We have imaged CO(J=7-6) and CI(3P2-3P1) emission in the host galaxy of the z=6.42 quasar SDSS J114816.64+525150.3 (hereafter: J1148+5251) through observations with the Plateau de Bure Interferometer. The region showing CO(J=7-6) emission is spatially resolved, and its size of 5 kpc is in good agreement with earlier CO(J=3-2) observations. In combination with a revised model of the collisional line excitation in this source, this indicates that the highly excited molecular gas traced by the CO J=7-6 line is subthermally excited (showing only 58+/-8% of the CO J=3-2 luminosity), but not more centrally concentrated. We also detect CI(3P2-3P1) emission in the host galaxy of J1148+5251, but the line is too faint to enable a reliable size measurement. From the CI(3P2-3P1) line flux, we derive a total atomic carbon mass of M_CI=1.1x10^7 M_sun, which corresponds to ~5x10^-4 times the total molecular gas mass. We also searched for H2O(J_KaKc=2_12-1_01) emission, and obtained a sensitive line luminosity limit of L_H2O<4.4x10^9 K kms pc^2, i.e., <15% of the CO(J=3-2) luminosity. The warm, highly excited molecular gas, atomic gas and dust in this quasar host at the end of cosmic reionization maintain an intense starburst that reaches surface densities as high as predicted by (dust opacity) Eddington limited star formation over kiloparsec scales.
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