  We report on the observation of a Zeeman shift (order of 100 MHz) of the
Doppler-broadened D2 transition of both 85Rb and 87Rb isotopes via transmission
through a tapered optical nanofiber in the presence of a DC magnetic field.
Linearly-polarized light propagating in the nanofiber is analyzed as a
superposition of two orthogonally circularly-polarized orientations, {\sigma}+
and {\sigma}-. In the absence of the magnetic field, the absorption of these
polarizations by the atomic vapor, via the evanescent field at the waist of the
nanofiber, is degenerate. When a weak magnetic field is applied parallel to the
propagating light, this degeneracy is lifted and relative shifts in the
resonance frequencies are detected. Typical linear shift rates of 1.6 MHz/G and
-2.0 MHz/G were observed. We also demonstrate a dichroic atomic vapor laser
lock line shape by monitoring the real-time subtraction of the two
magnetically-shifted absorption spectra. This is particularly interesting for
magneto-optical experiments as it could be directly implemented for diode laser
frequency-stabilization.
