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Neutral-atom arrays trapped in optical potentials are a powerful platform forstudying quantum physics, combining precise single-particle control anddetection with a range of tunable entangling interactions. For example, thesecapabilities have been leveraged for state-of-the-art frequency metrology aswell as microscopic studies of entangled many-particle states. In this work, wecombine these applications to realize spin squeezing - a widely studiedoperation for producing metrologically useful entanglement - in an opticalatomic clock based on a programmable array of interacting optical qubits. Inthis first demonstration of Rydberg-mediated squeezing with a neutral-atomoptical clock, we generate states that have almost 4 dB of metrological gain.Additionally, we perform a synchronous frequency comparison between independentsqueezed states and observe a fractional frequency stability of $1.087(1)\times10^{-15}$ at one-second averaging time, which is 1.94(1) dB below the standardquantum limit, and reaches a fractional precision at the $10^{-17}$ levelduring a half-hour measurement. We further leverage the programmable controlafforded by optical tweezer arrays to apply local phase shifts in order toexplore spin squeezing in measurements that operate beyond the relativecoherence time with the optical local oscillator. The realization of thisspin-squeezing protocol in a programmable atom-array clock opens the door to awide range of quantum-information inspired techniques for optimal phaseestimation and Heisenberg-limited optical atomic clocks.

Realizing spin squeezing with Rydberg interactions in a programmable optical clock