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Acta Sinica Quantum Optica

The Time-evolution of the Atomic Population in the System of Atoms in Bell States Interacting with Two-mode Entangled Coherent Field

Zhuo‐Liang Cao

Published Jan 1, 2007• 0 citations
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Abstract

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.

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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.
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.
The time-evolution of the atom′s occupancy in the system of two-mode entangled coherent fields interacting with two atoms in Bell states via two-photon process is investigated by means of quantum theory.The results show that the atom′s occupancy is zero if the two atoms are initially in Bell state |β11.If the two atoms are initially in the other three Bell states,the oscillation frequency of the atom′s occupancy accelerates and the amplitude decreases apparently with the increase of mean photon numbers of field.The degree of the entanglement for the entangled coherent fields can′t influence the oscillation frequency and the position of the atom′s occupancy curve.If the two atoms are initially in Bell state |β01,the Rabi oscillation frequency of the atom′s occupancy accelerates apparently with the increase of the coupling strength of interaction between atoms.While the two atoms are initially in Bell state |β10 or |β00,the collapse-revival phenomenon of the atom′s occupancy disappears gradually.
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 field entropy time evolution in Bell state|β_(01) and |β_(11) interacting with the two-mode entangled coherent field is investigated by means of full quantum theory. 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 entropy evolution properties of the field are discussed. The results shows that the entropy will forever be zero when the initial state is |β_(11) . For the state |β(01) the oscillation of the field entropy presents periodicity with the increasing of the mean photon number. And the coupling strength of interaction between atoms plays a major role in the entropy evolution properties.
The statistic properties of photon of a light-atoms interaction system,and two atoms in Bell states interacting with two-mode entangled coherent field,were investigated by means of quantum theory and numerical method.The effect on the statistic properties of photon induced by the atomic initial state,mean photon numbers of field,the degree of the entanglement for the entangled coherent fields,and the coupling strength of dipole-dipole interaction between atoms were analyzed by numerical calculations.The results indicate that photon anti-bunching effect does not appear for the Bell state ｜β00〉 or ｜β10〉,however there can appear the photon anti-bunching effect under some conditions for the Bell state ｜β01〉 or ｜β11〉 appears.In the case,the photon anti-bunching effect depends on the mean photon numbers intensively.The influence of the degree of entanglement for the two-mode entangled coherent fields and the coupling strength of dipole-dipole interaction between atoms on the statistic properties of photon is small.