  We study the quantum critical effect enhanced spin-nematic squeezing and
quantum Fisher information (QFI) in the spin-1 dipolar atomic Bose-Einstein
condensate. We show that the quantum phase transitions can improve the
squeezing and QFI in the nearby regime of critical point, and the
Heisenberg-limited high-precision metrology can be obtained. The different
properties of the ground squeezing and entanglement under even and odd number
of atoms are further analyzed, by calculating the exact analytical
expressions.We also demonstrate the squeezing and entanglement generated by the
spin-mixing dynamics around the phase transition point. It is shown that the
steady squeezing and entanglement can be obtained, and the Bogoliubov
approximation can well describe the dynamics of spin-nematic squeezed vacuum
state.
