Optimal Displacement Sensing with Spin-Dependent Squeezed States

TL;DR

This paper introduces optimal many-body displacement sensing schemes using spin-dependent squeezed states, achieving Heisenberg-limited precision and demonstrating scalable preparation in trapped ions with potential applications in quantum metrology.

Contribution

It proposes and proves the optimality of spin-dependent squeezed states for displacement sensing, along with practical measurement sequences and a scalable state-preparation protocol.

Findings

Achieved 8.7 dB of spin-dependent squeezing in trapped ions.

Demonstrated preparation speed 15 times faster than standard methods.

Proposed sensing protocols applicable to dark matter detection and quantum measurements.

Abstract

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.