Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasiperiodic optical lattices

We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasiperiodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the noncommensurate case, mapping the problem to the Anderson model allows us to study the Bose-glass phase. Surprisingly, we find that a perturbative treatment in both cases, weak and strong disorders, gives a good description at all frequencies. In particular, we find that the infrared-absorption rate in the thermodynamic limit is quadratic in frequency. This result is unexpected since for other quantities, like the conductivity in one-dimensional systems, perturbation theory is only applicable at high frequencies. We discuss applications to recent experiments on optical lattice systems and, in particular, the effect of the harmonic trap.This work was partly supported by ANR under Grant No. 08-BLAN-0165-01 and by the Swiss National Fund under MaNEP and Division II. A.I. gratefully acknowledges financial support from CONICET and UNLP. During the initial stage of this project, G.O. was also supported by the European Commission under Contract No. EDUG-038970. M.A.C. was supported by MEC Spain under Grant No. FIS2007-066711-C02-02 and CSIC Spain through Grant No. PIE 200760/007.Peer reviewe