  Trapped ions offer a pristine platform for quantum computation and
simulation, but improving their coherence remains a crucial challenge. Here, we
propose and analyze a new strategy to enhance the coherent interactions in
trapped ion systems via parametric amplification of the ions' motion--by
squeezing the collective motional modes (phonons), the spin-spin interactions
they mediate can be significantly enhanced. We illustrate the power of this
approach by showing how it can enhance collective spin states useful for
quantum metrology, and how it can improve the speed and fidelity of two-qubit
gates in multi-ion systems, important ingredients for scalable trapped ion
quantum computation. Our results are also directly relevant to numerous other
physical platforms in which spin interactions are mediated by bosons.
