This thesis presents a theoretical analysis of light scattered from atoms trapped in optical lattices. The work presented here focuses on the case in which atoms trapped in an optical lattice are described by a Hubbard model. It is shown that the scattered light can be used to probe the ground state correlations and excitations of the system. Both scattered intensity and scattered spectrum are shown to contain relevant information. Scattered intensity is shown to carry information about the magnetic ordering and correlation functions in the system. Scattered spectrum sheds light on the excitations of the system and can be used to study single~particle and collective excitations. In the case studied here the behaviour of fermionic atoms in an optical lattice is well described by the repulsive half-filled Fermi-Hubbard model. Within the random phase approximation the well known analytic expressions for the system correlations are rederived for the antiferromagnetic ground state. These expressions are input in the light scattering formulae and the scattered intensity and spectrum are evaluated numerically. As a particular example the experimentally relevant case of 40K is studied. This is done using the level structure that is used routinely in experiments to realise the FermiHubbard model in optical lattices. The scattered light and spectrum experiments are analysed theoretically. It is shown that within a certain experimental range the scattered light intensity offers a direct probe of the antiferromagnetic order parameter. Different experimental parameters and configurations are studied thoroughly and a set of quasioptimised experimental parameter values is prescribed. The number of necessary experimental realisations to obtain such accuracy is also calculated and shown to be a realistic figure. Lastly, the same formalism is applied to the Bose-Hubbard model. It is simulated using a worm-type algorithm and the computed correlations are used to evaluate the scattered intensity. 5
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:603446 |
| Date | January 2013 |
| Creators | Cordobes Anguilar, Francisco |
| Publisher | University of London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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