  In the atmospheric plasma of a strongly magnetized neutron star, vacuum
polarization can induce a Mikheyev-Smirnov-Wolfenstein like resonance across
which a X-ray photon may (depending on its energy) convert from one mode into
the other, with significant changes in opacities and polarizations. We show
that this vacuum resonance effect gives rise to an unique energy-dependent
polarization signature in the surface emission from neutron stars. The
detection of polarized X-rays from neutron stars can provide a direct probe of
strong-field quantum electrodynamics and constrain the neutron star magnetic
field and geometry.
