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 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. (c) 2017 Optical Society of America