Controlling many-body entanglement promises to yield both fundamental insights and practical advances. In particular, generating squeezed states for entanglement-enhanced metrology is an important near-term application of quantum systems. In past work, squeezing has been achieved in a clean, controlled setting using all-to-all Ising interactions between ultracold atoms in an optical cavity. By contrast, optically-addressable spin defects in solids, such as the nitrogen-vacancy center in diamond, are far more practical and versatile sensors, but it is not known whether the requisite ingredients for generating and detecting squeezing are attainable in this platform.

In this talk, I will discuss two complementary approaches for generating squeezed states using XXZ interactions. The first approach centers around a cavity QED platform designed to realize programmable, nonlocal spin-spin couplings. Specifically, we implement an all-to-all XXZ Hamiltonian with tunable anisotropy, strength, and sign. Images of the resulting magnetization dynamics show that XXZ interactions protect spin coherence against spatial inhomogeneities, which may enhance the robustness of future spin-squeezing protocols.

The robustness of the XXZ model against disorder opens the door to squeezing via long-range dipolar interactions within an ensemble of spin defects in diamond, for which we identify and achieve the key required ingredients: (i) a theory that elucidates if and how power-law XXZ interactions generate squeezing; (ii) a two-dimensional ensemble of strongly-interacting, optically-polarizable spins; (iii) methods for detecting squeezing despite significant technical noise.