  We dispersively interface an ensemble of one thousand atoms trapped in the
evanescent field surrounding a tapered optical nanofiber. This method relies on
the azimuthally-asymmetric coupling of the ensemble with the evanescent field
of an off-resonant probe beam, transmitted through the nanofiber. The resulting
birefringence and dispersion are significant; we observe a phase shift per atom
of $\sim$\,1\,mrad at a detuning of six times the natural linewidth,
corresponding to an effective resonant optical density per atom of 0.027.
Moreover, we utilize this strong dispersion to non-destructively determine the
number of atoms.
