We present spatially-resolved imaging obtained with the Australia Telescope Compact Array (ATCA) of three CO lines in two high-redshift gravitationally lensed dusty star-forming galaxies, discovered by the South Pole Telescope. Strong lensing allows us to probe the structure and dynamics of the molecular gas in these two objects, at z=2.78 and z=5.66, with effective source-plane resolution of less than 1kpc. We model the lensed emission from multiple CO transitions and the dust continuum in a consistent manner, finding that the cold molecular gas as traced by low-J CO always has a larger half-light radius than the 870um dust continuum emission. This size difference leads to up to 50% differences in the magnification factor for the cold gas compared to dust. In the z=2.78 galaxy, these CO observations confirm that the background source is undergoing a major merger, while the velocity field of the other source is more complex. We use the ATCA CO observations and comparable resolution Atacama Large Millimeter/submillimeter Array dust continuum imaging of the same objects to constrain the CO-H_2 conversion factor with three different procedures, finding good agreement between the methods and values consistent with those found for rapidly star-forming systems. We discuss these galaxies in the context of the star formation - gas mass surface density relation, noting that the change in emitting area with observed CO transition must be accounted for when comparing high-redshift galaxies to their lower redshift counterparts.
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