Started writing

.gitignore

@@ -36,3 +36,4 @@ thesis.run.xml*
 *run.xml*
 *.latexmkrc*
 *_latexmk*
+*.pdf*

Chapter2/chapter2.tex

@@ -0,0 +1,50 @@
+%*******************************************************************************
+%*********************************** Second Chapter ****************************
+%*******************************************************************************
+
+%Title of the Second Chapter
+\chapter{Quantum Optics of Quantum Gases}  
+
+\ifpdf
+    \graphicspath{{Chapter2/Figs/Raster/}{Chapter2/Figs/PDF/}{Chapter2/Figs/}}
+\else
+    \graphicspath{{Chapter2/Figs/Vector/}{Chapter2/Figs/}}
+\fi
+
+
+%********************************** % First Section  ****************************
+
+\section{Ultracold Atoms in Optical Lattices}
+
+%********************************** % Second Section  ***************************
+
+\section{Quantum Optics of Quantum Gases}
+
+Having introduced and described the behaviour of ultracold bosons
+trapped and manipulated using classical light, it is time to extend
+the discussion to quantized optical fields. We will first derive a
+general Hamiltonian that describes the coupling of atoms with
+far-detuned optical beams \cite{mekhov2012}. This will serve as the
+basis from which we explore the system in different parameter regimes,
+such as nondestructive measurement in free space or quantum
+measurement backaction in a cavity.
+
+We consider $N$ two-level atoms in an optical lattice with $M$
+sites. For simplicity we will restrict our attention to spinless
+bosons, although it is straightforward to generalise to fermions,
+which yields its own set of interesting quantum phenomena
+\cite{atoms2015, mazzucchi2016, mazzucchi2016af}, and other spin
+particles. The theory can be also be generalised to continuous
+systems, but the restriction to optical lattices is convenient for a
+variety of reasons. Firstly, it allows us to precisely describe a
+many-body atomic state over a broad range of parameter values due to
+the inherent tunability of such lattices. Furthermore, this model is
+capable of describing a range of different experimental setups ranging
+from a small number of sites with a large filling factor (e.g.~BECs
+trapped in a double-well potential) to a an extended multi-site
+lattice with a low filling factor (e.g.~a system with one atom per
+site will exhibit the Mott insulator to superfluid quantum phase
+transition). \mynote{extra fermion citations, Piazza?}
+
+
+

References/references.bib

@@ -0,0 +1,38 @@
+@article{mekhov2012,
+  title={Quantum optics with ultracold quantum gases: towards the full quantum regime of the light--matter interaction},
+  author={Mekhov, Igor B and Ritsch, Helmut},
+  journal={Journal of Physics B: Atomic, Molecular and Optical Physics},
+  volume={45},
+  number={10},
+  pages={102001},
+  year={2012},
+  publisher={IOP Publishing}
+}
+@article{mazzucchi2016,
+  title = {Quantum measurement-induced dynamics of many-body ultracold bosonic and fermionic systems in optical lattices},
+  author = {Mazzucchi, Gabriel and Kozlowski, Wojciech and Caballero-Benitez, Santiago F. and Elliott, Thomas J. and Mekhov, Igor B.},
+  journal = {Physical Review A},
+  volume = {93},
+  issue = {2},
+  pages = {023632},
+  numpages = {12},
+  year = {2016},
+  month = {Feb},
+  publisher = {American Physical Society}
+}
+@article{atoms2015,
+  title={Probing and Manipulating Fermionic and Bosonic Quantum Gases with Quantum Light},
+  author={Elliott, Thomas J and Mazzucchi, Gabriel and Kozlowski, Wojciech and Caballero-Benitez, Santiago F and Mekhov, Igor B},
+  journal={Atoms},
+  volume={3},
+  number={3},
+  pages={392--406},
+  year={2015},
+  publisher={Multidisciplinary Digital Publishing Institute}
+}
+@article{mazzucchi2016af,
+  title={Quantum measurement-induced antiferromagnetic order and density modulations in ultracold Fermi gases in optical lattices},
+  author={Mazzucchi, Gabriel and Caballero-Benitez, Santiago F and Mekhov, Igor B},
+  journal={arXiv preprint arXiv:1510.04883},
+  year={2015}
+}

thesis.tex

@@ -136,7 +136,7 @@
 \mainmatter
 
 \include{Chapter1/chapter1}
-%\include{Chapter2/chapter2}
+\include{Chapter2/chapter2}
 %\include{Chapter3/chapter3}
 %\include{Chapter4/chapter4}
 %\include{Chapter5/chapter5}
@@ -156,8 +156,8 @@
 % Bibliography style previews: http://nodonn.tipido.net/bibstyle.php
 % Reference styles: http://sites.stat.psu.edu/~surajit/present/bib.htm
 
-\bibliographystyle{apalike}
-%\bibliographystyle{unsrt} % Use for unsorted references  
+%\bibliographystyle{apalike}
+\bibliographystyle{unsrt} % Use for unsorted references  
 %\bibliographystyle{plainnat} % use this to have URLs listed in References
 \cleardoublepage
 \bibliography{References/references} % Path to your References.bib file