Abstract
For a system composed of a three-mode cavity field interacting with a movable mirror, the time evolution operator of the system and its transformation are given, and the time evolution of the system state is obtained by means of quantum theory. The result shows that the state of the three-mode cavity field is in an entangled coherent state when the mirror returns to its original state, and the preparations of different entangled coherent states can be controlled. Nine different three-mode entangled coherent states are given, and the different phase factors of these states indicate the different reactions between the field and the movable mirror, which provides an important theoretical basis for the experimental preparations of controllable entangled coherent states.
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