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

TL;DR

This paper develops a detailed two-dimensional quantum model for a nanodiamond in an inverted harmonic potential, demonstrating how magnetic fields influence its motion and stability for creating macroscopic quantum superpositions.

Contribution

It introduces a comprehensive 2D dynamical model including rotational degrees of freedom for a nanodiamond in a magnetic potential, advancing understanding of quantum superposition stability.

Findings

Magnetic-field bias affects classical motion but not wave packet width.

Libration mode remains harmonic and stable under initial angular velocity.

The model enhances realism in nanoparticle quantum dynamics simulations.

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 (SGI) scheme, which utilises linear and quadratic magnetic fields to generate a harmonic potential (linear magnetic field) and a non-linear potential (non-linear/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.