  OH+ absorption is a powerful tracer of inflowing and outflowing gas in the
predominantly atomic diffuse and turbulent halo surrounding galaxies. In this
letter, we present observations of OH+(1_1-1_0), CO(9-8) and the underlying
dust continuum in 5 strongly lensed z~2-4 QSOs, using ALMA to detect outflowing
neutral gas. Blue-shifted OH+ absorption is detected in 3/5 QSOs and
tentatively detected in a 4th. Absorption at systemic velocities is also
detected in one. OH+ emission is observed in 3/5 QSOs at systemic velocities
and CO(9-8) is detected in all 5 QSOs at high S/N, providing information on the
dense molecular gas within the host galaxy. We compare our sample to high-z
far-infrared (FIR) luminous star-forming and active galaxies from the
literature. We find no difference in OH+ absorption line properties between
active and star-forming galaxies with both samples following the same optical
depth-dust temperature relation, suggesting that these observables are driven
by the same mechanism in both samples. Similarly, star-forming and active
galaxies both follow the same OH+ emission-FIR relation. Obscured QSOs display
broader (>800 km/s) emission than the unobscured QSOs and all but one of the
high-z star-forming galaxies, likely caused by the warm molecular gas reservoir
obscuring the accreting nucleus. Broader CO(9-8) emission (>500 km/s) is found
in obscured versus unobscured QSOs, but overall cover a similar range in line
widths as the star-forming galaxies and follow the CO(9-8)-FIR luminosity
relation found in low-z galaxies. We find that outflows traced by OH+ are only
detected in extreme star-forming galaxies (broad CO emission) and in both types
of QSOs, which, in turn, display no red-shifted absorption. This suggests that
diffuse neutral outflows in galaxy halos may be associated with the most
energetic evolutionary phases leading up to and following the obscured QSO
phase.
