Towards Spin Squeezing in a Two-dimensional Ensemble of Nitrogen-Vacancy Centers

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 spin ensemble of nitrogen vacancy (NV) centers in a [111]-cut diamond. We work with the NV centers quantized along the out-of-plane direction, which evolves freely under the intrinsic dipole-dipole interaction to generate the spin squeezed states . Reduction of the spin projection noise can be probed via relaxometry of another group of NV centers, allowing a diagnosis of squeezing without sub-shot-noise detection resolution. Because the angular average of the dipolar interaction is zero in three dimensions, our two-dimensional sample uniquely enables squeezing via native interactions in a solid-state spin ensemble.