The Linear Entropy Of The ∧-type Three-level Atomic System

The research of the linear entropy of the system of the atom interacting with the field has an important significance to prepare the quantum states of the atom and the field, so much attention has been paid on it.We have studied three kinds of three-body systems, and the evolution of the linear entropies of the three subsystems depending on the initial state of the system,as well as the effects of the interaction between the three subsystems on the dependence.Firstly,we have investigated the three-body system that is composed of a static A-type three-level atom and a two-mode field.Only there is the interaction between two subsystems of the system(the atom and the coupled mode).So the linear entropy of the third subsystem(the idle mode) always remains unchanged,which has nothing to do with the initial states of the system.When the two-mode field is in the unrelated pure states at the initial moment,the linear entropy of the atom is always equal to the linear entropy of the coupled mode;when the initial state of the two-mode field is in SU(2) coherent state, the linear entropis of the atom and the coupled mode are no longer always the same. Obviously the linear entropy evolution characteristics of the atom and the coupled mode relates to the initial value of the linear entropy of the coupled mode.Secondly,we have explored the system of a single-mode field interacting with a degenerated A-type three-level atom in a harmonic trap,in which the strength of the interaction between two subsystems(the atomic internal state and the field) depends on the state of the third subsystems(the atomic center-of-mass motion).So only if the atomic center-of-mass motion is in Fock state,the linear entropy of the atomic center-of- mass motion always remain the same.Under this condition,if the atomic internal states and the field are in pure states in the initial moment,the linear entropy of the atom is always equal to the linear entropy of the field.When the atomic center-of-mass motion is in the coherent superposition states of Fock state,the linear entropy of the atomic center-of-mass motion is no longer always equal to zero.Under this condition,even if the initial states of the atomic internal state and the field are in the pure states,the linear entropies of the atomic internal states and the field are no longer always the same. Therefore,the characteristics of the evolution of linear entropies of the three subsystems is related to the initial state of the system.Finally,we have also studied the system of a single-mode field interacting with a non-degenerateΛ-type three-level atom in a harmonic trap,in which the three-body system is coupled between the three sub-systems.Even if the atomic center-of-mass motion is in Fock state,the linear entropy of the atomic center-of-mass motion no longer remains unchanged,and the linear entropies of the atomic internal state and the field is no longer always the same.However,the linear entropy of the atomic internal states is equal to the linear entropy of the atomic center-of-mass,but only if the law is set up when the atomic center-of-mass motion is in Fock state.