Abstract: Using the negative entropy method ,the quantum entanglement character of the system of the binomial optical field interacting with the moving atom is studied .The influences of the atomic initial state , the field-mode structure parameter ,the maximum photon number of the binomial field ,the coefficient of the binomial field ,the transition photon number and the detuning are discussed .The results shows that the value of the entanglement degree of the system appears regular evolution and ESD phenomenon when the atomic motion is considered .The increasing of the field-mode structure parameter shortens the period of the entanglement and results in a slight decreasing of the amplitude .The atomic initial state affects the entanglement degree of the system .When the atomic initial state tends to pure state ,the entanglement degree of the system is larger relatively .With the increase of the maximum photon number of the binomial field ,the value of the entanglement degree of the system becomes small ,but the period for the regular evolution is almost unchanged. When the field is in the middle states ,the entanglement degree is smaller relatively. With the increase of the transition photon number, the value of the entanglement degree of the system becomes larger ,the period of the oscillation becomes shorter ,meanwhile the oscillation of the system becomes faster and faster .With the detuning increasing, the entanglement becomes small.

Key words: quantum optics, quantum entanglement, binomial field, mixed state