Displacement sensing is a fundamental task in metrology. However, the development of quantum-enhanced sensors that fully utilize the available degrees of freedom in many-body quantum systems remains an outstanding challenge. We propose novel many-body displacement sensing schemes that use spin-dependent squeezed (SDS) states -- hybrid spin-boson states whose bosonic squeezed quadrature is conditioned on an auxiliary spin. We prove that SDS states are \emph{optimal}, i.e. their quantum Cram\'{e}r-Rao bound saturates the Heisenberg limit. We propose explicit measurement sequences that can be readily implemented in systems such as trapped ions. We also introduce a scalable state-preparation protocol and numerically demonstrate the preparation of 8.7~dB of spin-dependent squeezing 15 times faster than the standard approach using second-order sidebands in trapped ions. The potential applications of our sensing protocols range from measuring single-photon scattering to searches for dark matter.
@article{arxiv.2510.25870,
title = {Optimal Displacement Sensing with Spin-Dependent Squeezed States},
author = {Liam J. Bond and Christophe H. Valahu and Athreya Shankar and Ting Rei Tan and Arghavan Safavi-Naini},
journal= {arXiv preprint arXiv:2510.25870},
year = {2025}
}