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Acta Physica Sinica

Linear entropy evolution in a dissipative system of two atoms and cavity field

Xiong Yang, Zhao-Yang Tong, Shao-Hua Xiang, (1)湖南师范大学物理与信息科学学院，长沙 410081; (2)怀化学院物理与信息科学系，怀化 418008

Published Jan 1, 2007• 1 citation
Publisher

Abstract

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.

DOI
10.7498/aps.56.2148

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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.
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 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.
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.
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.
We have investigated the entangleable properties of two two-level atoms inside the dissipative cavity coupled to a single-mode radiation field under the big detuning,and discussed the influence of the initial state of the two atoms,the cavitity decay constant and the mean photon number on the entanglement degree.It have shown that if the two atoms are initially in the exicited or the ground states,they will be separate always;if the two atoms are initially in the coherent superposition of the excited and the ground states,the influence of cavity dissipation on the entanglement degree will vanish gradually with the time evolution,but the dipole-dipole interaction can enhance the entanglement degree.