Optimal Control of Spin Squeezing in 2D Finite-Range Interacting Systems

TL;DR

This paper develops an optimal control method for enhancing spin squeezing in 2D finite-range interacting systems, surpassing traditional benchmarks and maintaining robustness under realistic conditions.

Contribution

It introduces a scalable rotor-spin-wave control strategy that significantly improves spin squeezing in 2D dipolar systems, enabling practical quantum metrology applications.

Findings

Achieved squeezing beyond the two-axis-twisting benchmark.

Single collective transverse field optimization suffices for enhancement.

Control protocol remains effective under noise and open boundary conditions.

Abstract

Spin squeezing serves as both a fundamental witness of quantum entanglement and a critical resource for quantum-enhanced metrology. While generating substantial spin squeezing in finite-range interacting systems remains challenging, such capability is important for advancing quantum technologies. In this work, we develop an optimal control strategy for achieving enhanced spin squeezing in a two-dimensional XX model with dipolar interactions. Leveraging rotor-spin-wave theory for periodic boundary conditions, we circumvent computational bottlenecks to explore control strategies at unprecedented scales. Remarkably, optimizing a single collective transverse field is sufficient to achieve substantial squeezing enhancement, exceeding the two-axis-twisting benchmark. The optimized control field achieves this breakthrough by dynamically suppressing inter-subspace mixing induced by the finite-range interactions, thereby confining the system evolution predominantly within the maximal spin subspace. We further extend rotor-spin-wave theory to open boundary conditions and incorporate dephasing noise, providing a scalable framework for realistic systems. Under these conditions, the optimized protocol remains effective, highlighting its robustness and suitability for experimental implementation.