Dynamic Structure Factor of Ultracold Bosons in Optical Lattice |

T.A. Zaleski and T.K. Kopeć
Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Okólna 2, 50-422 Wrocław, Poland |

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Ultracold atoms in optical lattices have been intensively investigated in recent years as they provide a very well controllable environment for observation of many-body quantum phenomena, closely mimicking physics of strongly interacting electronic systems. Here, we use the quantum rotor approach supplemented by the Bogolyubov method to investigate one- and two-particle excitations, which are a measure of inter-particle correlations. We calculate one-particle spectral function and dynamic structure factor, which can be observed using spectroscopy of cold atomic systems. Our calculations require a significant numerical effort to determine multidimensional convolutions of momentum and frequency dependent constituents functions, which we achieve using parallelised fast Fourier transform. We observe the appearance of sharp coherence peaks in the superfluid phase of the cold bosons, which closely resembles the formation of sharply defined quasiparticle excitations below T_{c} in cuprates or smeared excitation spectra characteristic for strongly interacting systems. |

DOI: 10.12693/APhysPolA.130.564 PACS numbers: 03.75.Hh, 05.30.Jp, 67.85.Hj |