  Recent observations have successfully detected [O III] $88.3\,{\rm \mu m}$
and [C II] $157.6\,{\rm \mu m}$ lines from galaxies in the early Universe with
the Atacama Large Millimeter Array (ALMA). Combining cosmological hydrodynamic
simulations and radiative transfer calculations, we present relations between
the metal line emission and galaxy evolution at $z=6-15$. We find that galaxies
during their starburst phases have high [O III] luminosity of $\sim 10^{42}~\rm
erg~s^{-1}$. Once supernova feedback quenches star formation, [O III]
luminosities rapidly decrease and continue to be zero for $\sim 100\,{\rm
Myr}$. The slope of the relation between $\log{(\rm SFR/M_{\odot}~yr^{-1})}$
and $\log{(L_{\rm [O_{III}]}/{\rm L_{\odot}})}$ at $z=6-9$ is 1.03, and 1.43
for $\log{(L_{\rm [C_{II}]}/{\rm L_{\odot}})}$. As gas metallicity increases
from sub-solar to solar metallicity by metal enrichment from star formation and
feedback, the line luminosity ratio $L_{\rm [O_{III}]} / L_{\rm [C_{II}]}$
decreases from $\sim 10$ to $\sim 1$ because the O/C abundance ratio decreases
due to carbon-rich winds from AGB stars and the mass ratio of {\sc H\,ii} to
{\sc H\,i} regions decreases due to rapid recombination. Therefore, we suggest
that the combination of [O III] and [C II] lines is a good probe to investigate
the relative distribution of ionized and neutral gas in high-$z$ galaxies. In
addition, we show that deep [C II] observations with a sensitivity of $\sim
10^{-2}~{\rm mJy~arcsec^{-2}}$ can probe the extended neutral gas disks of
high-$z$ galaxies.
