  In this paper, we mainly study the global strong solutions and its long time
decay rates of all order spatial derivatives to a micro-macro model for
compressible polymeric fluids with small initial data. This model is a coupling
of isentropic compressible Navier-Stokes equations with a nonlinear
Fokker-Planck equation. We first prove that the micro-macro model admits a
unique global strong solution provided the initial data are close to
equilibrium state for $d\geq2$. Moreover, for $d\geq3$, we also show a new
critical Fourier estimation that allow us to give the long time decay rates of
$L^2$ norm for all order spatial derivatives.
