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    \title{Cavity QED with cold particles\\
    \vspace{2em}
    Bachelorarbeit\\
    \vspace{2em}
    \smaller[2]{}zur Erlangung des akademischen Grades\\
    Bachelor of Science (BSc)\\
    \vspace{2em}
    eingereicht an der\\
    Fakult{\"a}t f{\"u}r Mathematik, Informatik und Physik\\
    der\\
    Leopold-Franzens-Universit{\"a}t Innsbruck\\
    \vspace{1.5em}
    von}

    \author{
 	\LARGE Bernhard Gstrein\\
 	\vspace{.5em} \\
 	Betreuer:\\
 	Univ.Prof. Dr. Helmut Ritsch\\
 	\small Institut f{\"u}r Theoretische Physik\\
 	\vspace{1em}
	}
    
\date{Innsbruck, 2019}

\maketitle
   
\begin{abstract}
\noindent We motivate and derive a theoretical model arranging atoms in a lattice to simulate a solid. For that, we'll make use of atom-light field interaction which is enhanced in a cavity. After deriving the Hamiltonians for our systems, we'll discuss some of their properties. We'll then conduct simulations in the language Julia with the framework QuantumOptics.jl to see if we can observe the properties we expect our systems to have.
\end{abstract}
   
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\input{texfiles/theoretical.tex}
\input{texfiles/simulation.tex}
\input{texfiles/results.tex}
\input{texfiles/conclusion.tex}


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