Perfect revivals of Rabi oscillations and hybrid Bell states in a trapped ion

Abstract We show that perfect revivals of Rabi oscillations are possible, under certain conditions, in the population inversion of a trapped ion. Based on this property, we find that Schrödinger cat states of the atomic motion are naturally generated by the unitary dynamics. Using a pair of symmetric and antisymmetric Schrödinger cat states of motion, together with an electronic excited or ground state, we find that the interaction leads to four orthonormal maximally entangled states or hybrid Bell states as they are encoded in two partitions of different nature. We also study a quadratic Kerr-type evolution that is possible for short interaction times.