Gap-Protected Heisenberg-Limited Squeezing with Locally Interacting Multi-Level Spins
Abstract
We demonstrate a general mechanism to generate scalable, metrologically useful entanglement in the form of generalized spin squeezing in multi-level (qudit) spin systems with power-law interactions. We demonstrate this for spin-changing dynamics, extending the physics of spin-nematic squeezing known from spinor BECs to spatially extended lattice geometries. In the absence of all-to-all connectivity, the dynamics generally suffers from leakage into non-collective finite-momentum modes, destroying Heisenberg scaling. We show that introducing local su(D) exchange interactions establishes an energy gap that protects the fully symmetric collective manifold, suppressing non-collective excitations, and achieving Heisenberg scaling ξ2∝1/N in one to three dimensions for any power-law exponent. We provide an analytical understanding of the mechanism via the analysis of the Bogoliubov excitation spectrum, and demonstrate its effectiveness via numerical simulations of the quantum many-body dynamics. Our findings more broadly apply to other spin-squeezing Hamiltonians, and directly generalize to larger internal spin dimensions. Our results provide a practical pathway towards scalable Heisenberg-limited qudit entanglement generation in experimental platforms such as arrays of (polar) molecules, magnetic atoms, and Rydberg atoms realizing multi-level spin systems.
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BibTeX
@misc{bahamnia2026gapprotected,
title = {{Gap-Protected Heisenberg-Limited Squeezing with Locally Interacting Multi-Level Spins}},
author = {Sakshi Bahamnia and Sagar Chaudhary and Arman Duha and Thomas Bilitewski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02314},
eprint = {2610.02314},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02314},
note = {CC0},
}
RIS
TY - UNPB
TI - Gap-Protected Heisenberg-Limited Squeezing with Locally Interacting Multi-Level Spins
AU - Sakshi Bahamnia
AU - Sagar Chaudhary
AU - Arman Duha
AU - Thomas Bilitewski
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.02314
UR - https://arxiv.org/abs/2610.02314
AB - We demonstrate a general mechanism to generate scalable, metrologically useful entanglement in the form of generalized spin squeezing in multi-level (qudit) spin systems with power-law interactions. We demonstrate this for spin-changing dynamics, extending the physics of spin-nematic squeezing known from spinor BECs to spatially extended lattice geometries. In the absence of all-to-all connectivity, the dynamics generally suffers from leakage into non-collective finite-momentum modes, destroying Heisenberg scaling. We show that introducing local su(D) exchange interactions establishes an energy gap that protects the fully symmetric collective manifold, suppressing non-collective excitations, and achieving Heisenberg scaling ξ^2∝1/N in one to three dimensions for any power-law exponent. We provide an analytical understanding of the mechanism via the analysis of the Bogoliubov excitation spectrum, and demonstrate its effectiveness via numerical simulations of the quantum many-body dynamics. Our findings more broadly apply to other spin-squeezing Hamiltonians, and directly generalize to larger internal spin dimensions. Our results provide a practical pathway towards scalable Heisenberg-limited qudit entanglement generation in experimental platforms such as arrays of (polar) molecules, magnetic atoms, and Rydberg atoms realizing multi-level spin systems.
ER -