A Universal Theory of Spin Squeezing

Quantum metrology makes use of many-body entangled states to perform measurements with greater precision than would be possible using only classically correlated particles. Discerning states suitable for quantum metrology is a delicate challenge: nearly all states in Hilbert space are highly entangled, but nearly none of them exhibit the structured entanglement required for enhanced sensing. Identifying universal principles for finding metrologically-useful states remains an important challenge, especially in the context of efficiently preparing such states from unentangled product states. One such principle stems from the observation that the metrological gain from a pure state is fundamentally connected to spontaneous symmetry breaking. In this work, we apply this principle to the case of U(1) symmetry breaking and provide extensive numerical and analytic evidence for the following conjecture: Finite temperature easy-plane ferromagnetism (i.e. XY magnets) enables scalable spin squeezing. In particular, we consider the quench dynamics of a low-energy initial state and show it undergoes squeezing as a precursor to the equilibration of long-range order. Our main results are threefold. First, we establish a phase diagram for spin-squeezing, with a sharp transition distinguishing scalable squeezing from non-squeezing. Second, we demonstrate that this transition precisely coincides with the phase boundary for finite temperature XY order. Finally, we show that the squeezing manifests a novel scaling with system size that leads to a sensitivity ~ N^-7/10, in between the standard quantum limit ~ N^-1/2 and the Heisenberg limit ~ N^-1.