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Instabilities and "phonons" of optical lattices in hollow optical fibers

Instabilities are predicted for a sufficiently long hollow photonic optical fiber, or "cavity", containing a one dimensional Bose-gas in the presence of a classical, far red-detuned, confined weak electromagnetic mode. We examine both a single beam with Bose gas (a type of Brillouin instability) and the case of a standing wave, or optical lattice. The instabilities of these driven systems have pronounced spatial structure, of combined modulational instabilities in the electromagnetic and Bose density fields. Near the critical wave vectors for the instability the coupled modes of the BEC and light can be interpreted as "phonons" of the optical lattice. We conjecture these spatially-structured instabilities for the optical lattice, which we predict at weak fields, develop into the source of spatially homogeneous heating predicted for strong fields.