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Journal of Henan Normal University

Entropy Properties of Atom-Field System with Raman Coupling In a Cavity

Lai Zhen-jiang

Published Jan 1, 2011• 0 citations
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Abstract

Using the method of super-operator that describes the dissipative effects,the study has obtained exact solution of the master equation that represents a Raman interaction between three-level atoms and cavity-field.The linear entropy of the system,along with atoms and cavity-field in the system is formulated.The influences of the Stark shift between two atomic levels,intensity of the cavity-field and the dissipative coefficient of the cavity on the linear entropy are discussed.It is found that the more intense the cavity-field,the longer the persistent time of the exchange of entropy between the cavity field and atoms.Because the cavity field leaks,the cavity dissipation blocks entropy exchange between the subsystems;to make the entropy of the system and subsystem increase irreversibly and reduce the amount of the coherent information,and so that it is finally to zero.When the Stark shifts between the atomic levels changes and the cavity dissipation coefficient remain has unchanged,the coupling between atom and cavity field enhances,the entropy exchange of the system speed up and the steady-state values become smaller.When the dissipation of the cavity is absent,the entropy of the light field and the atoms follow the same evolutionary regularity and reversible,show saturated and retreat saturated natures corresponding to the collapse and restoration of the atomic levels,respectively.Along with the increase of atomic number in saturated and retreat saturated time the entropy evolution characteristics is becoming more and more complicated.

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Using the method of super-operator that describes the dissipative effects,the study has obtained exact solution of the master equation that represents a Raman interaction between three-level atoms and cavity-field.The linear entropy of the system,along with atoms and cavity-field in the system is formulated.The influences of the Stark shift between two atomic levels,intensity of the cavity-field and the dissipative coefficient of the cavity on the linear entropy are discussed.It is found that the more intense the cavity-field,the longer the persistent time of the exchange of entropy between the cavity field and atoms.Because the cavity field leaks,the cavity dissipation blocks entropy exchange between the subsystems;to make the entropy of the system and subsystem increase irreversibly and reduce the amount of the coherent information,and so that it is finally to zero.When the Stark shifts between the atomic levels changes and the cavity dissipation coefficient remain has unchanged,the coupling between atom and cavity field enhances,the entropy exchange of the system speed up and the steady-state values become smaller.When the dissipation of the cavity is absent,the entropy of the light field and the atoms follow the same evolutionary regularity and reversible,show saturated and retreat saturated natures corresponding to the collapse and restoration of the atomic levels,respectively.Along with the increase of atomic number in saturated and retreat saturated time the entropy evolution characteristics is becoming more and more complicated.
For studying the entropy exchange between the subsystems of the interaction system of a atom with the field in a leaking cavity,an exact solution of the master equation that describes the system by using the method of super-operator is obtained.The influences of the intensity of the cavity-field,the dissipative coefficient of the cavity and the Stark shift between two atomic levels on the linear entropy are discussed.The results show that: the more intense the cavity-field is,the longer the persistent time of the exchange of the entropy between the cavity field with other sub-systems is.When the two-level Stark shifts between the atomic levels changes to enhance the coupling between the atom and the cavity field increased and the cavity dissipation coefficient remain unchanged,the entropy of the system speed up the exchange and the steady-state values of the entropy become smaller.
The density operator was induced via V-type atom interacting with a cavity-field through Raman process system in an amplitude damping cavity, and the properties of linear entropies for atom-field system for atom and for field in the system were investigated. The results show that the linear entropy of the system and atom are larger than zero except the initial time in a dissipative cavity. The values remain a certain degree after some time and increase with the increase of mean photon number. At t_d, the atom is completely decoherent to the cavity. The field comes back to the initial pure state. But the atom is still in a mixed state. The larger the dissipation, the more rapid the linear entropies of the atom and system tend to the certain degree of mixture. And the larger the mean photon number, the more obvious the dissipation influence on the linear entropy.
Based on quantum theory, an investigation is conducted on the evolution characteristics of linear entropies of 1) atoms, 2) two cavities and 3) atom-cavity system in the interaction process of two entangled dissipative cavities and a single two-level atom which runs through one of cavities. The effect of the dissipative constant and the coupling strength of interaction between atom and cavity field on all three linear entropies is discussed for the resonant case.The results show that all three linear entropies strongly depend on the dissipative constant of cavity and the coupling strength between cavity field and atoms. Furthermore, the dissipative constant and the strength of interaction between atoms and cavity field affect not only the amplitude of the oscillation of field quantum entropy evolution but also its periodicity.
The time evolution of linear entropy of atom-field coupling system, atom and field in the system of two two-level atoms inside a single-mode cavity with amplitude-damping under the condition of large detuning were investigated. The effects of the initial preparation of two atoms, the decay rate of cavity field and the mean photon number of field on all kinds of linear entropy were discussed. The results show that if both the two atoms are in their excited states or ground states, all the linear entropies equal to zero. But when the two atoms are in their coherent superposition state of excited state and ground state, the cavity dissipation will lead to the system to evolve into a mixed state, the linear entropy of atom and field exhibits periodic oscillations with damped amplitude.
The entanglement between two Λ-type three-level atoms interacting with coherent field in a dissipative cavity is investigated by means of the entanglement degree of quantum conditional entropy.A solution of the master equation is obtained by super operator method.The authors discuss the entanglement between the two atoms based on two kinds of different initial states(|ψa(0),|Φa(0)) and analyze the influence of decay coefficient of the cavity and mean photon number of the field on entanglement degree.In conclusion,when the atoms are initially in entangled state |ψa(0),the evolution of the entanglement degree depends on decay coefficient of the cavity and intensity of the field.If there is absence of dissipation,the entanglement degree evolves periodically;otherwise,the entanglement degree decays sharply and approaches a stable value.The weaker the intensity of the field is,the greater the stable value becomes.The greater the decay coefficient is,the faster it reaches the stable value.But for the other initial entangled state |Φa(0),the entanglement between the two atoms doesn't evolve with the time.It implies that the entangled state |Φa(0) can be preserved in such a dissipative system.