Theory of scalable spin squeezing with disordered quantum dipoles

Quantum-enhanced metrology with entangled states allows for sensing with precision beyond the classical limit. Recent results show that high sensitivity entangled states may be generated via "spin squeezing" using only coarse control in systems with continuous symmetry broken order. This presents a route to quantum-enhanced sensing with solid state defect ensembles. A significant hurdle is the deleterious effect of strong quenched disorder in these systems. We establish how disorder hinders spin squeezing in defect ensembles of quantum dipoles realizing an XXZ model in 2D. We determine the phase boundary for scalable spin squeezing, and find that as disorder increases, the squeezing phase occurs only for anisotropies close to the Heisenberg point. Our quantum Monte Carlo and analytic modeling attribute this effect to strongly interacting "dimers." We demonstrate the success of an experimentally feasible protocol to mitigate the impact of such dimers in nitrogen vacancy ensembles, thus establishing the feasibility of quantum-enhanced sensing with this platform.