  We present a detailed study of the molecular gas content and stellar
population properties of three massive galaxies at 1 < z < 1.3 that are in
different stages of quenching. The galaxies were selected to have a quiescent
optical/near-infrared spectral energy distribution and a relatively bright
emission at 24 micron, and show remarkably diverse properties. CO emission from
each of the three galaxies is detected in deep NOEMA observations, allowing us
to derive molecular gas fractions Mgas/Mstar of 13-23%. We also reconstruct the
star formation histories by fitting models to the observed photometry and
optical spectroscopy, finding evidence for recent rejuvenation in one object,
slow quenching in another, and rapid quenching in the third system. To better
constrain the quenching mechanism we explore the depletion times for our sample
and other similar samples at z~0.7 from the literature. We find that the
depletion times are highly dependent on the method adopted to measure the star
formation rate: using the UV+IR luminosity we obtain depletion times about 6
times shorter than those derived using dust-corrected [OII] emission. When
adopting the star formation rates from spectral fitting, which are arguably
more robust, we find that recently quenched galaxies and star-forming galaxies
have similar depletion times, while older quiescent systems have longer
depletion times. These results offer new, important constraints for physical
models of galaxy quenching.
