We present constraints on the dust continuum flux and inferred gas content of a gravitationally lensed massive quiescent galaxy at $z$=1.883$pm$0.001 using AzTEC 1.1mm imaging with the Large Millimeter Telescope. MRG-S0851 appears to be a prototypical massive compact quiescent galaxy, but has evidence that it experienced a centrally concentrated rejuvenation event in the last 100 Myr (see Akhshik et al. 2020). This galaxy is undetected in the AzTEC image but we calculate an upper limit on the millimeter flux and use this to estimate the H$_2$ mass limit via an empirically calibrated relation that assumes a constant molecular gas-to-dust ratio of 150. We constrain the 3$sigma$ upper limit of the H$_2$ fraction from the dust continuum in MRG-S0851 to be ${M_{H_2}/M_{star}}$ $leq$ 6.8%. MRG-S0851 has a low gas fraction limit with a moderately low sSFR owing to the recent rejuvenation episode, which together results in a relatively short depletion time of $<$0.6 Gyr if no further H$_2$ gas is accreted. Empirical and analytical models both predict that we should have detected molecular gas in MRG-S0851, especially given the rejuvenation episode; this suggests that cold gas and/or dust is rapidly depleted in at least some early quiescent galaxies.
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