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Acta Physica Sinica

The influence of the field frequency modulation on quantum entanglement via two-photon process

Cheng Qiu-Li, Xie Shuang-Yuan, Yang Ya-Ping, 同济大学物理系,上海 200092

Published Jan 1, 2008• 4 citations
Publisher

Abstract

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.

DOI
10.7498/aps.57.6968

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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 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 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.
In the rotating-wave approximation,the evolution of the field quantum entropy in the system that consists of a two-level atom interacting with a single-mode field was studied,considering the atomic motion and the field frequency varying with the time in the form of sine-function at the same time.In two cases of neglecting atomic motion and considering atomic motion,figures of the time evolutions of the field entropy were plotted respectively using numerical calculations.Influences of the atomic motion,the field-model structure parameter,amplitude and angular frequency of the field-frequency variation on the field entropy were also discussed.The atom-field entangled states,field fock states and atomic high fidelity states were prepared by analytic method according to the decomposition theorem of Schmidt,and the related system parameters of these quantum states operation were acquired.The results show that:the time evolution behavior of the field entropy is modulated by the frequency variation of field;the interaction between the field and atom will weaken with the increase of the amplitude of variation of the field frequency;the period of the field entropy agrees with the period of field-frequency variation;the atomic motion will result in the period of the field entropy doubled;the evolution of the field entropy is related to the parity of field-mode structure parameter;the approximate EPR states of field-atom can be prepared periodically whether the atom moves or not.
The entanglement time evolution of atoms in Bell states |β and |β interacting with the two-mode entangled coherent field is investigated by means of full quantum theory and numerical calculations.The effects of the atoms′ initial state,mean photon numbers of field,the degree of the entanglement for the entangled coherent fields,and the coupling strength of interaction between atoms on the entanglement are discussed.The results show that the entropy time evolutions appear regular with the increase of the mean photon numbers of field.The frequency and amplitude of the oscillation decrease with the increase of the coupling strength of interaction between atoms.But when the degree of the entanglement for the entangled coherent fields changes,the frequency and amplitude of the entropy oscillation won′t change.
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.
By using the multiphoton Jaynes-Cummings model,the dynamical properties of the field entropy in the system that consists of a two-level atom interacting with a single-mode field via multiphoton transition are studied.The frequency of the field varying with time in the form of u sin wt has been considered.The results show that the time-evolution behavior of the field entropy is modulated by the frequency variation of field using the numerical.The modulation intensity is enchanced as the amplitude u of frequency variation of field increases.When the amplitude u of the time varying fields is larger than a fixed value,the time-evolution behavior of the field entropy will display periodic oscillation behavior.Its oscillation period agrees with the period of frequency varying.It shows that the evolution of field entropy is influenced by the frequency parameters w and u of the field varying with time.