We investigate numerically the zero-temperature physics of the one-dimensional Bose-Hubbard model in an incommensurate cosine potential, recently realized in experiments with cold bosons in optical superlattices [L. Fallani et al., Phys. Rev. Lett. 98, 130404 (2007)]. An incommensurate cosine potential has intermediate properties between a truly periodic and a fully random potential, displaying a characteristic length scale (the quasiperiod) which is shown to set a finite lower bound to the excitation energy of the system at special incommensurate fillings. This leads to the emergence of gapped incommensurate band-insulator (IBI) phases along with gapless Bose-glass (BG) phases for strong quasiperiodic potential for both hard-core and soft-core bosons. Enriching the spatial features of the potential by the addition of a second incommensurate component appears to remove the IBI regions, stabilizing a continuous BG phase over an extended parameter range. Moreover, we discuss the validity of the local-density approximation in the presence of a parabolic trap, clarifying the notion of a local BG phase in a trapped system; we investigate the behavior of first- and second-order coherence upon increasing the strength of the quasiperiodic potential; and we discuss the ab initio derivation of the Bose-Hubbard Hamiltonian with quasiperiodic potential starting from the microscopic Hamiltonian of bosons in an incommensurate superlattice.

• Received 21 December 2007
• Publisher error corrected 13 June 2008

DOI:https://doi.org/10.1103/PhysRevA.77.063605