Extremely Low Molecular Gas Content in a Compact, Quiescent Galaxy at z=1.522

One of the greatest challenges to theoretical models of massive galaxy formation is the regulation of star formation at early times. The relative roles of molecular gas expulsion, depletion, and stabilization are uncertain as direct observational constraints of the gas reservoirs in quenched or quenching galaxies at high redshift are scant. We present ALMA observations of CO(2-1) in a massive ($\log M_{\star}/M_{\odot}=11.2$), recently quenched galaxy at $z=1.522$. The optical spectrum of this object shows strong Balmer absorption lines, which implies that star formation ceased $\sim$0.8 Gyr ago. We do not detect CO(2-1) line emission, placing an upper limit on the molecular $\mathrm{H_2}$ gas mass of 1.1$\times10^{10}\,M_{\odot}$. The implied gas fraction is $f_{\rm{H_2}}{\equiv M_{H_2}/M_{\star}}<7\%$, $\sim10\times$ lower than typical star forming galaxies at similar stellar masses at this redshift, among the lowest gas fractions at this specific star formation rate at any epoch, and the most stringent constraint on the gas contents of a $z>1$ passive galaxy to date. Our observations show that the depletion of $\mathrm{H_2}$ from the interstellar medium of quenched objects can be both efficient and fairly complete, in contrast to recent claims of significant cold gas in recently quenched galaxies. We explore the variation in observed gas fractions in high-$z$ galaxies and show that galaxies with high stellar surface density have low $f_{\rm{H_2}}$, similar to recent correlations between specific star formation rate and stellar surface density.