The Entanglement Evolution Of Two Atoms In Double Jaynes-Cummings Model

Quantum information science is an emerging subject,which is formed by the intersection of quantum physics and information science,including quantum communication,quantum computing,and quantum control.Microscopic objects can be in a superposition of different states,which is an important feature that distinguishes quantum physics from classical physics.The entanglement and non-locality of quantum states are the most prominent features in quantum effects.Quantum entanglement in quantum information science occupies a very important position,and has been widely used in quantum computing,quantum communication,quantum teleportation and quantum dense coding and so on.Typically,the quantum system will inevitably be affected by the surrounding environment,the interaction between the system and the environment can cause decoherence in quantum systems,resulting in entanglement decay,and even sudden death.This is also in recent years,the sudden death and sudden birth of quantum entanglement has become a research hot spot in the field of quantum entanglement.This paper studies the system in which an ideal single-mode light field interacts with a single ideal two-level atom,which is called the Jaynes-Cummings model(J-C model for short).The article considers a four-body complex composed of two standard J-C models.Combined system,the two J-C models are independent of each other.We will consider the resonance of the transition frequency of a two-level atom with the eigenfrequency of a single-mode light field,and discuss the entanglement dynamics between two atoms A and B in different initial states in a single excitatory subspace(Two single-mode light fields are represented by a and b).The entanglement between A and B atoms can be measured by the degree of concurrence.The research work has achieved the following innovative results:1.First,we consider that the initial state of the composite system is that the two subsystems are separable and the other two subsystems are in a Bell-like entangled state,which we call a partial Bell entangled state.The results show Whether the evolution of the concurrence of two atoms with time has periodicity depends on the ratio of the coupling strength between the two J-C models.When the ratio of the two coupling strengths is a rational number,the entanglement evolution of the two atoms has time periodicity;conversely,If the ratio is an irrational number,the entangled evolution of two atoms will not be periodic.2.Based on the periodicity of the entanglement evolution between the two atoms A and B,consider that the ratio of the coupling strength between the two J-C models is a positive integer,it is found that(1)Regardless of the initial state and the value of the ratio n,the evolution period of the concurrence of the two atoms is always ?/gB.(2)If the ratio n is an odd number,it is found that when the initial state is |?AB),that is the two atoms A and B are entangled with each other,and the two light fields of a and b can be separated,the entanglement evolution law of two atoms after half a period is the same as the entanglement evolution law of two atoms when the initial state is |?ab>,that is the two atoms A and B can be separated and the two light fields a and b are entangled with each other.Similarly,the initial state where the A atom and the b light field are entangled and the B atom a light field can be separated,that is |?Ab>,after half a period,the entanglement of the two atoms under the entangled state with the initial B atom and the light field of a and the light field of A atom b can be separated state,that is |?aB>,The evolutionary dynamics are the same.If the ratio is an even number,when the initial states are |?AB>and |?aB>,after half a period,the entanglement evolution law of the two atoms is the same as when the initial states are |?Ab>and|?ab>.3.Considering that the initial state of the composite system is that the three subsystems constitute the W-type entangled state direct product remaining subsystem state,which is called the partial W entangled state,we find that:(1)The ratio of the coupling intensities of the two cavities has nothing to do with whether the evolution of the entanglement concurrence of the two atoms is periodic,and in the initial state where the b light field can be separated(|?ABa>)and in the initial state where the B atom can be separated(|?Aab>),the evolution period of the concurrence of the two atoms is ?/gB,and if in the initial state where the a light field can be separated(|?ABb>)and in the initial state where the A atom can be separated(|?Bab)),the evolution cycle is ?/gA.(2)Initial state|?ABa)and |?Aab),|?ABb)and |?Bab)have a half-period time gap respectively,which is initial state|?ABa)and |?ABb)after half a period of translation are compared with the initial state|?Aab)and |?Bab),the entanglement evolution law of the two atoms is the same.(3)Especially,when gA=gB=g,no matter whether the initial moment is the state where the light field a is separable or the state where the light field b is separable,the entanglement evolution law of the two atoms studied is the same.Of course,whether it is the separable state of A atom or the separable state of B atom at the initial moment,the law of entanglement evolution of the two atoms will still be the same.