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Spatial superposition for a two-dimensional matter-wave interferometer in an inverted harmonic potential with gyroscopic rotational stability

Ryan Rizaldy1,*, Tian Zhou1, Run Zhou2, and Anupam Mazumdar1

  • 1Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, 9747AG Groningen, The Netherlands
  • 2Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China

  • *Contact author: r.rizaldy@rug.nl
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APS Open Sci. 1, 000130 – Published 11 September, 2026

DOI: https://doi.org/10.1103/cwm2-6vgp

Abstract

This study presents a mathematical model of the spatial and rotational motion of a nanodiamond in an inverted harmonic potential to create a macroscopic quantum spatial superposition. The model is based on the Stern-Gerlach interferometer scheme, which utilizes linear and quadratic magnetic fields to generate a harmonic potential (linear magnetic field) and a nonlinear potential (nonlinear/quadratic magnetic field). By incorporating two-dimensional dynamics into the model, we provide a more realistic and accurate depiction of nanoparticle dynamics in linear and inverted harmonic potentials and explore the interaction between motion in a two-dimensional plane. Importantly, we derive the equations of motion for the rotational degrees of freedom, i.e., libration, precession, and rotation. The results show that adding a magnetic-field bias term to the magnetic-field profile in the linear stage affects the classical equations of motion but does not affect the width of the wave packet. Moreover, the libration mode always forms a harmonic potential at each stage because the applied initial angular velocity is dominated by the nanoparticle's defect axis, making it more stable in the presence of the trap frequency in the orthogonal direction along the axis that enables the creation of a macroscopic quantum superposition.

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APS Open Sci. 1, 000130– Published 11 September, 2026
Vol. 1
  • Received 3 March 2026
  • Accepted 24 August 2026
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