Heisenberg-Limited Spin-Mechanical Gravimetry

TL;DR

This paper introduces a quantum-enhanced gravimeter using a spin-mechanical system that achieves Heisenberg-limited sensitivity, significantly improving measurement precision for gravitational acceleration beyond classical limits.

Contribution

The authors demonstrate a Heisenberg-limited gravimeter based on a conditional displacement spin-mechanical system, with quadratic scaling of precision with the number of spins and practical measurement protocols.

Findings

Achieves Heisenberg-limited sensitivity in gravimetry.

Predicts gravimetry uncertainty between 10^{-11} and 10^{-6} m/s^2.

Operates without free-fall, ground-state cooling, and is robust against anisotropies.

Abstract

Precision measurements of gravitational acceleration, or gravimetry, enable the testing of physical theories and find numerous applications in geodesy and space exploration. By harnessing quantum effects, high-precision sensors can achieve sensitivity and accuracy far beyond their classical counterparts when using the same number of sensing resources. Therefore, developing gravimeters with quantum-enhanced sensitivity is essential for advancing theoretical and applied physics. While novel quantum gravimeters have already been proposed for this purpose, the ultimate sensing precision, known as the Heisenberg limit, remains largely elusive. Here, we demonstrate that the gravimetry precision of a conditional displacement spin-mechanical system increases quadratically with the number of spins: a Heisenberg-limited spin-mechanical gravimeter. In general, the gravitational parameter is dynamically encoded into the entire entangled spin-mechanical probe. However, at some specific times, the mechanical degree of freedom disentangles from the spin subsystem, transferring all the information about the gravitational acceleration to the spin subsystem. Hence, we prove that a feasible spin magnetization measurement can reveal the ultimate gravimetry precision at such disentangling times. We predict an absolute gravimetry uncertainty of $10^{-11}\text{m/s}^2$ to $10^{-6}\text{m/s}^2$, without relying on free-fall methodologies, ground-state cooling of the mechanical object, and robust against spin-mechanical coupling anisotropies.