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International Journal of Quantum Information

ENTANGLEMENT CONTROLLING OF A THREE-LEVEL CASCADE ATOM INTERACTING WITH A TIME-DEPENDENT COHERENT FIELD

Shuangyuan Xie, FEI JIA, Yaping Yang

Published May 29, 2009• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0219749909005444

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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.
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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.
Using the multiphoton 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 via multiphoton transition 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 is 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 quasiperiodic oscillation behavior.Its oscillation period is in agreement with the period of frequency varying.The initial state of atom influences the time-evolution behavior of the fidelity of atom.
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.
We have studied the effect of phase shifted frequency modulation on two level atom with field interaction using Jaynes—Cummings model. Here the frequency of the interacting field is sinusoidally varying with time with a constant phase. Due to the presence of phase in the frequency modulation, the variation of population inversion with time is different from the standard case. There are no exact collapses and revivals in the variation of population inversion but it oscillates sinusoidally with time. In coherent field atom interaction the population inversion behaves as in the case of Fock state atom interaction, when frequency modulation with a non zero phase is applied. The study done with squeezed field has shown the same behavior of the population inversion.