Neutral-atom arrays trapped in optical potentials are a powerful platform for
studying quantum physics, combining precise single-particle control and
detection with a range of tunable entangling interactions. For example, these
capabilities have been leveraged for state-of-the-art frequency metrology as
well as microscopic studies of entangled many-particle states. In this work, we
combine these applications to realize spin squeezing - a widely studied
operation for producing metrologically useful entanglement - in an optical
atomic clock based on a programmable array of interacting optical qubits. In
this first demonstration of Rydberg-mediated squeezing with a neutral-atom
optical clock, we generate states that have almost 4 dB of metrological gain.
Additionally, we perform a synchronous frequency comparison between independent
squeezed states and observe a fractional frequency stability of 1.087(1)×10−15 at one-second averaging time, which is 1.94(1) dB below the standard
quantum limit, and reaches a fractional precision at the 10−17 level
during a half-hour measurement. We further leverage the programmable control
afforded by optical tweezer arrays to apply local phase shifts in order to
explore spin squeezing in measurements that operate beyond the relative
coherence time with the optical local oscillator. The realization of this
spin-squeezing protocol in a programmable atom-array clock opens the door to a
wide range of quantum-information inspired techniques for optimal phase
estimation and Heisenberg-limited optical atomic clocks.Comment: 13 pages, 4 figures; Supplementary Informatio