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Journal of Northeast Normal University

Study of linear entropy evolution in system of two atom-two dissipative cavity

Zheng Tai-Yu

Published Jan 1, 2011• 0 citations
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Abstract

In this paper,by using J-C model and the density operator theory in interaction picture,the evolution features of linear entropy were studied in the system of two two-level Rydberg atom and two entangled dissipative cavities with single-photon resonant interaction.The derivation was done of the linear entropy formula of a single atom,a single cavity,as well as two atoms,two cavities,and analyzed how the cavity dissipation coefficients and the atom-cavity interaction coupling coefficient influenced the oscillation model and the evolution period of linear entropies.The evolution periods of all linear entropies are inversely proportional to the constant g,the cavity dissipation constants k1 and k2 influence the modes and the periods of the linear entropies' evolution.

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In this paper,by using J-C model and the density operator theory in interaction picture,the evolution features of linear entropy were studied in the system of two two-level Rydberg atom and two entangled dissipative cavities with single-photon resonant interaction.The derivation was done of the linear entropy formula of a single atom,a single cavity,as well as two atoms,two cavities,and analyzed how the cavity dissipation coefficients and the atom-cavity interaction coupling coefficient influenced the oscillation model and the evolution period of linear entropies.The evolution periods of all linear entropies are inversely proportional to the constant g,the cavity dissipation constants k1 and k2 influence the modes and the periods of the linear entropies' evolution.
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.
Some investigations have been made on the evolution of the linear entropies of atom-field system, in which two identical two-level atoms simultaneously interact with a single-mode dissipative cavity field under large detuning. The effects of the initial atom states and the dissipative factors of the cavity on all linear entropies are also discussed. The results show that the influence of the cavity decay constant on different kinds of Bell states is completely different, and the state |Ψ〉12 is a robust entangled state against the decoherence while the state |Φ〉12 is a fragile entangled state.
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 evolution of the linear entropies of the field,atoms and field-atoms coupling system in the system of two completely identical two-level atoms inside a phase-damping cavity interacting with a coherent field under large detuning are investigated.The effects of atomic initial state,the mean photon number of the field and the dissipation coefficient on the above linear entropies are discussed.The results show that the linear entropies of both the field and the atom are strongly dependent on the atomic initial state,but the evolution of the linear entropy of the system is independent of the atomic initial preparation.With the increasing of the mean photon number,the linear entropies of field,atoms and field-atoms increase;And the larger the dissipation,the more rapid the linear entropies of the field and system tend to the certain degree of mixture,but the linear entropies of atoms don't vary with the dissipation coefficient.
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.