Multi-parameter quantum metrology with stabilized multi-mode squeezed state

TL;DR

This paper demonstrates the generation and stabilization of a multi-mode squeezed state in a trapped ion system, enabling enhanced simultaneous estimation of multiple parameters beyond classical limits, with potential applications in quantum sensing and imaging.

Contribution

It introduces a method to generate and stabilize multi-mode squeezed states in trapped ions for multi-parameter quantum metrology, surpassing classical measurement limits.

Findings

Achieved stabilization of two-mode squeezed states in trapped ions.

Demonstrated simultaneous displacement estimation surpassing classical limits.

Achieved up to 6.9 and 7.0 dB improvements in measurement precision.

Abstract

Squeezing a quantum state along a specific direction has long been recognized as a crucial technique for enhancing the precision of quantum metrology by reducing parameter uncertainty. However, practical quantum metrology often involves the simultaneous estimation of multiple parameters, necessitating the use of high-quality squeezed states along multiple orthogonal axes to surpass the standard quantum limit for all relevant parameters. In addition, a temporally stabilized squeezed state can provide an event-ready probe for parameters, regardless of the initial state, and robust to the timing of the state preparation process once stabilized. In this work, we generate and stabilize a two-mode squeezed state along two secular motional modes in a vibrating trapped ion with reservoir engineering, despite starting from a thermal state of the motion. Leveraging this resource, we demonstrate an estimation of two simultaneous collective displacements along the squeezed axes, achieving improvements surpassing the classical limit by up to 6.9(3) and 7.0(3) decibels (dB), respectively. Our demonstration can be readily scaled to squeezed states with even more modes. The practical implications of our findings span a wide range of applications, including quantum sensing, quantum imaging, and various fields that demand precise measurements of multiple parameters.