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Observing the interstellar medium (ISM) in $z \gtrsim 6$ quasars host galaxies is essential for understanding the co-evolution between the supermassive black holes and their hosts. To probe the gas physical conditions and search for imprints of Active Galactic Nuclei (AGN) on the ISM, we report ALMA observations of the $\rm [N\ II]_{122 \mu m}$ and $\rm [O\ I]_{146 \mu m}$ lines and the underlying continuum from the $z=6.003$ quasar SDSS J231038.88+185519.7. Together with previous $\rm [C\ II]_{158 \mu m}$ and $\rm [O\ III]_{88 \mu m}$ observations, we use the ratios of these fine-structure lines to probe the ISM properties. Similar to other high-$z$ systems, this object exhibits a $\rm [C\ II]_{158 \mu m}$/$\rm [O\ I]_{146 \mu m}$ ratio comparable to the lowest values found in local (Ultra) luminous infrared galaxies, suggesting a "warmer" and "denser" gas component compared to typical local systems. The $\rm [O\ III]_{88 \mu m}$/$\rm [O\ I]_{146 \mu m}$ ratio is lower than that of other local and high-$z$ systems, indicating a smaller ionized gas fraction in this quasar. The $\rm [O\ III]_{88 \mu m}$/$\rm [N\ II]_{122 \mu m}$ ratio is comparable to that of local systems, and suggests a metallicity of $Z/Z_{\odot}$=1.5$-$2.1. Based on the $\rm [N\ II]_{122 \mu m}$ detection, we estimate that $17\%$ of the $\rm [C\ II]_{158 \mu m}$ emission is associated with ionized gas. The $\rm [N\ II]_{122 \mu m}$ line shows a "flux deficit" comparable to local systems. The $\rm [O\ I]_{146 \mu m}$ line, with a $\rm [O\ I]_{146 \mu m}$/FIR ratio $\ge 2\times$ than expected from the local relation, indicates no $\rm [O\ I]_{\rm 146 \mu m}$ deficit. The low $\rm [C\ II]_{158 \mu m}$/$\rm [O\ I]_{146 \mu m}$ ratio, together with the high $\rm [O\ I]_{146 \mu m}$/FIR ratio in J2310+1855, reveals that the warm and dense gas is likely a result of AGN heating to the ISM.

Ionized and Atomic Interstellar Medium in the z = 6.003 Quasar SDSS J2310+1855