezed-state light and a two-level atom is considered based on the K-photon Jaynes–Cummings model. Time evolution of quantum fluctuation and photon statistical properties of the initial squeezing light are discussed. It is found that through interaction with a two-level atom, larger squeezing levels cannot be achieved in one-photon or multiphoton processes. For photon antibunching behavior of the light field, it is shown that a smaller initial squeezing level and an appropriately larger coherent part of the initial average photon number of the radiation field favor the generation of this nonclassical behavior, especially in the lower-order interaction processes.