  We generate high-fidelity massively entangled states in an antiferromagnetic
spin-1 Bose-Einstein condensate (BEC) by utilizing multilevel oscillations.
Combining the multilevel oscillations with additional adiabatic drives, we
greatly shorten the necessary evolution time and relax the requirement on the
control accuracy of quadratic Zeeman splitting, from micro-Gauss to
milli-Gauss, for a $^{23}$Na spinor BEC. The achieved high fidelities over
$96\%$ show that two kinds of massively entangled states, the many-body singlet
state and the twin-Fock state, are almost perfectly generated. The generalized
spin squeezing parameter drops to a value far below the standard quantum limit
even with the presence of atom number fluctuations and stray magnetic fields,
illustrating the robustness of our protocol under real experimental conditions.
The generated many-body entangled states can be employed to achieve the
Heisenberg-limit quantum precision measurement and to attack nonclassical
problems in quantum information science.
