Multi-qubit gates and Schrödinger cat states in an optical clock.

Many-particle entanglement is a key resource for achieving the fundamental precision limits of a quantum sensor. Optical atomic clocks, the current state of the art in frequency precision, are a rapidly emerging area of focus for entanglement-enhanced metrology. Augmenting tweezer-based clocks featuring microscopic control and detection with the high-fidelity entangling gates developed for atom-array information processing offers a promising route towards making use of highly entangled quantum states for improved optical clocks. Here we develop and use a family of multi-qubit Rydberg gates to generate Schrödinger cat states of the Greenberger-Horne-Zeilinger (GHZ) type with up to nine optical clock qubits in a programmable atom array. In an atom-laser comparison at sufficiently short dark times, we demonstrate a fractional frequency instability below the standard quantum limit (SQL) using GHZ states of up to four qubits. However, because of their reduced dynamic range, GHZ states of a single size fail to improve the achievable clock precision at the optimal dark time compared with unentangled atoms. Towards overcoming this hurdle, we simultaneously prepare a cascade of varying-size GHZ states to perform unambiguous phase estimation over an extended interval. These results demonstrate key building blocks for approaching Heisenberg-limited scaling of optical atomic clock precision.