  We determine the leading Fock-state light front wave functions (LF-LFWFs) of
the $\rho$ and J/$\psi$ mesons, for the first time from the Dyson-Schwinger and
Bethe-Salpeter equations (DS-BSEs) approach. A unique advantage of this method
is that it renders a direct extraction of LF-LFWFs in presence of a number of
higher Fock-states. Modulated by the current quark mass and driven by the
dynamical chiral symmetry breaking (DCSB), we find the $\rho$ and $J/\psi$
LF-LFWFs different in profile, i.e., the former are broadly distributed in $x$
(the longitudinal light-cone momentum fraction of meson carried by quark) while
the latter are narrow. Moreover, the $\rho$ LF-LFWFs contribute less than 50%
to the total Fock-state normalization, suggesting considerable higher
Fock-states in $\rho$. We then use these LF-LFWFs to study the diffractive
$\rho$ and $J/\psi$ electroproduction within the dipole picture. The calculated
cross section shows general agreement with HEAR data, except for growing
discrepancy in $\rho$ production at low photon virtuality. Our work provides a
first dipole picture analysis on diffractive $\rho$ electroproduction that
confronts the parton nature of the light (anti)quarks.
