Now you see it, now you don't: Star formation truncation precedes the
  loss of molecular gas by ~100 Myr in massive post-starburst galaxies at z~0.6
  We use ALMA observations of CO(2-1) in 13 massive ($M_{\star}\gtrsim 10^{11}
M_{\odot}$) post-starburst galaxies at $z\sim0.6$ to constrain the molecular
gas content in galaxies shortly after they quench their major star-forming
episode. The post-starburst galaxies in this study are selected from the Sloan
Digital Sky Survey spectroscopic samples (DR14) based on their spectral shapes,
as part of the SQuIGGLE program. Early results showed that two post-starburst
galaxies host large H$_2$ reservoirs despite their low inferred star formation
rates. Here we expand this analysis to a larger statistical sample of 13
galaxies. Six of the primary targets (45%) are detected, with
$M_{H_2}\gtrsim10^9 M_{\odot}$. Given their high stellar masses, this mass
limit corresponds to an average gas fraction of $\langle f_{H_2} \equiv
M_{H_2}/M_{\star} \rangle \sim7\%$, or ${\sim}14\%$ using lower stellar masses
estimates derived from analytic, exponentially declining star formation
histories. The gas fraction correlates with the $D_n4000$ spectral index,
suggesting that the cold gas reservoirs decrease with time since burst, as
found in local K+A galaxies. Star formation histories derived from flexible
stellar population synthesis modeling support this empirical finding: galaxies
that quenched $\lesssim 150$ Myr prior to observation host detectable CO(2-1)
emission, while older post-starburst galaxies are undetected. The large
$\mathrm{H_2}$ reservoirs and low star formation rates in the sample imply that
the quenching of star formation precedes the disappearance of the cold gas
reservoirs. However, within the following 100-200 Myrs, the SQuIGGLE galaxies
require the additional and efficient heating or removal of cold gas to bring
their low star formation rates in line with standard $\mathrm{H_2}$ scaling
relations.
