Abstract: Quantum entanglement not only has important significance in knowing the basic concept of quantum mechanics, but also is one of useful information resources. It is a key problem in quantum teleportation, quantum dense coding, quantum key distribution, quantum computation, quantum error correction and error prevention. In actual problem, the coupling coefficient of atom and field is possibly variational, therefore, to some extent, it is valuable in considering the entangled properties of motorial atom and cavity field.This paper will expand standard Jaynes-Cummings model to the condition of considering atomic motion, the parameter of field-mode, Gaussian coupling, and mostly investigate the entangled properties of motorial two-level atom and cavity field, and Compare the atoms which are static with that of motion. This paper contants the following five parts:In the first part, the paper will mainly introduce the quantum entanglementâ€™s concept, development history and applying value in quantum communication, and then elaborate the paperâ€™s subject-selecting background, significance and main work. In the second part, we will present quantum theory, squeezing vacuum field and its character, then expand standard Jaynes-Cummings model to the condition of considering atomic motion, the basic dynamic model with atomic motion will be established, as the theoretical basic of the work in the below.The third part is made of three facets.1. The entangled properties of motorial atom and field in the two-photon Jaynes-Cummings model with atomic motion are studied by using the quantum information theory. It is shown that:(1) When the parameter p of the field model structure with atomic motion is smaller, the entanglement of system is not provided with the characteristic of periodic oscillations, when the value of p is greater, the entanglement of system is obviously provided with the characteristic of periodic oscillations, the oscillation period is as much again as atom is resting . when motorial atom is prepared in ground state or excited state ,the system is in the disentangled state; when motorial atom is prepared in coherent superpositions states, the entanglement occurs between motorial atom and field.2. We investigate the entanglement properties of two entangled two-level atoms that interact resonantly with a single-mode vacuum field with atomic motion using quantum theory. The results show that if the two atoms are prepared in maximum entangled (EPR) state initially, the maximum of three-body entanglement measure is equated with the perfect three-body W entangled state. The parameter of field-mode structure p influences the time evolution oscillation property of three-body entanglement measure, with the gradually increasing of p, the average of three-body entanglement measure will gradually decrease, three-body entangled state will tend to disentangled state inch by inch.3. The properties of the entanglement between squeezing vacuum state field and moving atom with Gaussian coupling are studied. The influence of atomic motion perpendicularity to the axes of resonant cavity , the initial states of atom, the squeezing parameter on entanglement degree are discussed. The results show that: with the increase of atomic velocity, effective interaction time of the atom and field will shorten, the entanglement degree will also reach the maximum quickly. The squeezing parameter r have a obvious role of concocting the evolution curve of degree of entanglement, if the squeezing parameter is take appropriate value(such as r =2), the system of quantum state will be maximally entangled state for a long time, without disentangled-free state or disentangled state, and the degree of entanglement is stationary…

Key words: atomic motion; field-mode structure; entanglement degree; squeezing vacuum state; Gaussian coupling

# The Research of Entangle Properties between Moving Two-level Atom and Light Field

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