Phase-coherent sensing of the center-of-mass motion of trapped-ion crystals

TL;DR

This paper demonstrates phase-coherent measurement of trapped-ion crystal motion, achieving high displacement sensitivity and surpassing previous phase-incoherent methods, enabling detection of extremely weak forces and electric fields.

Contribution

It introduces a phase-coherent sensing protocol for ion crystals that significantly improves displacement measurement precision over prior methods.

Findings

Detected 49 pm displacement with SNR of 1, an order-of-magnitude improvement.

Achieved displacement sensitivity of 8.4 pm/√Hz, enabling detection of forces below 10^{-3} yN.

Revealed potential for sensing electric fields below 1 nV/m.

Abstract

Trapped ions are sensitive detectors of weak forces and electric fields that excite ion motion. Here measurements of the center-of-mass motion of a trapped-ion crystal that are phase-coherent with an applied weak external force are reported. These experiments are conducted far from the trap motional frequency on a two-dimensional trapped-ion crystal of approximately 100 ions, and determine the fundamental measurement imprecision of our protocol free from noise associated with the center-of-mass mode. The driven sinusoidal displacement of the crystal is detected by coupling the ion crystal motion to the internal spin-degree of freedom of the ions using an oscillating spin-dependent optical dipole force. The resulting induced spin-precession is proportional to the displacement amplitude of the crystal, and is measured with near-projection-noise-limited resolution. A $49\,$pm displacement is detected with a single measurement signal-to-noise ratio of 1, which is an order-of-magnitude improvement over prior phase-incoherent experiments. This displacement amplitude is $40$ times smaller than the zero-point fluctuations. With our repetition rate, a $8.4\,$pm$/\sqrt{\mathrm{Hz}}$ displacement sensitivity is achieved, which implies $12\,$yN$/\mathrm{ion}/\sqrt{\mathrm{Hz}}$ and $77\,\mu$V$/$m$/\sqrt{\mathrm{Hz}}$ sensitivities to forces and electric fields, respectively. This displacement sensitivity, when applied on-resonance with the center-of-mass mode, indicates the possibility of weak force and electric field detection below $10^{-3}\,$yN/ion and $1\,$nV/m, respectively.