  The Greenberger-Horne-Zeilinger (GHZ) state is a key resource for quantum
information processing and quantum metrology. The atomic GHZ state can be
generated by one-axis twisting (OAT) interaction $H_{\mathrm{OAT}}=\chi
J_{z}^{2}$ with $\chi $ the interaction strength, but it requires a long
evolution time $\chi t=\pi /2$ and is thus seriously influenced by decoherence
and losses. Here we propose a three-body collective-spin XYZ model which
creates a GHZ-like state in a very short timescale $\chi t\sim \ln {N}/N$ for
$N$ particles. We show that this model can be effectively produced by applying
Floquet driving to an original OAT Hamiltonian. Compared with the ideal GHZ
state, the GHZ-like state generated using our model can maintain similar
metrological properties reaching the Heisenberg-limited scaling, and it shows
better robustness to decoherence and particle losses. This work opens the
avenue for generating GHZ-like states with a large particle number, which holds
great potential for the study of macroscopic quantum effects and for
applications in quantum metrology and quantum information.
