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Acta Physica Sinica

The dynamic effect of a field with a time-varying frequency on the atom-atom entanglement in a double J-C model

Cui Cong-Cong, Xie Shuang-Yuan, Yang Ya-Ping

Published Jan 1, 2012• 3 citations
Publisher

Abstract

The entanglement between the two atoms of two separate Jaynes-Commings models is investigated by means of the concurrence. We restrict our attention to two cases, the field frequency varying with time in the forms of sine and rectangle. When the field frequency varies with time in the form of sine, the period and the amplitude of the atom-atom concurrence will decrease as the amplitude of the sine frequency modulation increases. Not only the sine field frequency modulation but also the rectangular field frequency modulation can affect the interaction of the field with atom between resonance and off-resonance. The field frequency modulation can also affect the atom-atom entanglement. The suitable field frequency modulation is favorable for improving, enhancing and stabilizing the degree of the atom-atom entanglement. The suitable field frequency modulation can also prevent the atom-atom entanglement from entanglement sudden death and control it dynamically.

DOI
10.7498/aps.61.124206

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The entanglement between the two atoms of two separate Jaynes-Commings models is investigated by means of the concurrence. We restrict our attention to two cases, the field frequency varying with time in the forms of sine and rectangle. When the field frequency varies with time in the form of sine, the period and the amplitude of the atom-atom concurrence will decrease as the amplitude of the sine frequency modulation increases. Not only the sine field frequency modulation but also the rectangular field frequency modulation can affect the interaction of the field with atom between resonance and off-resonance. The field frequency modulation can also affect the atom-atom entanglement. The suitable field frequency modulation is favorable for improving, enhancing and stabilizing the degree of the atom-atom entanglement. The suitable field frequency modulation can also prevent the atom-atom entanglement from entanglement sudden death and control it dynamically.
The entanglement degree is investigated by means of the entropy theory between a two-level atom and a coherent field with varying frequency via two-photon transition. We restrict our attention to two cases, the field frequency varying with time in the forms of sine and rectangle. When the field frequency varies with time in the form of sine, the entanglement degree will increase sharply and maintain high values. By changing the amplitude α and angular frequency β of the field-frequency variation respectively, we find that the evolution process is more sensitive to the former. In the rectangular modulation case, different results will be produced when the pulses appear at different time. Comparing the pulses appearing at every minimum value with that at every maximum value, the entanglement degree will increase and reach stability more quickly and easily in the lattev case. The sudden change caused by the rectangular modulation is particularly beneficias to the control of the value of the field entropy.
The interaction between a three-level cascade atom and an initial coherent field with a time-varying frequency has been investigated, including the dynamic behavior of the atomic level occupation probabilities and the entanglement between the atom and the field. The frequency of the field is modulated in the forms of sine and rectangle. It is found that the field-frequency variation has a great influence on the properties of the generalized Jaynes-Cummings model. Appropriate frequency modulation can enhance and stabilize the degree of entanglement between the atom and the field.
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.
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.
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.