In this paper the quantum dynamics of the trapped atom which acts with a standing light field and a travelling light field is investigated. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse-revival which implies that the vibration states of the system have squeezing effect. The larger the nonlinearity of the system, the higher the frequency of collapse-revival of the system, and the smaller the quantum mean energy of the ion. The higher the intensity of the travelling light field, the higher the degree of squeezing of the vibration states of the system can be observed.