  Massive quiescent galaxies in the young universe are expected to be quenched
rapidly, but it is unclear whether they all experience starbursts before
quenching and what physical mechanism drives rapid quenching. We study 16
massive quiescent galaxies ($\log(M_\star/M_\odot) > 10$) at $z\sim2$ selected
from a representative sample of the Blue Jay survey. We reconstruct their star
formation histories by fitting spectral energy distribution models to the
JWST/NIRSpec $R\sim1000$ spectra. We find that massive quiescent galaxies can
be split into three categories with roughly equal numbers of galaxies according
to their SFHs: 1) Relatively old galaxies quenched at early epochs; 2) Galaxies
that are rapidly and recently quenched after a flat or bursty formation history
(depending on the assumed prior); 3) Galaxies that are rapidly and recently
quenched after a major starburst. Most recently quenched galaxies show neutral
gas outflows, probed by blueshifted $\rm Na\,I\,D$ absorption, and ionized gas
emission, with line ratios consistent with active galactic nucleus (AGN)
diagnostics. This suggests that AGN activity drives multi-phase gas outflows,
leading to rapid quenching. By tracing back the SFHs of the entire sample, we
predict the number density of massive quiescent galaxies at $z=4-6$:
$n=3.0\pm1.4\times10^{-5}\,\rm Mpc^{-3}$. The two oldest massive quiescent
galaxies in our sample appear to have extremely early formation and quenching
($z\gtrsim6$), possibly descendants of early post-starbursts at $z>3$. These
galaxies still show neutral gas reservoirs and low-level star formation,
consistent with weak H$\alpha$ emission, perhaps because the ejective AGN
feedback that caused rapid quenching has weakened over time.
