  We consider the Cauchy problem for incompressible viscoelastic fluids in the
whole space $\mathbb{R}^d$ ($d=2,3$). By introducing a new decomposition via
Helmholtz's projections, we first provide an alternative proof on the existence
of global smooth solutions near equilibrium. Then under additional assumptions
that the initial data belong to $L^1$ and their Fourier modes do not degenerate
at low frequencies, we obtain the optimal $L^2$ decay rates for the global
smooth solutions and their spatial derivatives. At last, we establish the
weak-strong uniqueness property in the class of finite energy weak solutions
for the incompressible viscoelastic system.
