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Acta Sinica Quantum Optica

Solution to Nonlinear Jaynes-Cummings Models with Nonlinearities of both Two-Mode Field and Atom-Field Interaction

Yu Wan‐Lun

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

We use the Lewis-Riesenfeld invariant and superoperator methods to solve the system of the interaction of a two-level atom with two modes of a quantized field via multiphoton process,including any form of both intensity-dependent interaction and nonlinearity of the two-mode radiation field.The corresponding general atom-field wave function and time evolution operator as well as the time-evolving expressions for both the atomic inversion and the photon numbers of two modes field are evaluated.

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

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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.

Journal of Baoji University of Arts and Sciences•Jan 1, 2007•0 citations
We use the Lewis-Riesenfeld invariant and superoperator methods to solve the system of the interaction of a two-level atom with two modes of a quantized field via multiphoton process,including any form of both intensity-dependent interaction and nonlinearity of the two-mode radiation field.The corresponding general atom-field wave function and time evolution operator as well as the time-evolving expressions for both the atomic inversion and the photon numbers of two modes field are evaluated.
Photon statistics in some fully quantized models of the interaction of a two-level atom with a single-mode radiation field have been studied using the operator equations of motion. Expressions for the photon number distribution and the mean photon number are presented for various initial conditions. It is found that the mean photon number may show decays and revivals of coherence similar to those of the atomic inversion in the coherent-state Jaynes-Cummings model. Application of these models to the study of multiphoton laser, absorption, and emission processes is also discussed.
We investigate the atomic inversion dynamics when a multilevel atom interacts with a two-mode quantized radiation field in a Raman-type process. By utilizing the rotating-wave approximation and adiabatically eliminating all but two of the atomic levels, we derive a nonlinear-interaction Hamiltonian for this system. Working in the Schr\"odinger picture, we obtain numerical results that depend on the width and average photon number of the field statistics. Varying these photon statistics allows us to uncover secondary revivals that arise due to the complicated double sum over the two field modes that appear in the solutions. The origin of this phenomenon is described analytically.
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.