Towards spin squeezing in a two-dimensional dipolar spin system

Using entangled states to enhance quantum metrology represents an exciting near-term application for NISQ hardware. In particular, spin-squeezed states have been demonstrated to enhance phase resolution beyond the standard quantum limit. Generating squeezed states via unitary evolution traditionally requires all-to-all Ising interactions, whereas native interactions on a variety of platforms are typically local. Recently, squeezing via a broader class of power-law XXZ Hamiltonians has been explored numerically, motivating experimental investigations of squeezing with dipolar interactions. Our platform consists of a two-dimensional hybrid spin ensemble of nitrogen vacancy (NV) and substitutional nitrogen (P1) centers in diamond. The dilute NV probe spins are used to spin-polarize the surrounding P1 ensemble, which subsequently evolves freely under the intrinsic dipole-dipole interaction. Distortions of the P1 spin projection noise alter the decoherence profile of the NV probe spins, allowing a diagnosis of squeezing without sub-shot-noise detection resolution. Because the angular average of the dipolar coefficient is zero in three dimensions, our two-dimensional sample uniquely enables squeezing via native interactions in a solid-state spin ensemble.