Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasi-periodic optical lattices

Abstract

We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasi-periodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the non-commensurate 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 disorder, 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.

11 pages, 8 figures

References in corpus (5)

• Many-Body Physics with Ultracold Gases
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Phase diagram and momentum distribution of an interacting Bose gas in a bichromatic lattice
• Are the Tonks regimes in the continuum and on the lattice truly equivalent?
• Ultracold Bose gases in time-dependent 1D superlattices: response and quasimomentum structure