We investigate a two-dimensional matter-wave interferometer where both spatial and rotational dynamics of a nanoparticle are intertwined in closing the one-loop interferometer in the Stern-Gerlach type setup. We consider the spin-contrast of the nitrogen-vacancy (NV) centred nanodiamond in combination with a two-dimensional magnetic field setup to extend the one-dimensional Stern--Gerlach interferometry. We analyse the dynamical motion along with the rigid rotation under the influence of the external magnetic field. Regarding rotation, we incorporate Euler-angle dynamics to analyse the stability of rotational degrees of freedom and their influence on the spin contrast to address the Humpty-Dumpty problem. We show that by imparting external rotation provides the gyroscopic stability to the liberating mode of the NV-spin and hence helps to improve the contrast. Our scheme creates a tiny spatial superposition of size ∼0.21μm for mass m=10−17kg in less than t∼0.013s.
Cite
@article{arxiv.2603.05595,
title = {Two-dimensional matter-wave interferometer, rotational dynamics, and spin contrast},
author = {Ryan Rizaldy and Shrestha Mishra and Anupam Mazumdar},
journal= {arXiv preprint arXiv:2603.05595},
year = {2026}
}