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Journal of Jiangxi Normal University

Atomic Population Evolution of the Stimulated Three-Level Atom withoutRotating Wave Approximation

Liu San-qiu

Published Jan 1, 2002• 0 citations
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Abstract

In this paper,the atomic population evolution vs.time in the system of three-level casade atom interacting with a single-mode coherent light field is investigated without rotating wave approximation.The influence of the initial mean photon number n of field,of the atom-field coupling sonstant λ and of the light frequency ω on the atomic population is also discussed.And we compare without rotating wave approximation with rotating wave approximation,and find many differences of the atomic population evolution curves on the identical initial field-strength.It has been shown that because of the influence of the virtual-photon process,the little saw-tooth which represents the quantum noise of the system appear in the evolution curves of thae atomic population of the stimulated radiation field.With the increase of light frequency ω,the quantum noise of the system decreases,and then disappears.And with the increases of the initial field-strength n,the quantum noise of the system increases gradually.Meanwhile,the initial field-strength n and atom-field coupling constant λ influence the oscillation period the quantum collapse-revival of the atomic population evolution curves of stimulated radiation field,too.

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Journal of Jiangxi Normal University•Jan 1, 2001•0 citations
In this paper,the atomic population evolution vs.time in the system of three-level casade atom interacting with a single-mode coherent light field is investigated without rotating wave approximation.The influence of the initial mean photon number n of field,of the atom-field coupling sonstant λ and of the light frequency ω on the atomic population is also discussed.And we compare without rotating wave approximation with rotating wave approximation,and find many differences of the atomic population evolution curves on the identical initial field-strength.It has been shown that because of the influence of the virtual-photon process,the little saw-tooth which represents the quantum noise of the system appear in the evolution curves of thae atomic population of the stimulated radiation field.With the increase of light frequency ω,the quantum noise of the system decreases,and then disappears.And with the increases of the initial field-strength n,the quantum noise of the system increases gradually.Meanwhile,the initial field-strength n and atom-field coupling constant λ influence the oscillation period the quantum collapse-revival of the atomic population evolution curves of stimulated radiation field,too.
The dynamics of a cascade three-level atom interacting with the single mode coherent state under the Counter-Rotating-Wave approximation (C-RWA) is investigated.The properties of the mean-photon number (N(t)) and the degree of second-order coherence (g2(t)) are analyzed in this model.The little indentation which represents the quantum noise of the system appears in the evolution curves of the mean-photon number and the degree of second-order coherence under the C-RWA.The quantum noise which is caused by the virtual photon field gradually becomes weak when ω increases.The quantum noise increases when increases.The anti-bunching effect of the system under the C-RWA is stronger than the one under the RWA.Besides,the relation of N(t) and g2(t) with the atom-field coupling constant λ is revealed in our results.
The time evolution of atomic population of the system, where the two identical two-level atoms in Bell states interact with two-mode entangled coherent field in a cavity filled with the Kerr medium, was investigated by means of quantum theory and numerical method. The effects of the atomic initial state, mean photon numbers of field, the degree of the entanglement for the entangled coherent field, and the coupling strength between the Kerr medium and field on the atom’s population are discussed via numerical calculations. The results show that the atomic population is time-independent provided that the atoms are in β11〉 state. For the other three Bell states, there will appear the periodical collapse-revival of atomic population if the initial mean photon number reaches some special values. With the increase of the initial mean photon number, the oscillation frequency of the time-evolution of atomic population increases correspondingly, and the amplitude decreases. The degree of the entanglement of the two-mode entangled coherent field has no effect on the frequency of the Rabi oscillation, but has an obvious effect on the amplitude of Rabi oscillation. When the coupling strength between the Kerr medium and field reaches some special values, it has the obvious effects on the cycle of collapse-revival of atomic population, the frequency and the amplitude of Rabi oscillation.
By the method of coherent-state orthogonalization expansion, the evolution of atomic population inversion is investigated in the non-rotating-wave approximation. The numerical results indicate that, when field frequency and coupling do not change with time, the collapse-revival period of population inversion increases with the mean photon number of the field increasing, and the quick oscillation due to virtual photon process increases with couplings strengthening. When the frequency changes with time in the sine form, amplitude α and angle frequency β of the field both have a great influence on atomic population inversion. The sudden jumping of the field frequency can lead to some new collapses and rebibals in the evolution of atomic population inversion. Both of the field frequency forms can have an influence on quick oscillation due to virtual photon process.
The time-evolution of atomic population of a light-atoms interaction system,two atoms in Bell states Interacting with two-mode entangled coherent field,are investigated by means of quantum thoery and numerical method.The effect of the atomic initial state,mean photon numbers of field,the degree of the entanglment for the entangled coherent fields,and the coupling strength of dipole-dipole interaction between atoms on the atom's population are discussed by numerical calculation.The results show that the atomic population is time-independent provided that the atom is in |β11〉 state.For the other three Bell states,there will appear the periodical collapse-revival of the atomic population if the initial mean photon number reaches some special value.With the increase of the initial mean photon number,the oscillation frequency of the time-evolution of atomic population increases correspondingly,and the amplitude decreases.The revival period of the atomic population for the initial states |β00〉 and |β10〉 is twice of that for the initial state |β01〉.The degree of entanglement of the two-mode entangled coherent field and the intensity of two dipole-dipole interaction between atoms have no effects on the frequency of the Rabi oscillation,but have obvious effects on the amplitude of the oscillation.
In this paper, the atomic population evolution vs. time in the system of three-level cascade atom interacting with squeezed coherent light field in a Kerr medium is investigated by means of the interacting picture and the quantum theory. Meanwhile, the influence of Kerr medium μ, the squeezed light field factor γ and the coherent vibration amplitude |α| 2 of the field-atom on the atomic population is also discussed. It has been shown that the intensity coefficient μ of Kerr medium, the squeezed light field factor γ and the coherent vibration amplitude |α| 2 of the light field influence the quantum collapse-revival periodicity of the evolution curves of atomic population directly. And the non-linearity Kerr medium μ can weaken the interaction of the atom with the field. When Kerr medium μ and the interaction of the field-atom increase to a certain value, the correlation degree of light-field and atom will weaken and disappear.