Properties of the cold interstellar medium of low-metallicity galaxies are not well-known due to the faintness and extremely small scale on which emission is expected. We present deep ALMA band 6 (230GHz) observations of the nearby, low-metallicity (12 + log(O/H) = 7.25) blue compact dwarf galaxy SBS0335-052 at an unprecedented resolution of 0.2 arcsec (52 pc). The 12CO J=2-1 line is not detected and we report a 3-sigma upper limit of LCO(2-1) = 3.6x10^4 K km/s pc^2. Assuming that molecular gas is converted into stars with a given depletion time, ranging from 0.02 to 2 Gyr, we find lower limits on the CO-to-H2 conversion factor alpha_CO in the range 10^2-10^4 Msun pc^-2 (K km/s)^-1. The continuum emission is detected and resolved over the two main super star clusters. Re-analysis of the IR-radio spectral energy distribution suggests that the mm-fluxes are not only free-free emission but are most likely also associated with a cold dust component coincident with the position of the brightest cluster. With standard dust properties, we estimate its mass to be as large as 10^5 Msun. Both line and continuum results suggest the presence of a large cold gas reservoir unseen in CO even with ALMA.
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