  The evanescent field outside an optical nanofiber (ONF) can create optical
traps for neutral atoms. We present a non-destructive method to characterize
such trapping potentials. An off-resonance linearly polarized probe beam that
propagates through the ONF experiences a slow axis of polarization produced by
trapped atoms on opposite sides along the ONF. The transverse atomic motion is
imprinted onto the probe polarization through the changing atomic index of of
refraction. By applying a transient impulse, we measure a time-dependent
polarization rotation of the probe beam that provides both a rapid and
non-destructive measurement of the optical trapping frequencies.
