  We study the growth of the red sequence through the number density and
structural evolution of a sample of young and old quiescent galaxies at 0<z<2.
The galaxies are selected from the NEWFIRM Medium-Band Survey (NMBS) in the
Cosmic Evolution Survey (COSMOS) field. We find a large population of massive
young recently quenched ("post-starburst") galaxies at z>1 that are almost
non-existent at z<1; their number density is 5 x 10^{-5} Mpc^{-3} at z=2,
whereas it is a factor of 10 less at z=0.5. The observed number densities of
young and old quiescent galaxies at z>1 are consistent with a simple model in
which all old quiescent galaxies were once identified as post-starburst
galaxies. We find that the overall population of quiescent galaxies have
smaller sizes and slightly more elongated shapes at higher redshift, in
agreement with other recent studies. Interestingly, the most recently quenched
galaxies at 1<z<2 are not larger, and possibly even smaller, than older
galaxies at those redshifts. This result is inconsistent with the idea that the
evolution of the average size of quiescent galaxies is largely driven by
continuous transformations of larger, star-forming galaxies: in that case, the
youngest quiescent galaxies would also be the largest. Instead, mergers or
other mechanisms appear to be required to explain the size growth of quiescent
galaxies from z=2 to the present.
