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.

Toward improved quantum simulations and sensing with trapped two-dimensional ion crystals via parametric amplification



Matthew Affolter, Wenchao Ge, Bryce Bullock, Shaun Burd, Kevin Gilmore, Jennifer Lilieholm, Allison Carter, John J. Bollinger


Improving coherence is a fundamental challenge in quantum simulation and sensing experiments with trapped ions. Here we discuss, experimentally demonstrate, and estimate the potential impacts of two different protocols that enhance, through motional parametric excitation, the coherent spin-motion coupling of ions obtained with a spin-dependent force. The experiments are performed on two-dimensional crystal arrays of approximately 100 9Be+ ions confined in a Penning trap. By modulating the trapping potential at close to twice the center-of-mass mode frequency, we squeeze the motional mode and enhance the spin-motion coupling while maintaining spin coherence. With a stroboscopic protocol, we measure 5.4±0.9 dB of motional squeezing below the ground-state motion, from which theory predicts a 10-dB enhancement in the sensitivity for measuring small displacements using a recently demonstrated protocol [K. A. Gilmore et al., Science 373, 673 (2021)]. With a continuous squeezing protocol, we measure and accurately calibrate the parametric coupling strength. Theory suggests this protocol can be used to improve quantum spin squeezing, limited in our system by off-resonant light scatter. We illustrate numerically the trade-offs between strong parametric amplification and motional dephasing in the form of center-of-mass frequency fluctuations for improving quantum spin squeezing in our setup.
Physical Review A


Quantum Simulation, Quantum Sensing


Affolter, M. , Ge, W. , Bullock, B. , Burd, S. , Gilmore, K. , Lilieholm, J. , Carter, A. and Bollinger, J. (2023), Toward improved quantum simulations and sensing with trapped two-dimensional ion crystals via parametric amplification, Physical Review A, [online],, (Accessed July 25, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created March 29, 2023, Updated January 9, 2024