Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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



Matthew Affolter, Kevin Gilmore, Elena Jordan, John Bollinger


Measurements of the center-of-mass motion of a trapped-ion crystal that are phase- coherent with an 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 this protocol free from noise associated with the center-of-mass mode. The driven sinusoidal displacement of the crystal is detected by coupling the axial 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. This corresponds to an amplitude 40 times smaller than the zero-point fluctuations. After averaging down the noise, a 5.8 pm amplitude is detected. The sensitivity of the amplitude detection documented here, when applied on-resonance with the center-of-mass mode, indicates the possibility of weak force and electric field detection below 10−3yN/ion and 1 nV/m, respectively.
Physical Review A


2D Crystal, Force/E-Field Sensing, Penning Trap, Quantum Metrology


Affolter, M. , Gilmore, K. , Jordan, E. and Bollinger, J. (2020), Phase-coherent sensing of the center-of-mass motion of trapped-ion crystals, Physical Review A, [online], (Accessed April 15, 2024)
Created November 9, 2020, Updated April 23, 2021