Generation of two-mode nonclassical states and a quantum-phase-gate operation in trapped-ion cavity QED

Abstract
We propose a scheme to generate nonclassical states of a quantum system, which is composed of the one-dimensional trapped-ion motion and a single-cavity field mode. We show that two-mode SU(2), entangled coherent states, two-mode squeezed vacuum states, and their superposition can be generated. If the vibration mode and the cavity mode are used to represent separately a qubit, a quantum phase gate can be implemented.