used the CO (1–0) and CO (2–1) lines as tracers. The CO (1–0) line is sensitive to molecular gas at densities $\sim 100$ cm$^{-3}$. Other molecules, such as HCN (1–0) and HCO$^+$ (1–0), trace denser gas. The critical densities of HCN (1–0) and HCO$^+$ (1–0) are $3\times10^6$ cm$^{-3}$ and $2\times10^5$ cm$^{-3}$ [e.g., @Juneau2009], although they are also sensitive to less dense gas, with effective excitation densities of $8.4\times10^3$ cm$^{-3}$ and $950$ cm$^{-3}$, respectively [@Shirley2015]. The HCN (1–0) luminosity correlates more linearly with SFR, and with less scatter, than does the CO (1–0) luminosity [@Gao2004], even down to the scales of star-forming clumps [@Wu2005; @Wu2010]. In starburst galaxies, which have high CO-traced SFEs, the ratio of HCN to CO luminosity is high, resulting in a high dense gas mass consistent with the high SFRs. An analogous situation may apply in the post-starburst galaxies: if we measure a low dense gas mass, this would be consistent with the low SFRs in these galaxies, despite the higher CO luminosities.

We must measure the properties of this denser gas in post-starburst galaxies to understand why there is no significant star formation and why CO-traced molecular gas remains. Here, we present an ALMA survey of 