  The Lamb shift of a quantum emitter very close to a plasmonic nanostructure,
mainly induced by the higher-order plasmonic dark modes, can be three or more
orders of magnitude larger than that in the free space and it is
ultra-sensitive to the emitter position and polarization. We show that this
giant Lamb shift can be sensitively observed from the scattering spectrum dip
shift of coupled system when the plasmonic nanoparticle or tip scans through
the emitter. Based on these observations, we propose an optical localization
and polarization microscopy scheme with sub-nanometer precision for a quantum
emitter via detecting the scattering spectrum instead of fluorescence. Our
method is free of fluorescence quenching problem and it is relatively easier to
be implemented in the plasmon-emitter coupling system. Moreover, the sample in
our method does not need to be placed inside a plasmonic picocavity to enhance
the radiative fluorescence rate and it also works even if the quantum emitter
is slightly below a dielectric surface which can bring about broader
applications in various fields, such as physics, chemistry, medicine, life
science and materials science.
