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We present MUSE/VLT imaging spectroscopy of rest-frame ultraviolet emissionlines and ALMA observations of the [CI] $^3$P$_1$-$^3$P$_0$ emission line,probing both the ionized and diffuse molecular medium around the radio galaxy4C 19.71 at z~3.6. This radio galaxy has extended Ly$\alpha$ emission over aregion ~100 kpc in size preferentially oriented along the axis of the radiojet. Faint Ly$\alpha$ emission extends beyond the radio hot spots. We also findextended CIV and HeII emission over a region of ~150 kpc in size, where themost distant emission lies ~40 kpc beyond the north radio lobe and has narrowFWHM line widths of ~180 km/s and a small relative velocity offset$\Delta$v~130 km/s from the systemic redshift of the radio galaxy. The [CI] isdetected in the same region with FWHM~100 km/s and $\Delta$v~5 km/s, while [CI]is not detected in the regions south of the radio galaxy. We interpret thecoincidence in the northern line emission as evidence of relatively quiescentmulti-phase gas residing within the halo at a projected distance of ~75 kpcfrom the host galaxy. To test this hypothesis, we performed photoionization andphoto-dissociated region (PDR) modeling, using the code Cloudy, of the threeemission line regions: the radio galaxy proper and the northern and southernregions. We find that the [CI]/CIV$\lambda\lambda$1548,1551 andCIV$\lambda\lambda$1548,1551/HeII ratios of the two halo regions are consistentwith a PDR or ionization front in the circumgalactic medium likely energized byphotons from the active galactic nuclei. This modeling is consistent with arelatively low metallicity, 0.03<[Z/Z$_{\odot}$]<0.1, and diffuse ionizationwith an ionization parameter (proportional to the ratio of the photon numberdensity and gas density) of log U~3 for the two circumgalactic line emissionregions. Using rough mass estimates for the molecular [...]

ALMA and MUSE observations reveal a quiescent multi-phase circumgalactic medium around the z~3.6 radio galaxy 4C 19.71