  Recent measurements of Jupiter's gravitational moments by the Juno spacecraft
and seismology of Saturn's rings suggest that the primordial composition
gradients in the deep interior of these planets have persisted since their
formation. One possible explanation is the presence of a double-diffusive
staircase below the planet's outer convection zone, which inhibits mixing
across the deeper layers. However, hydrodynamic simulations have shown that
these staircases are not long-lasting and can be disrupted by overshooting
convection. In this paper we suggests that planetary rotation could be another
factor for the longevity of primordial composition gradients. Using rotational
mixing-length theory and 3D hydrodynamic simulations, we demonstrate that
rotation significantly reduces both the convective velocity and the mixing of
primordial composition gradients. In particular, for Jovian conditions at
$t\sim10^{8}~\mathrm{yrs}$ after formation, rotation reduces the convective
velocity by a factor of 6, and in turn, the kinetic energy flux available for
mixing gets reduced by a factor of $6^3\sim 200$. This leads to an entrainment
timescale that is more than two orders of magnitude longer than without
rotation. We encourage future hydrodynamic models of Jupiter and other gas
giants to include rapid rotation, because the decrease in the mixing efficiency
could explain why Jupiter and Saturn are not fully mixed.
