  This paper is concerned with the Cauchy problem of the 3D compressible
bipolar Navier--Stokes--Poisson (BNSP) system with unequal viscosities, and our
main purpose is three--fold: First, under the assumption that $H^l\cap
L^1$($l\geq 3$)--norm of the initial data is small, we prove the optimal time
decay rates of the solution as well as its all--order spatial derivatives from
one--order to the highest--order, which are the same as those of the
compressible Navier--Stokes equations and the heat equation. Second, for
well--chosen initial data, we also show the lower bounds on the decay rates.
Therefore, our time decay rates are optimal. Third, we give the explicit
influences of the electric field on the qualitative behaviors of solutions,
which are totally new as compared to the results for the compressible unipolar
Navier--Stokes--Poisson(UNSP) system [Li et al., in Arch. Ration. Mech. Anal.,
{196} (2010), 681--713; Wang, J. Differ. Equ., { 253} (2012), 273--297]. More
precisely, we show that the densities of the BNSP system converge to their
corresponding equilibriums at the same $L^2$--rate $(1+t)^{-\frac{3}{4}}$ as
the compressible Navier--Stokes equations, but the momentums of the BNSP system
and the difference between two densities decay at the $L^2$--rate
$(1+t)^{-\frac{3}{2}(\frac{1}{p}-\frac{1}{2})}$ and
$(1+t)^{-\frac{3}{2}(\frac{1}{p}-\frac{1}{2})-\frac{1}{2}}$ with $1\leq p\leq
\frac{3}{2}$, respectively, which depend directly on the initial low frequency
assumption of electric field, namely, the smallness of $\|\nabla
\phi_0\|_{L^p}$.
