We show that two-photon absorption (TPA) in Rubidium atoms can be greatly enhanced by the use of a hollow-core photonic bandgap fiber. We investigate off-resonant, degenerate Doppler-free TPA on the 5S1/2 - 5D5/2 transition and observe 1% absorption
of a pump beam with a total power of only 1 mW in the fiber. These results are verified by measuring the amount of emitted blue fluorescence and are consistent with the theoretical predictions which indicate that transit time effects play an important role in determining the two-photon absorption cross-section in a confined geometry.
