# Engineering spin squeezing in a 3D optical lattice with interacting spin-orbit-coupled fermions

## TL;DR

This paper presents a novel protocol that uses inhomogeneities and interactions in a 3D optical lattice with spin-orbit-coupled fermions to generate robust, metrologically useful spin-squeezed states, enhancing quantum sensing.

## Contribution

It introduces a spin-locking protocol leveraging inhomogeneities and interactions to produce strong, robust spin squeezing in 3D optical lattice clocks, compatible with current technologies.

## Key findings

- Achieves 10-14 dB of spin squeezing in about 1 second.
- Proposes a method compatible with existing 3D optical lattice clock schemes.
- Demonstrates robustness of the protocol even with experimental imperfections.

## Abstract

One of the most important tasks in modern quantum science is to coherently control and entangle many-body systems, and to subsequently use these systems to realize powerful quantum technologies such as quantum-enhanced sensors. However, many-body entangled states are difficult to prepare and preserve since internal dynamics and external noise rapidly degrade any useful entanglement. Here, we introduce a protocol that counterintuitively exploits inhomogeneities, a typical source of dephasing in a many-body system, in combination with interactions to generate metrologically useful and robust many-body entangled states. Motivated by current limitations in state-of-the-art three-dimensional (3D) optical lattice clocks (OLCs) operating at quantum degeneracy, we use local interactions in a Hubbard model with spin-orbit coupling to achieve a spin-locking effect. In addition to prolonging inter-particle spin coherence, spin-locking transforms the dephasing effect of spin-orbit coupling into a collective spin-squeezing process that can be further enhanced by applying a modulated drive. Our protocol is fully compatible with state-of-the-art 3D OLC interrogation schemes and may be used to improve their sensitivity, which is currently limited by the intrinsic quantum noise of independent atoms. We demonstrate that even with realistic experimental imperfections, our protocol may generate $\sim10$--$14$ dB of spin squeezing in $\sim1$ second with $\sim10^2$--$10^4$ atoms. This capability allows OLCs to enter a new era of quantum enhanced sensing using correlated quantum states of driven non-equilibrium systems.