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 task: 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 a long-standing 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 analytical 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. In particular, we establish a phase diagram for spin-squeezing, and demonstrate that the phase transition precisely coincides with the phase boundary for finite-temperature XY order. Moreover, we show that the squeezing manifests a novel scaling with system size that leads to a sensitivity ∼ N- 10 7 , in between the standard quantum limit ∼ N- 1 2 and the Heisenberg limit ∼ N-1. Finally, I will present two experimental pursuits to realize scalable spin squeezing. In a 87Rb atom tweezer array, we observe scalable spin squeezing with the presence of dipolar XY interaction. Recently developed technique to implant nitrogenvacancy defects in a 2D layer may also enable scalable squeezing in solid state systems, which paves a more practical way to implement spin squeezing in real-life quantum sensing.
Bingtian is a physics PhD candidate at Harvard University, advised by Prof. Norman Y. Yao. He received his Bachelor’s degree in physics from Peking University. His research lies at the interface between condensed matter theory and atomic, molecular and optical theory. He is particularly interested in non-equilibrium dynamics of quantum systems.