The quantum motion of an ion in a quadrupole radio-frequency trap is explicitly solved in terms of coherent states for the dynamical symplectic group in connection with the classical motion. The coherent states are built over extremal and nonextremal weight states. The geometrical Berry phases and the quasienergy spectrum are also obtained.

• Received 10 October 1991

DOI:https://doi.org/10.1103/PhysRevA.45.4828