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Journal of Modern Optics

Nonclassical properties of a time-varying Jaynes–Cummings model

Shuangyuan Xie, Yaping Yang, Hong Chen

Published Jun 27, 2006• 0 citations
Publisher

Abstract

The interactions between a two-level atom and a 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. The dynamic behaviour of the field squeezing, photon antibunching and atomic dipole squeezing are investigated numerically as a function of time. A number of novel phenomena are discovered and discussed.

DOI
10.1080/09500340600736850

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The interactions between a two-level atom and a 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. The dynamic behaviour of the field squeezing, photon antibunching and atomic dipole squeezing are investigated numerically as a function of time. A number of novel phenomena are discovered and discussed.
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.
Using the multiphoton Jaynes-Cummings model,the squeezing effect of the field in the system of a two-level atom interacting with the single mode coherent field through mutiphoton transition was studied.The frequency of the field varying with time in the form of sine was considered.The influences of amplitude and angular frequency of the field-frequency variation on squeezing effects of the field were discussed by numerical calculations.The influences of mean photon number of the field on squeezing effects of the field were also discussed.Calculation results indicate that the squeezing effects of field strengthens with the increase of the amplitude u of field-frequency variation and weaken with the increase of mean photon number of the field.The time-evolution behavior of quadrature squeezing function Q1 is modulated by the field-frequency variation.The modulation intensity is enchanced with the increase of the amplitude u of field-frequency variation,and when the amplitude u of field-frequency variation is larger than a fixed value,the time-evolution of quadrature squeezing function Q1 will display quasi-periodicity oscillation behavior.Its oscillation frequency agrees with the angular frequency of field-frequency variation.
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.
Using the Jaynes-Cummings model,the dynamical properties of the fidelity of quantum states in the system that consists of a two-level atom interacting with a single-mode field are studied.The frequency of the field varying with time in the form of sine is considered.The results obtained by numerical calculations show that the time-evolution behavior of the fidelities of field and system are not influenced by the frequency variation of field,but the time-evolution behavior of the fidelity of atom is modulated by the frequency variation of field.The larger the amplitude of the field frequency variance u is,the stronger modulation interaction of the field frequency variance is.When the amplitude u is larger than a fixed value,the time-evolution behavior of the fidelity of atom will display periodic oscillation behavior.Its oscillation period is in agreement with the period of frequency varying.