State-dependent motional squeezing of a trapped ion: Proposed method and applications

We show that the motion of a cold trapped ion can be squeezed by modulating the intensity of a phase-stable optical lattice placed inside the trap. The method we propose is reversible (unitary) and state selective: it effectively implements a controlled-squeeze gate. This resource could be useful for quantum information processing with continuous variables. We show that the controlled-squeeze gate can prepare coherent superpositions of states which are squeezed along complementary quadratures. Furthermore, we show that these states, which we denote "chi states," exhibit a high sensitivity to small displacements along two complementary quadratures, which makes them useful for quantum metrology.