Progress on a method of barium tagging for the nEXO double beta decay experiment is reported. Absorption and emission spectra for deposits of barium atoms and ions in solid xenon matrices are presented. Excitation spectra for prominent emission lines, temperature dependence, and bleaching of the fluorescence reveal the existence of different matrix sites. A regular series of sharp lines observed in Ba+ deposits is identified with some type of barium hydride molecule. Lower limits for the fluorescence quantum efficiency of the principal Ba emission transition are reported. Under current conditions, an image of fewer than or equal to 10(4) Ba atoms can be obtained. Prospects for imaging single Ba atoms in solid xenon are discussed.