Red quasars blow out molecular gas from galaxies during the peak of cosmic star formation

Recent studies have suggested that red quasars are a phase in quasar evolution when feedback from black hole accretion evacuates obscuring gas from the nucleus of the host galaxy. Here, we report a direct link between dust-reddening and molecular outflows in quasars at $z\sim2.5$. By examining the dynamics of warm molecular gas in the inner region of galaxies, we detect outflows with velocities 500--1000 km s$^{-1}$ and infer timescales of $\approx0.1$ Myr that are due to ongoing quasar energy output. We observe outflows only in systems where quasar radiation pressure on dust in the vicinity of the black hole is sufficiently large to expel their obscuring gas column densities. This result is in agreement with theoretical models that predict radiative feedback regulates gas in the nuclear regions of galaxies and is a major driving mechanism of galactic-scale outflows of cold gas. Our findings suggest that radiative quasar feedback ejects star-forming gas from within nascent stellar bulges at velocities comparable to those seen on larger scales, and that molecules survive in outflows even from the most luminous quasars.