  Many massive quiescent galaxies have been discovered at $z>2$ thanks to
multi-wavelength deep and wide surveys, however, substantial deep near-infrared
spectroscopic observations are needed to constrain their star-formation
histories statistically. Here, we present a new technique to select quiescent
galaxies with a short quenching timescale ($\leq0.1$ Gyr) at $z\sim2$
photometrically. We focus on a spectral break at $\sim1600$ \AA~that appears
for such fast-quenching galaxies $\sim1$ Gyr after quenching when early A-type
stars go out, but late A-type stars still live. This spectral break at $z\sim2$
is similar to a Lyman break at $z\sim4$. We construct a set of color criteria
for $z\sim2$ fast-quenching galaxies on $g-r$ vs. $r-i$ and $i-J$ vs. $J-H$ or
$\rm i-[3.6]$ vs. $\rm [3.6]-[4.5]$ color diagrams, which are available with
the existing and/or future wide imaging surveys, by simulating various model
galaxy spectra and test their robustnesses using the COSMOS2020 catalog.
Galaxies with photometric and/or spectroscopic redshifts $z\sim2$ and low
specific star formation rates are successfully selected using these colors. The
number density of these fast-quenching galaxy candidates at $z\sim2$ suggests
that massive galaxies not so far above the star-formation main sequence at
$z=3-4$ should be their progenitors.
