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Acta Physica Sinica

The interactions of a two-level atom with a coherent field of time-varying frequency: the two-photon transition

Li Zheng-Hong, Yu Ming-Zhang, Yang Ya-Ping, 同济大学物理系，上海 200092

Published Jan 1, 2008• 2 citations
Publisher

Abstract

The two-photon transition for a two-level atom interacting with a single-mold electromagnetic field has been investigated. The initial coherent states with time-varying frequency are considered. The effects of the frequency modulation in sinusoidal form on the atomic population inversion and the squeezing properties of the atom and field are studied. The frequency change can lead the collapse-revival period of population inversion to increase, the maximum value of the revival to decrease, and the squeezing effects of the field and atom are weakened.

DOI
10.7498/aps.57.1693

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Acta Physica Sinica•Jan 1, 2004•3 citations
The two-photon transition for a two-level atom interacting with a single-mold electromagnetic field has been investigated. The initial coherent states with time-varying frequency are considered. The effects of the frequency modulation in sinusoidal form on the atomic population inversion and the squeezing properties of the atom and field are studied. The frequency change can lead the collapse-revival period of population inversion to increase, the maximum value of the revival to decrease, and the squeezing effects of the field and atom are weakened.
The interactions between a two-level atom and a squeezed field of time-varying frequency have been investigated. The properties of the atomic population inversion for two typical cases——the frequency of the field varying with time in the forms of sine function and rectangular pulses——have been considered. For the frequency changing with time in sinusoidal form, the collapse-revival phenomenon of the atomic population inversion is deformed not only by the frequency-modulation but also by the squeeze coefficient and the squeeze phase of the field. The sudden jumping of the field with rectangular pulsed frequency-modulation can lead to new collapses and revivals in the evolution of the atomic population inversion. The rectangular pulsed frequency-modulation can also lead to small-amplitude fast oscillations of the atomic population inversion during the pulse. There is no relation between the latter phenomena and the squeeze coefficient of the field.
The interactions between a two-level atom and a coherent field with a time-varying frequency have been investigated. The two typical cases---the frequency of the field varying with time in the forms of sine and rectangle---have been considered. It is found that the collapse-revival phenomena of the atomic population inversion are deformed as the frequency changing with time in sine form and the rectangular frequency modulation can lead to some new collapses and new revivals in the evolution of the atomic population inversion.
The present study described about the interaction of a two level atom and squeezed field with time varying frequency. By applying a sinusoidal variation\nin the frequency of the field, the randomness in population inversion is reduced and the collapses and periodic revivals are regained. Quantum optics is an emerging field in physics which mainly deals with the interaction of atoms with quantised electromagnetic fields. Jaynes-Cummings Model (JCM) is a key model among them, which describes the interaction between a two level atom and a single mode radiation field. Here the study begins with a brief history of light, atom and their interactions. Also discussed the interaction between atoms and electromagnetic fields. The study suggest a method to manipulate the population inversion due to interaction and control the randomness in it, by applying a time dependence on the frequency of the interacting squeezed field.The change in behaviour of the population inversion due to the presence of a phase factor in the applied frequency variation is explained here.This study also describes the interaction between two level atom and electromagnetic field in nonlinear Kerr medium. It deals with atomic and field state evolution in a coupled cavity system. \nOur results suggest a new method to control and manipulate the population of states in two level atom radiation interaction,which is very essential for quantum information processing.We have also studied the variation of atomic population inversion with time, when a two level atom interacts with light field, where\nthe light field has a sinusoidal frequency variation with a constant phase. In both coherent field and squeezed field cases, the population inversion variation is completely different from the phase zero frequency modulation case. It is observed that in the presence of a non zero phase φ, the population inversion oscillates sinusoidally.Also the collapses and revivals gradually disappears when φ increases\nfrom 0 to π/2. When φ = π/2 the evolution of population inversion is identical to the case when a two level atom interacts with a Fock state. Thus, by applying a phase shifted frequency modulation one can induce sinusoidal oscillations of atomic inversion in linear medium, those normally observed in Kerr medium. \nWe noticed that the entanglement between the atom and field can be controlled by\nvarying the period of the field frequency fluctuations. The system has been solved numerically and the behaviour of it for different initial conditions and different susceptibility values are analysed. It is observed that, for weak cavity coupling the effect of susceptibility is minimal. In cases of strong cavity coupling, susceptibility factor modifies the nature in which the probability oscillates with time. Effect\nof susceptibility on probability of states is closely related to the initial state of the system.
The interactions between a two-level atom and a field via two-photon transition without rotating wave approximation have been investigated. We emphasize the dynamic behaviors of the atomic population inversion, the field squeezing, and the atomic dipole squeezing numerically when the field frequency varies with time in the forms of sine and rectangle. Some interesting phenomena are discovered and discussed. The good periodic character of the atomic population inversion in the standard two-photon Jaynes–Cummings model is weakened by the influence of the sine field frequency modulation. The rectangular field frequency modulation can change the correlation among different oscillations suddenly and induce new collapse-revival processes of the atomic population inversion. The field squeezing increases at the beginning of time, but then decreases and loses as the time increases after it reaches the maximum due to the sine modulation. The effects of the rectangular modulation on the field squeezing depend mostly on the appearance time of the modulation. The atomic dipole squeezing is weakened under the influence of the sine or rectangular modulation. Our results indicate that it is possible to perform the dynamic controlling of the system properties by changing the parameters of the system with time. This implies that one can dynamically control a quantum information process by choosing the system modulation properly.
The interactions between a two-level atom and a coherent field with a time-varying frequency without rotating-wave approximation have been investigated. The typical cases of the frequency of the field varying with time in the sine and rectangle forms have been considered. It is found that the collapse-revival phenomena and quick oscillations due to virtual photon processes of the atomic population inversion are deformed as the frequency changes with time in the sine form. The rectangular frequency modulation can lead to some new collapses and revivals in the evolution of the atomic population inversion. The sudden jumping of the field frequency can also lead to the sudden change of the quick oscillations due to virtual photon processes.
In this paper, the interactions between a two-level atom and a coherent field with a time-varying frequency have been studied. The two typical cases, in which the frequency of the field varies with time in the form of sine or impulse, have been considered. It is found that the collapse and revival phenomena of the atomic population inversion will disappear as the frequency changing with time in sine form; and the frequency varying in impulse form can lead to some new collapses and new revivals in the evolution of the atomic population inversion.