  We demonstrate frequency-bin entanglement between ultra-narrowband photons
generated by cavity enhanced spontaneous parametric down conversion. Our source
generates photon pairs in widely non-degenerate discrete frequency modes, with
one photon resonant with a quantum memory material based on praseodymium doped
crystals and the other photon at telecom wavelengths. Correlations between the
frequency modes are analyzed using phase modulators and narrowband filters
before detection. We show high-visibility two photon interference between the
frequency modes, allowing us to infer a coherent superposition of the modes. We
develop a model describing the state that we create and use it to estimate
optimal measurements to achieve a violation of the Clauser-Horne (CH) Bell
inequality under realistic assumptions. With these settings we perform a Bell
test and show a significant violation of the CH inequality, thus proving the
entanglement of the photons. Finally we demonstrate the compatibility with a
quantum memory material by using a spectral hole in the praseodymium (Pr) doped
crystal as spectral filter for measuring high-visibility two-photon
interference. This demonstrates the feasibility of combining frequency-bin
entangled photon pairs with Pr-based solid state quantum memories.
