Exploiting nonclassical motion of a trapped ion crystal for quantum-enhanced metrology of global and differential spin rotations

Identifying and demonstrating robust methods to prepare entangled atomic states is a continuing challenge for the realization of state-of-the-art quantum-enhanced sensors. In this spirit, we theoretically investigate prospects for the creation of squeezed and nonclassical spin states in trapped ion arrays by resonantly coupling the spin degrees of freedom to a squeezed state of the collective motion of the ions. By selecting the specific vibrational modes of the ion array to which the spins are coupled according to their spatial structure, the projection noise of the resulting spin states can be tailored for quantum-enhanced sensing of global or differential phase shifts imprinted on sub-ensembles of the spins. We propose a pair of interferometric protocols to utilize the generated states and examine the impact of finite size effects, spin-motion entanglement and technical noise. Our results demonstrate our protocols are competitive with other techniques to create spin squeezing as it is scalable, requires only global control of the qubit ensemble and can be readily applied to arrays of varying dimensionality. Our work suggests new opportunities for the preparation of many-body states with tailored correlations for quantum-enhanced metrology in spin-boson systems by exploiting currently available tools for coherent control.