Molecular Gas Inflows and Outflows in Ultraluminous Infrared Galaxies at
  $z\sim0.2$ and one QSO at $z=6.1$
  Aims. We aim to search and characterize inflows and outflows of molecular gas
in four ultraluminous infrared galaxies (ULIRGs) at $z\sim0.2-0.3$ and one
distant QSO at $z=6.13$.
  Methods. We use Herschel PACS and ALMA Band 7 observations of the hydroxyl
molecule (OH) line at rest-frame wavelength 119 $\mu$m which in absorption can
provide unambiguous evidence for inflows or outflows of molecular gas in
nuclear regions of galaxies. Our study contributes to double the number of OH
observations of luminous systems at $z\sim0.2-0.3$, and push the search for
molecular outflows based on the OH transition to $z\sim6$.
  Results. We detect OH high-velocity absorption wings in three of the four
ULIRGs. In two cases, IRAS F20036-1547 and IRAS F13352+6402, the blueshifted
absorption profiles indicate the presence of powerful and fast molecular gas
outflows. Consistent with an inside-out quenching scenario, these outflows are
depleting the central reservoir of molecular gas at a similar rate than the
intense star formation activity. In the case of the starburst-dominated system
IRAS 10091+4704, we detect an inverted P-Cygni profile that is unique among
ULIRGs and indicates the presence of a fast ($\sim400$ km s$^{-1}$) inflow of
molecular gas at a rate of $\sim100~M_{\odot}~{\rm yr}^{-1}$ towards the
central region. Finally, we tentatively detect ($\sim3\sigma$) the OH doublet
in absorption in the $z=6.13$ QSO ULAS J131911+095051. The OH feature is
blueshifted with a median velocity that suggests the presence of a molecular
outflow, although characterized by a modest molecular mass loss rate of
$\sim200~M_{\odot}~{\rm yr}^{-1}$. This value is comparable to the small mass
outflow rates found in the stacking of the [CII] spectra of other $z\sim6$ QSOs
and suggests that ejective feedback in this phase of the evolution of ULAS
J131911+095051 has subsided.
