  The standard quantum limit bounds the precision of measurements that can be
achieved by ensembles of uncorrelated particles. Fundamentally, this limit
arises from the non-commuting nature of quantum mechanics, leading to the
presence of fluctuations often referred to as quantum projection noise. Quantum
metrology relies on the use of non-classical states of many-body systems in
order to enhance the precision of measurements beyond the standard quantum
limit. To do so, one can reshape the quantum projection noise -- a strategy
known as squeezing. In the context of many-body spin systems, one typically
utilizes all-to-all interactions (e.g. the one-axis twisting model) between the
constituents to generate the structured entanglement characteristic of spin
squeezing. Motivated by recent theoretical work, here we explore the prediction
that short-range interactions -- and in particular, the two-dimensional dipolar
XY model -- can also enable the realization of scalable spin squeezing. Working
with a dipolar Rydberg quantum simulator of up to 100 atoms, we demonstrate
that quench dynamics from a polarized initial state lead to spin squeezing that
improves with increasing system size up to a maximum of -3.5 dB (prior to
correcting for detection errors, or approximately -5 dB after correction).
Finally, we present two independent refinements: first, using a multistep
spin-squeezing protocol allows us to further enhance the squeezing by
approximately 1 dB, and second, leveraging Floquet engineering to realize
Heisenberg interactions, we demonstrate the ability to extend the lifetime of
the squeezed state by freezing its dynamics.
