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Parametric amplification of spin-motion coupling in three-dimensional trapped-ion crystals

Samarth Hawaldar1,*,†, N. Nikhil2,3,*, Ana Maria Rey4,5, John J. Bollinger6, and Athreya Shankar7,8,‡

  • *These two authors contributed equally to this work.
  • †Contact author: samarth.hawaldar@ist.ac.at
  • ‡Contact author: athreya@physics.iitm.ac.in
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Phys. Rev. Applied 25, 034004 – Published 2 March, 2026

DOI: https://doi.org/10.1103/h1m9-h3yw

Abstract

Three-dimensional (3D) crystals offer a route to scaling up trapped-ion systems for quantum sensing and quantum simulation applications; however, engineering coherent spin-motion couplings and effective spin-spin interactions in large crystals poses technical challenges associated with decoherence and prolonged timescales to generate appreciable entanglement. Here, we explore the possibility of speeding up these interactions in 3D crystals via parametric amplification. For this purpose, we derive a general Hamiltonian for the parametric amplification of spin-motion coupling that is broadly applicable to normal modes with motion transverse to or along the spatial extent of the crystal. Unlike in lower-dimensional crystals, we find that the ability to faithfully (uniformly) amplify the spin-spin interactions in 3D crystals depends on the physical implementation of the spin-motion coupling. We consider the light-shift gate, and the so-called phase-insensitive and phase-sensitive Mølmer-Sørensen (MS) gates, and we find that only the phase-sensitive MS gate can be faithfully amplified in general 3D crystals. We discuss a situation where nonuniform amplification can be advantageous. We also reconsider the effect of counter-rotating terms on parametric amplification and find that they are not as detrimental as previous studies suggest.

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References (26)

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Phys. Rev. Applied 25, 034004– Published 2 March, 2026
  • Received 12 August 2025
  • Revised 8 December 2025
  • Accepted 12 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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