  We present a lattice QCD calculation of the polarizability of the neutron and
other neutral hadrons that includes the effects of the background field on the
sea quarks. This is done by perturbatively reweighting the charges of the sea
quarks to couple them to the background field. The main challenge in such a
calculation is stochastic estimation of the weight factors, and we discuss the
difficulties in this estimation. Here we use an extremely aggressive dilution
scheme to reduce the stochastic noise to a manageable level. The pion mass in
our calculation is 306 MeV and the lattice size is 3 fm. For neutron, we find
that $\alpha_E = 2.70(55) * 10^{-4}fm^3$, which is the most precise lattice QCD
determination of the polarizability to date that includes sea effects.
