Ultrafast neutral-atom entangling gate via collective ultrastrong coupling

We present a high-speed neutral-atom entangling gate enabled by collective coupling to a shared bosonic mode in the ultrastrong regime. Unlike Rydberg blockade or measurement-based schemes, this protocol uses strong, tunable spin–boson interactions beyond the rotating-wave approximation to generate an effective quadratic spin coupling $(J_x)^2$. At specific disentangling times, the dynamics produce Bell, GHZ, or spin-squeezed states while the bosonic field acquires only a global phase. The gate time $t_\mathrm{gate} $ scales inversely with the coupling strength $G$, allowing ultrafast operation before decoherence acts. Analytical and numerical results show robustness against detuning and dephasing, with fidelities remaining high for realistic parameters where $G/\omega \gtrsim 0.1\!-\!1$. The approach extends neutral-atom quantum computing to the ultrastrong-coupling frontier, enabling deterministic multiqubit entanglement and macroscopic state engineering for scalable quantum technologies.