We generate spin squeezed ground states in an atomic spin-1 Bose-Einstein condensate tuned near the quantum critical point between the polar and ferromagnetic quantum phases of the interacting spin ensemble. In contrast to typical non-equilibrium methods for preparing atomic squeezed states by quenching through a quantum phase transition, squeezed ground states are time-stationary and remain squeezed for the lifetime of the condensate. A squeezed ground state with a metrological improvement up to 6-8 dB and a constant squeezing angle maintained over 2 s is demonstrated.

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