**A theoretical study of optical detection methods for ultracold atoms in optical lattices.** / Cordobes Aguilar, Francisco.

Research output: Thesis › Doctoral Thesis

Unpublished

**A theoretical study of optical detection methods for ultracold atoms in optical lattices.** / Cordobes Aguilar, Francisco.

Research output: Thesis › Doctoral Thesis

Cordobes Aguilar, F 2013, 'A theoretical study of optical detection methods for ultracold atoms in optical lattices', Ph.D., Royal Holloway, University of London.

Cordobes Aguilar, F. (2013). *A theoretical study of optical detection methods for ultracold atoms in optical lattices*.

Cordobes Aguilar F. A theoretical study of optical detection methods for ultracold atoms in optical lattices. 2013. 145 p.

@phdthesis{00b2a874e2644e53ab1807adbd8379ab,

title = "A theoretical study of optical detection methods for ultracold atoms in optical lattices",

abstract = "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 of40 K is studied. This is done using the level structure that is used routinely in experiments to realise the Fermi-Hubbard 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 quasi-optimised 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 simulatedusing a worm-type algorithm and the computed correlations are used to evaluate thescattered intensity.",

author = "{Cordobes Aguilar}, Francisco",

year = "2013",

month = dec,

day = "16",

language = "English",

school = "Royal Holloway, University of London",

}

TY - THES

T1 - A theoretical study of optical detection methods for ultracold atoms in optical lattices

AU - Cordobes Aguilar, Francisco

PY - 2013/12/16

Y1 - 2013/12/16

N2 - 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 of40 K is studied. This is done using the level structure that is used routinely in experiments to realise the Fermi-Hubbard 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 quasi-optimised 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 simulatedusing a worm-type algorithm and the computed correlations are used to evaluate thescattered intensity.

AB - 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 of40 K is studied. This is done using the level structure that is used routinely in experiments to realise the Fermi-Hubbard 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 quasi-optimised 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 simulatedusing a worm-type algorithm and the computed correlations are used to evaluate thescattered intensity.

M3 - Doctoral Thesis

ER -