Neutral atoms confined in evanescent optical potentials in nanotapered optical fibers are a promising platform for developing quantum technologies and exploring fundamental sciences such as quantum networks and quantum electrodynamics. Building on successful advances in trapped alkali atoms, here we demonstrate state-independent optical dipole trapping of an alkaline-earth atom, strontium-88, using the evanescent field of a nanotapered optical fiber. Taking advantage of the easily achievable low laser cooling temperature for strontium at $\sim\!\!1~\mu$K, we Demonstrate trapping at depth. In addition, we employ a double magic wavelength trapping scheme for state-independent trapping in $5s^{2}\;^{1}\!S_{0}-5s5p\;^{3}\!P_ in kilohertz widths Realize {1,|m|=1}$ cooling transition. This is verified by performing near-surface high-resolution spectroscopy of atomic transitions. This allows us to experimentally find and verify the state insensitivity of traps around 435.827(25) nm, the theoretically predicted magic wavelength. Given the non-magnetic ground state and short collisional scattering length of strontium-88, this work also lays the groundwork for developing versatile and robust matter-wave atomtronic circuits via nanophotonic waveguides.
