We report sensitive [ion{C}{1}]~$^3P_1$--$^3P_0$ and $^{12}$CO~$J$=4--3 observations of the nearby merging galaxy NGC 6052 using the Morita (Atacama Compact) Array of ALMA. We detect $^{12}$CO~$J$=4--3 toward the northern part of NGC 6052, but [ion{C}{1}]~$^3P_1$--$^3P_0$ is not detected with a [ion{C}{1}]~$^3P_1$--$^3P_0$ to $^{12}$CO~$J$=4--3 line luminosity ratio of$~lesssim0.07$. According to models of photodissociation regions, the unusual weakness of [ion{C}{1}]~$^3P_1$--$^3P_0$ relative to $^{12}$CO~$J$=4--3 can be explained if the interstellar medium has a hydrogen density larger than $10^5,{rm cm}^{-3}$, conditions that might arise naturally in the ongoing merging process in NGC 6052. Its [ion{C}{1}]~$^3P_1$--$^3P_0$ emission is also weaker than expected given the molecular gas mass inferred from previous measurements of $^{12}$CO~$J$=1--0 and $^{12}$CO~$J$=2--1. This suggests that [ion{C}{1}]~$^3P_1$--$^3P_0$ may not be a reliable tracer of molecular gas mass in this galaxy. NGC 6052 is a unique laboratory to investigate how the merger process impacts the molecular gas distribution.
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