Gap-Protected Quantum Sensing with Hyperfine and Clock Levels

Optical lattice clocks based on ultranarrow optical transitions are among the most precise sensors ever realized. Yet despite their exquisite performance, state-of-the-art clocks still operate with coherent spin states, leaving a major opportunity for quantum-enhanced metrology. A unique feature of leading clock atoms such as 87Sr is that, beyond the two clock states, each manifold contains a large hyperfine (nuclear-spin) structure that remains largely unused during clock operation. Here we propose to turn these “idle” hyperfine states into a resource for metrologically useful entanglement. Our central idea is to leverage the naturally present orbital–nuclear spin coupling within each atom and convert it into a collective entangling operation in the presence of a many-body energy gap generated by cavity-mediated interactions. Within this gap-protected collective subspace, we design an echo-based protocol that maps and amplifies a small optical phase imprinted on the clock pseudo-spins onto the hyperfine degrees of freedom, enabling enhanced readout after time reversal of the dynamics. In principle, this approach yields a signal-to-noise ratio with Heisenberg-like scaling, opening a route toward entanglement-enhanced optical clocks.