Even and Odd Coherent States of the Motion of a Trapped Ion

We propose a scheme for generating even and odd coherent states of the motion of a trapped ion via laser excitation of two vibronic transitions. These quantum superposition states emerge from the long-time dynamics, when the ion decouples from the laser fields and remains in a pure state given by the product of the electronic ground state with a quantum superposition of coherent states of the vibrational motion.