  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.
