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arXiv:cond-mat/0405492 · Physical Review A

Inelastic light scattering from a Mott insulator

D. van Oosten, D. B. M. Dickerscheid, Behnam Farid, P. van der Straten, Henk T. C. Stoof

Published Feb 1, 2005• 47 citations
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Abstract

We propose to use Bragg spectroscopy to measure the excitation spectrum of the Mott-insulator state of an atomic Bose gas in an optical lattice. We calculate the structure factor of the Mott insulator taking into account both the self-energy corrections of the atoms and the corresponding dressing of the atom-photon interaction. We determine the scattering rate of photons in the stimulated Raman transition and show that by measuring this scattering rate in an experiment, in particular, the excitation gap of the Mott insulator can be determined.

DOI
10.1103/physreva.71.021601

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We propose to use Bragg spectroscopy to measure the excitation spectrum of the Mott-insulator state of an atomic Bose gas in an optical lattice. We calculate the structure factor of the Mott insulator taking into account both the self-energy corrections of the atoms and the corresponding dressing of the atom-photon interaction. We determine the scattering rate of photons in the stimulated Raman transition and show that by measuring this scattering rate in an experiment, in particular, the excitation gap of the Mott insulator can be determined.
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We report the Bragg spectroscopy of interacting one-dimensional Bose gases loaded in an optical lattice across the superfluid to the Mott-insulator phase transition. Elementary excitations are created with a nonzero momentum and the response of the correlated 1D gases is in the linear regime. The complexity of the strongly correlated quantum phases is directly displayed in the spectra which exhibit novel features. This work paves the way for a precise characterization of the state of correlated gases in optical lattices.
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We investigate theoretically light scattering of photons by ultracold atoms in an optical lattice in the linear regime. A full quantum theory for the atom-photon interactions is developed as a function of the atomic state in the lattice along the Mott-insulator--superfluid phase transition, and the photonic-scattering cross section is evaluated as a function of the energy and of the direction of emission. The predictions of this theory are compared with the theoretical results of a recent work on Bragg scattering in time-of-flight measurements [A.M. Rey et al., Phys. Rev. A 72, 023407 (2005)]. We show that, when performing Bragg spectroscopy with light scattering, the photon recoil gives rise to an additional atomic site-to-site hopping, which can interfere with ordinary tunneling of matter waves and can significantly affect the photonic-scattering cross section.
We study 1D trapped Bose gases in the strongly interacting regime. The systems are created in an optical lattice and are subject to a longitudinal periodic potential. Bragg spectroscopy enables us to investigate the excitation spectrum in different regimes. In the superfluid phase a broad continuum of excitations is observed which calls for an interpretation beyond the Bogoliubov spectrum taking into account the effect of strong interactions. In the Mott insulating phase a discrete spectrum is measured. Both phases are compared to the 3D situation and to the crossover regime from 1D to 3D. The coherence length and coherent fraction of the gas are measured in all configurations. We observe signatures for increased fluctuations characteristic for 1D systems. Moreover, the collective oscillations cease near the transition to the Mott insulator phase.