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Abstract: We compute the absorption spectrum of strongly repulsive one-dimensionalbosons in a disordered or quasi-periodic optical lattice. At commensuratefilling, the particle-hole resonances of the Mott insulator are broadened asthe disorder strength is increased. In the non-commensurate case, mapping theproblem to the Anderson model allows us to study the Bose-glass phase.Surprisingly we find that a perturbative treatment in both cases, weak andstrong disorder, gives a good description at all frequencies. In particular wefind that the infrared absorption rate in the thermodynamic limit is quadraticin frequency. This result is unexpected, since for other quantities like theconductivity in one dimensional systems, perturbation theory is only applicableat high frequencies. We discuss applications to recent experiments on opticallattice systems, and in particular the effect of the harmonic trap.



Author: G. Orso, A. Iucci, M. A. Cazalilla, T. Giamarchi

Source: https://arxiv.org/



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