Abstract
Quantum metrology with nonclassical states offers a promising route to improved precision in physical measurements. The quantum effects of Schr{\"o}dinger-cat superpositions or entanglements allow measurement uncertainties to reach below the standard quantum limit. However, the challenge in keeping a long coherence time for such nonclassical states often prevents full exploitation of the quantum advantage in metrology. Here we demonstrate a long-lived Schr{\"o}dinger-cat state of optically trapped ¹⁷³Yb (\textit{I}\ =\ 5/2) atoms. The cat state, a superposition of two oppositely-directed and furthest-apart spin states, is generated by a non-linear spin rotation. Protected in a decoherence-free subspace against inhomogeneous light shifts of an optical lattice, the cat state achieves a coherence time of 1.4(1)× 10³ s. A magnetic field is measured with Ramsey interferometry, demonstrating a scheme of Heisenberg-limited metrology for atomic magnetometry, quantum information processing, and searching for new physics beyond the Standard Model.