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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 withthe Atacama Large Millimeter Array (ALMA). Combining cosmological hydrodynamicsimulations and radiative transfer calculations, we present relations betweenthe metal line emission and galaxy evolution at $z=6-15$. We find that galaxiesduring their starburst phases have high [O III] luminosity of $\sim 10^{42}~\rmerg~s^{-1}$. Once supernova feedback quenches star formation, [O III]luminosities rapidly decrease and continue to be zero for $\sim 100\,{\rmMyr}$. 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 1.43for $\log{(L_{\rm [C_{II}]}/{\rm L_{\odot}})}$. As gas metallicity increasesfrom sub-solar to solar metallicity by metal enrichment from star formation andfeedback, 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 decreasesdue 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 suggestthat the combination of [O III] and [C II] lines is a good probe to investigatethe relative distribution of ionized and neutral gas in high-$z$ galaxies. Inaddition, we show that deep [C II] observations with a sensitivity of $\sim10^{-2}~{\rm mJy~arcsec^{-2}}$ can probe the extended neutral gas disks ofhigh-$z$ galaxies.

Starbursting [O III] emitters and quiescent [C II] emitters in the reionization era