We report sub-arcsecond resolution IRAM PdBI millimeter CO interferometry of four z~2 submillimeter galaxies (SMGs), and sensitive CO (3-2) flux limits toward three z~2 UV-/optically selected star forming galaxies. The new data reveal for the first time spatially resolved CO gas kinematics in the observed SMGs. Two of the SMGs show double or multiple morphologies, with complex, disturbed gas motions. The other two SMGs exhibit CO velocity gradients of ~500 km/s across 0.2 arcsec (1.6 kpc) diameter regions, suggesting that the star forming gas is in compact, rotating disks. Our data provide compelling evidence that these SMGs represent extreme, short-lived maximum star forming events in highly dissipative mergers of gas rich galaxies. The resulting high mass surface and volume densities of SMGs are similar to those of compact quiescent galaxies in the same redshift range, and much higher than those in local spheroids. From the ratio of the comoving volume densities of SMGs and quiescent galaxies in the same mass and redshift ranges, and from the comparison of gas exhaustion time scales and stellar ages, we estimate that the SMG phase duration is about 100 Myrs. Our analysis of SMGs and optically/UV selected high redshift star forming galaxies supports a universal Chabrier IMF as being valid over the star forming history of these galaxies. We find that the 12CO luminosity to total gas mass conversion factors at z~2-3 are probably similar to those assumed at z~0. The implied gas fractions in our sample galaxies range from 20 to 50%.
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