  It is known that vacuum polarization can modify the photon propagation modes
in the atmospheric plasma of a strongly magnetized neutron star. A resonance
occurs when the effect of vacuum polarization on the photon modes balances that
of the plasma. We show that a photon (with energy $E\go$ a few keV) propagating
outward in the atmosphere can convert from one polarization mode into another
as it traverses the resonant density, $\rho_{res}\simeq
Y_e^{-1}\eta^{-2}(B/10^{14} G)^2(E/1 keV)^2$ g cm$^{-3}$, where $Y_e$ is the
electron fraction, and $\eta\sim 1$ is a slowly varying function of the
magnetic field $B$. The physics of this mode conversion is analogous to the
Mikheyev-Smirnov-Wolfenstein mechanism for neutrino oscillation. Because the
two photon modes have vastly different opacities in the atmosphere, this
vacuum-induced mode conversion can significantly affect radiative transport and
surface emission from strongly magnetized neutron stars.
