Fast and Robust Entanglement of Locally Interacting Spins for Quantum Sensing

We propose a fast and robust dynamical approach to spin squeezing with local interactions, employing a gap-protected countertwisting Hamiltonian, which adds a Heisenberg interaction term to an analog of the canonical two-axis countertwisting (TACT) Hamiltonian. The squeezing is robust against interaction-induced dephasing, and is therefore able to leverage the exponentially fast squeezing and Heisenberg scaling of all-to-all TACT. Moreover, it may be implemented by Floquet engineering using only Ising or spin-exchange interactions of a single sign, opening the door to applications in near-term experiments with Rydberg atoms, cold molecules, or solid-state spins. We demonstrate numerically that both the squeezing and the full metrological gain, attainable through an echo protocol, exhibit a Heisenberg scaling below a critical value of the power-law exponent that depends on dimensionality and increases with the strength of gap protection. Furthermore, we provide a general theoretical framework for studying spin squeezing Hamiltonians, based on a spin-wave analysis of the early-time squeezing dynamics of a generic XYZ model. This motivates our focus on gap-protected countertwisting, which enables resonant parametric amplification of zero-momentum spin waves, while suppressing excitation of higher-momentum modes.