Finished first rough draft

Abstract/abstract.tex

@@ -1,5 +1,36 @@
 % ************************** Thesis Abstract *****************************
 % Use `abstract' as an option in the document class to print only the titlepage and the abstract.
 \begin{abstract}
-This is where you write your abstract ...
+  Trapping ultracold atoms in optical lattices enabled the study of
+  strongly correlated phenomena in an environment that is far more
+  controllable and tunable than what was possible in condensed
+  matter. Here, we consider coupling these systems to quantized light
+  where the quantum nature of both the optical and matter fields play
+  equally important roles in order to push the boundaries of
+  what is possible in ultracold atomic systems.
+
+  We show that light can serve as a nondestructive probe of the
+  quantum state of the matter. By condering a global
+  measurement scheme we show that it is possible to distinguish a
+  highly delocalised phase like a superfluid from insulators. We also
+  demonstrate that light scattering reveals not only density
+  correlations, but also matter-field interference.
+
+  By taking into account the effect of measurement backaction we show
+  that the measurement can efficiently compete with the local atomic
+  dynamics of the quantum gas. This can generate long-range
+  correlations and entanglement which in turn leads to macroscopic
+  multimode oscillations accross the whole lattice when the
+  measurement is weak and correlated tunneling, as well as selective
+  suppression and enhancement of dynamical processes beyond the
+  projective limit of the quantum Zeno effect in the strong
+  measurement regime. 
+
+  We also consider quantum measurement backaction due to the
+  measurement of matter-phase-related variables such as global phase
+  coherence. We show how this unconventional approach opens up new
+  opportunities to affect system evolution and demonstrate how this
+  can lead to a new class of measurement projections, thus extending
+  the measurement postulate for the case of strong competition with
+  the system’s own evolution.
 \end{abstract}

Chapter1/chapter1.tex

@@ -12,46 +12,206 @@
 
 
 The field of ultracold gases has been a rapidly growing field ever
-since the first Bose-Einstein condensate was obtained in 1995. This
+since the first Bose-Einstein condensate (BEC) was obtained in 1995
-new quantum state of matter is characterised by a macroscopic
+\cite{anderson1995, bradley1995, davis1995}. This new quantum state of
-occupancy of the single particle ground state at which point the whole
+matter is characterised by a macroscopic occupancy of the single
-system behaves like a single quantum object. This was revolutionary as
+particle ground state at which point the whole system behaves like a
-it enabled the study of coherent properties of macroscopic systems
+single many-body quantum object \cite{PitaevskiiStringari}. This was
-rather than single atoms or photons. Furthermore, the advanced state
+revolutionary as it enabled the study of coherent properties of
-of laser cooling and manipulation technologies meant that the degree
+macroscopic systems rather than single atoms or photons. Furthermore,
-of control and isolation from the environment was far greater than was
+the advanced state of laser cooling and manipulation technologies
-possible in condensed matter systems. Initially, the main focus of the
+meant that the degree of control and isolation from the environment
+was far greater than was possible in condensed matter systems
+\cite{lewenstein2007, bloch2008}. Initially, the main focus of the
 research was on the properties of coherent matter waves, such as
-interference properties, long range phase coherence, or quantised
+interference properties \cite{andrews1997}, long range phase coherence
-vortices. Fermi degeneracy in ultracold gases was obtained shortly
+\cite{bloch2000}, or quantised vortices \cite{matthews1999,
-afterwards opening a similar field for fermions.
+  madison2000, abo2001}. Fermi degeneracy in ultracold gases was
+obtained shortly afterwards opening a similar field for fermions
+\cite{demarco1999, schreck2001, truscott2001}.
 
 In 1998 it was shown that a degenerate ultracold gas trapped in an
 optical lattice is a near-perfect realisation of the Bose-Hubbard
-model and in 2002 it was already demonstrated in a ground-breaking
+model \cite{jaksch1998} and in 2002 it was already demonstrated in a
-experiment. The Bose-Hubbard Hamiltonian was already known in the
+ground-breaking experiment \cite{greiner2002}. The Bose-Hubbard
-field of condensed matter where it was considered a simple toy
+Hamiltonian was previously known in the field of condensed matter
-model. Despite its simplicity the model exhibits a variety of
+where it was considered a simple toy model. Despite its simplicity the
-different interesting phenomena such as the quantum phase transition
+model exhibits a variety of different interesting phenomena such as
-from a delocalised superfluid state to a Mott insulator as the on-site
+the quantum phase transition from a delocalised superfluid state to a
-interaction is increased above a critical point. In contrast to a
+Mott insulator as the on-site interaction is increased above a
-thermodynamic phase transition, a quantum phase transition is driven
+critical point which was originally studied in the context of liquid
-by quantum fluctuations and can occur at zero temperature. The ability 
+helium \cite{fisher1989}. In contrast to a thermodynamic phase
-
+transition, a quantum phase transition is driven by quantum
-
+fluctuations and can occur at zero temperature. The ability to achieve
-
+a Bose-Hubbard Hamiltonian where the model parameters can be easily
+tuned by varying the lattice potential opened up a new regime in the
+many-body physics of atomic gases. Unlike Bose-Einstein condensates in
+free space which are described by weakly interacting theories
+\cite{dalfovo1999}, the behaviour of ultracold gases trapped in an
+optical lattice is dominated by atomic interactions opening the
+possibility of studying strongly correlated behaviour with
+unprecendented control.
 
 The modern field of ultracold gases is successful due to its
-interdisciplinarity [1, 2]. Originally condensed matter effects are
+interdisciplinarity \cite{lewenstein2007, bloch2008}. Originally
-now mimicked in controlled atomic systems finding applications in
+condensed matter effects are now mimicked in controlled atomic systems
-areas such as quantum information processing (QIP). A really new
+finding applications in areas such as quantum information
-challenge is to identify novel phenomena which were unreasonable to
+processing. A really new challenge is to identify novel phenomena
-consider in condensed matter, but will become feasible in new systems.
+which were unreasonable to consider in condensed matter, but will
-One such direction is merging quantum optics and many-body physics [3,
+become feasible in new systems. One such direction is merging quantum
-  4]. The former describes delicate effects such as quantum
+optics and many-body physics \cite{mekhov2012, ritsch2013}. Quantum
-measurement and state engineering, but for systems without strong
+optics has been developping as a branch of quantum physics
-many-body correlations (e.g. atomic ensembles).  In the latter,
+independently of the progress in the many-body community. It describes
-decoherence destroys these effects in conventional condensed
+delicate effects such as quantum measurement, state engineering, and
-matter. Due to recent experimental progress, e.g. Bose-Einstein
+systems that can generally be easily isolated from their environnment
-condensates (BEC) in cavities [5–7], quantum optics of quantum gases
+due to the non-interacting nature of photons \cite{Scully}. However,
-can close this gap.
+they are also the perfect candidate for studying open systems due the
+advanced state of cavity technologies \cite{carmichael,
+  MeasurementControl}. On the other hand ultracold gases are now used
+to study strongly correlated behaviour of complex macroscopic
+ensembles where decoherence is not so easy to avoid or control. Recent
+experimental progress in combining the two fields offered a very
+promising candidate for taking many-body physics in a direction that
+would not be possible for condensed matter \cite{baumann2010,
+  wolke2012, schmidt2014}. Two very recent breakthrough experiments
+have even managed to couple an ultracold gas trapped in an optical
+lattice to an optical cavity enabling the study of strongly correlated
+systems coupled to quantized light fields where the quantum properties
+of the atoms become imprinted in the scattered light
+\cite{klinder2015, landig2016}.
+
+There are three prominent directions in which the field of quantum
+optics of quantum gases has progressed in. First, the use of quantised
+light enables direct coupling to the quantum properties of the atoms
+\cite{mekhov2007prl, mekhov2007prl, mekhov2012}. This allows us to
+probe the many-body system in a nondestructive manner and under
+certain conditions even perform quantum non-demolition (QND)
+measurements. QND measurements were originally developed in the
+context of quantum optics as a tool to measure a quantum system
+without significantly disturbing it \cite{braginsky1977, unruh1978,
+  brune1990, brune1992}. This has naturally been extended into the
+realm of ultracold gases where such non-demolition schemes have been
+applied to both fermionic \cite{eckert2008qnd, roscilde2009} and
+bosonic \cite{hauke2013, rogers2014}. In this thesis, we consider
+light scattering in free space from a bosonic ultracold gas and show
+that there are many prominent features that go beyond classical
+optics. Even the scattering angular distribution is nontrivial with
+Bragg conditions that are significantly different from the classical
+case. Furthermore, we show that the direct coupling of quantised light
+to the atomic systems enables the nondestructive probing beyond a
+standard mean-field description. We demonstrate this by showing that
+the whole phase diagram of a disordered one-dimensional Bose-Hubbard
+Hamiltonian, which consists of the superfluid, Mott insulating, and
+Bose glass phases, can be mapped from the properties of the scattered
+light. Additionally, we go beyond standard QND approaches, which only
+consider coupling to density observables, by also considering the
+direct coupling of the quantised light to the interference between
+neighbouring lattice sites. We show that not only is this possible to
+achieve in a nondestructive manner, it is also achieved without the
+need for single-site resolution. This is in contrast to the standard
+destructive time-of-flight measurements currently used to perform
+these measurements \cite{miyake2011}. Within a mean-field treatment
+this enables probing of the order parameter as well as matter-field
+quadratures and their squeezing. This can have an impact on atom-wave
+metrology and information processing in areas where quantum optics has
+already made progress, e.g.,~quantum imaging with pixellized sources
+of non-classical light \cite{golubev2010, kolobov1999}, as an optical
+lattice is a natural source of multimode nonclassical matter waves.
+
+Second, coupling a quantum gas to a cavity also enables us to study
+open system many-body dynamics either via dissipation where we have no
+control over the coupling to the environment or via controlled state
+reduction using the measurement backaction due to photodetections. A
+lot of effort was expanded in an attempt to minimise the influence of
+the environment in order to extend decoherence times. However,
+theoretical progress in the field has shown that instead being an
+obstacle, dissipation can actually be used as a tool in engineering
+quantum states \cite{diehl2008}. Furthermore, as the environment
+coupling is varied the system may exhibit sudden changes in the
+properties of its steady state giving rise to dissipative phase
+transitions \cite{carmichael1980, werner2005, capriotti2005,
+  morrison2008, eisert2010, bhaseen2012, diehl2010,
+  vznidarivc2011}. An alternative approach to open systems is to look
+at quantum measurement where we consider a quantum state conditioned
+on the outcome of a single experimental run \cite{carmichael,
+  MeasurementControl}. In this approach we consider the solutions to a
+stochastic Schr\"{o}dinger equation which will be a pure state, which
+in contrast to dissipative systems is generally not the case. The
+question of measurement and its effect on the quantum state has been
+around since the inception of quantum theory and still remains a
+largely open question \cite{zurek2002}. It wasn't long after the first
+condenste was obtained that theoretical work on the effects of
+measurement on BECs appeared \cite{cirac1996, castin1997,
+  ruostekoski1997}. Recently, work has also begun on combining weak
+measurement with the strongly correlated dynamics of ultracold gases
+in optical lattices \cite{mekhov2009prl, mekhov2009pra, mekhov2012,
+  douglas2012, douglas2013, ashida2015, ashida2015a}.
+
+In this thesis we focus on the latter by considering a quantum gas in
+an optical lattice coupled to a cavity \cite{mekhov2012}. This
+provides us with a flexible setup where the global light scattering
+can be engineered. We show that this introduces a new competing energy
+scale into the system and by considering continuous measurement, as
+opposed to discrete projective measurements, we demonstrate the
+quantum backaction can effectively compete with the standard
+short-range processes of the Bose-Hubbard model. The global nature of
+the optical fields leads to new phenomena driven by long-range
+correlations that arise from the measurement. The flexibility of the
+optical setup lets us not only consider coupling to different
+observables, but by carefully choosing the optical geometry we can
+suppress or enhace specific dynamical processes, realising spatially
+nonlocal quantum Zeno dynamics.
+
+The quantum Zeno effect happens when frequent measurements slow the
+evolution of a quantum system \cite{misra1977, facchi2008}. This
+effect was already considered by von Neumann and it has been
+successfully observed in a variety of systems \cite{itano1990,
+  nagels1997, kwiat1999, balzer2000, streed2006, hosten2006,
+  bernu2008}. The generalisation of this effect to measurements with
+multidimensional projections leads to quantum Zeno dynamics where
+unitary evolution is uninhibited within this degenerate subspace,
+i.e. the Zeno subspace \cite{facchi2008, raimond2010, raimond2012,
+  signoles2014}. Here, by combining quantum optical measurements with
+the complex Hilbert space of a many-body quantum gas we go beyond
+conventional quantum Zeno dynamics. By considering the case of
+measurement near, but not in, the projective limit the system is still
+confined to a Zeno subspace, but intermediate transitions are allowed
+via virtual Raman-like processes. In a lattice system, like the
+Bose-Hubbard model we can use global measurement to engineer these
+dynamics to be highly nonlocal leading to the generation of long-range
+correlations and entanglement. Furthermore, we show that this
+behaviour can be approximated by a non-Hermitian Hamiltonian thus
+extending the notion of quantum Zeno dynamics into the realm of
+non-Hermitian quantum mechanics joining the two
+paradigms. Non-Hermitian systems themself exhibit a range of
+interesting phenomena ranging from localisation \cite{hatano1996,
+  refael2006} and $\mathcal{PT}$ symmetry \cite{bender1998,
+  giorgi2010, zhang2013} to spatial order \cite{otterbach2014} and
+novel phase transitions \cite{lee2014prx, lee2014prl}.
+
+Just like for the nondestructive measurements we also consider
+measurement backaction due to coupling to the interference terms
+between the lattice sites. This effectively amounts to coupling to the
+phase observables of the system. As this is the conjugate variable of
+density, this allows to enter a new regime of quantum control using
+measurement backaction. Whilst such interference measurements have
+been previously proposed for BECs in double-wells \cite{cirac1996,
+  castin1997, ruostekoski1997}, the extension to a lattice system is
+not straightforward, but we will show it is possible to achieve with
+our propsed setup by a careful optical arrangement. Within this
+context we demonstrate a novel type of projection which occurs even
+when there is significant competition with the Hamiltonian
+dynamics. This projection is fundamentally different to the standard
+formulation of the Copenhagen postulate projection or the quantum Zeno
+effect \cite{misra1977, facchi2008} thus providing an extension of the
+measurement postulate to dynamical systems subject to weak
+measurement.
+
+Finally, the cavity field that builds up from the scattered photons
+can also create a quantum optical potential which will modify the
+Hamiltonian in a way that depends on the state of the atoms that
+scatterd the light. This can lead to new quantum phases due to new
+types of long-range interactions being mediated by the global quantum
+optical fields \cite{caballero2015, caballero2015njp, caballero2016,
+  caballero2016a}. However, this aspect of quantum optics of quantum
+gases is beyond the scope of this thesis.

Chapter2/chapter2.tex

@@ -20,9 +20,9 @@ the system in different parameter regimes, such as nondestructive
 measurement in free space or quantum measurement backaction in a
 cavity. Another interesting direction for this field of research are
 quantum optical lattices where the trapping potential is treated
-quantum mechanically. However this is beyond the scope of this work.
+quantum mechanically \cite{caballero2015, caballero2015njp,
-
+  caballero2016, caballero2016a}. However this is beyond the scope of
-\mynote{insert our paper citations here}
+this work.
 
 We consider $N$ two-level atoms in an optical lattice with $M$
 sites. For simplicity we will restrict our attention to spinless
@@ -41,23 +41,21 @@ lattice with a low filling factor (e.g.~a system with one atom per
 site which will exhibit the Mott insulator to superfluid quantum phase
 transition).
 
-\mynote{extra fermion citations, Piazza? Look up Gabi's AF paper.}
+An optical lattice can be formed with classical light beams that form
-
+standing waves. Depending on the detuning with respect to the atomic
-As we have seen in the previous section, an optical lattice can be
+resonance, the nodes or antinodes form the lattice sites in which
-formed with classical light beams that form standing waves. Depending
+atoms accumulate. As shown in Fig. \ref{fig:LatticeDiagram} the
-on the detuning with respect to the atomic resonance, the nodes or
+trapped bosons (green) are illuminated with a coherent probe beam
-antinodes form the lattice sites in which atoms accumulate. As shown
+(red) and scatter light into a different mode (blue) which is then
-in Fig. \ref{fig:LatticeDiagram} the trapped bosons (green) are
+measured with a detector. The most straightforward measurement is to
-illuminated with a coherent probe beam (red) and scatter light into a
+simply count the number of photons with a photodetector, but it is
-different mode (blue) which is then measured with a detector. The most
+also possible to perform a quadrature measurement by using a homodyne
-straightforward measurement is to simply count the number of photons
+detection scheme. The experiment can be performed in free space where
-with a photodetector, but it is also possible to perform a quadrature
+light can scatter in any direction. The atoms can also be placed
-measurement by using a homodyne detection scheme. The experiment can
+inside a cavity which has the advantage of being able to enhance light
-be performed in free space where light can scatter in any
+scattering in a particular direction. Furthermore, cavities allow for
-direction. The atoms can also be placed inside a cavity which has the
+the formation of a fully quantum potential in contrast to the
-advantage of being able to enhance light scattering in a particular
+classical lattice trap.
-direction. Furthermore, cavities allow for the formation of a fully
-quantum potential in contrast to the classical lattice trap.
 
 \begin{figure}[htbp!]
   \centering

Chapter7/chapter7.tex

@@ -9,3 +9,111 @@
 \else
     \graphicspath{{Chapter7/Figs/Vector/}{Chapter7/Figs/}}
 \fi
+
+Quantum optics of quantum gases explores the ultimate quantum regime
+of light-matter interactions where both the optical and matter fields
+are fully quantised. It provides a very rich system in which new
+phenomena can be observed, engineered, and controlled beyond what
+would be possible in condensed matter. Combined with rapid and
+promising experimental progress in this field the theoretical
+proposals have the potential of directing the research in the
+foreseeable future \cite{baumann2010, wolke2012, schmidt2014,
+  klinder2015, landig2016}.
+
+In this thesis we focused on the coupling between global quantised
+optical fields and an ultracold bosonic quantum gas. By considering
+global fields as opposed to localised light-matter interactions we
+were able to introduce several nonlocal properties to the Hamiltonian
+in a controllable manner which would otherwise be impossible to
+implement. We showed how this can be useful in the context of
+nondestructive probing by showing that it can easily distinguish
+between a highly delocalised quantum state such as a superfluid and
+insulating states such as the Mott insulator and the Bose glass phases
+which is currently a challenge \cite{derrico2014}. Furthermore, we
+have seen how the correlation length, which would be inaccessible in
+localised measurements, was immediately visible in our scheme and lead
+to an angular scattering pattern that was far richer than it was for
+the classical case. This is best highlighted by the fact that it would
+be visible even when classically no light would scatter coherently at
+all.
+
+More interestingly, the global nature of the measurement was also
+capable of creating such long-range correlations itself when we
+considered measurement backaction. This was most visible when we saw
+how weak measurement was capable of driving global macroscopic
+multimode oscillations between different spatial modes, such as odd
+and even sites, across the whole lattice which could be used for
+quantum information and metrology. Such dynamical states show spatial
+density-density correlations with nontrivial periods and long-range
+coherence, thus having supersolid properties, but as an essentially
+dynamical version. Furthermore, the tunability of the optical
+arrangement meant that we had extreme flexibility in choosing our
+observables, effectively tailoring the long-range entanglement and
+correlations in the system. We have also shown how global measurement
+when combined with both atomic tunnelling and interactions leads to
+highly nontrivial dynamics in which backaction can either compete or
+cooperate with on-site repulsion in squeezing the atomic variables.
+
+In the limit of strong measurement when quantum Zeno dynamics occurs
+we showed that these nonlocal spatial modes created by the global
+measurement lead to long-range correlated tunnelling events whilst
+suppressing any other dynamics between different spatial modes of the
+measurement. Such globally paired tunneling due to a fundamentally
+novel phenomenon can enrich physics of long-range correlated systems
+beyond relatively shortrange interactions expected from standard
+dipole-dipole interactions \cite{sowinski2012, omjyoti2015}. These
+nonlocal high-order processes entangle regions of the optical lattice
+that are disconnected by the measurement. Using different detection
+schemes, we showed how to tailor density-density correlations between
+distant lattice sites. Quantum optical engineering of nonlocal
+coupling to environment, combined with quantum measurement, can allow
+the design of nontrivial system-bath interactions, enabling new links
+to quantum simulations \cite{stannigel2013} and thermodynamics
+\cite{erez2008}. Interestingly, these dynamics also provide a link to
+non-Hermitian quantum mechanics as this regime of measurement can be
+accurately described with a non-Hermitian Hamiltonian. Furthermore, we
+show that this allows for a rather novel type of competition between
+measurement and tunnelling where both processes actually cooperate to
+produce a steady state in which tunnelling is suppressed by
+destructive matter-wave interference.
+
+A unique feature of our global measurement scheme meant that we could
+couple directly to the phase observables of the system by coupling to
+the interference between the lattice sites, which represents the
+shortest meaningful distance in an optical lattice, rather than their
+on-site density. This defines most processes in optical lattices.  For
+example, matter-field phase changes may happen not only due to
+external gradients, but also due to intriguing effects such quantum
+jumps leading to phase flips at neighbouring sites and sudden
+cancellation of tunneling \cite{vukics2007}, which should be
+accessible by this method. Furthremore, in mean-field one can measure
+the matter-field amplitude (which is also the order parameter),
+quadratures and their squeezing. This can link atom optics to areas
+where quantum optics has already made progress, e.g., quantum imaging
+\cite{golubev2010, kolobov1999}, using an optical lattice as an array
+of multimode nonclassical matter- field sources with a high degree of
+entanglement for quantum information processing. We have also shown
+how this scheme of coupling to phase observables can be used in the
+context of quantum measurement backaction to achieve a new degree of
+control. We used this result to show a generalisation of weak
+measurement on dynamical systems by showing that there is now a new
+class of projections available even when the measurement is not a
+compatible observable of the Hamiltonian. This an interesting result
+as the projections themselves are unlike those postulated by the
+Copenhagen interpretation, those present in quantum Zeno dynamic, or
+even those possible to engineer using dissipative methods.
+
+In this thesis we have covered significant areas of the broad field
+that is quantum optics of quantum gases, but there is much more that
+has been left untouched. Here, we have only considered spinless
+bosons, but the theory can also been extended to fermions
+\cite{atoms2015, mazzucchi2016, mazzucchi2016af} and
+molecules \cite{LP2013} and potentially even photonic circuits
+\cite{mazzucchi2016njp}. Furthermore, the question of quantum
+measurement and its properties has been a subject of heated debate
+since the very origins of quantum theory yet it is still as mysterious
+as it was at the beginning of the $20^\mathrm{th}$ century. However,
+this work has hopefully demonstrated that coupling quantised light
+fields to many-body systems provides a very rich playground for
+exploring new quantum mechanical phenomena beyond what would otherwise
+be possible in other fields.

References/references.bib

@@ -2,6 +2,15 @@
 %% Books, theses, reference material
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
+@book{carmichael,
+  title={An open systems approach to quantum optics: lectures
+                  presented at the Universit{\'e} Libre de Bruxelles,
+                  October 28 to November 4, 1991},
+  author={Carmichael, Howard},
+  volume={18},
+  year={2009},
+  publisher={Springer Science \& Business Media}
+}
 @book{foot,
   author = {Foot, C. J.},
   title = {{Atomic Physics}},
@@ -243,8 +252,10 @@ year = {2010}
   publisher={IOP Publishing}
 }
 @article{caballero2016,
-  title = {Quantum simulators based on the global collective light-matter interaction},
+  title = {Quantum simulators based on the global collective
-  author = {Caballero-Benitez, Santiago F. and Mazzucchi, Gabriel and Mekhov, Igor B.},
+                  light-matter interaction},
+  author = {Caballero-Benitez, Santiago F. and Mazzucchi, Gabriel and
+                  Mekhov, Igor B.},
   journal = {Phys. Rev. A},
   volume = {93},
   issue = {6},
@@ -1225,3 +1236,513 @@ doi = {10.1103/PhysRevA.87.043613},
   year={1981},
   publisher={APS}
 }
+@article{anderson1995,
+  title={Observation of Bose-Einstein Condensation in a Dilute Atomic
+                  Vapor},
+  author={Anderson, MH and Ensher, JR and Matthews, MR and Wieman, CE
+                  and Cornell, EA},
+  journal={science},
+  volume={269},
+  pages={14},
+  year={1995}
+}
+@article{bradley1995,
+  title={Evidence of Bose-Einstein condensation in an atomic gas with
+                  attractive interactions},
+  author={Bradley, Cl C and Sackett, CA and Tollett, JJ and Hulet,
+                  Randall G},
+  journal={Physical Review Letters},
+  volume={75},
+  number={9},
+  pages={1687},
+  year={1995},
+  publisher={APS}
+}
+@article{davis1995,
+  title={Bose-Einstein condensation in a gas of sodium atoms},
+  author={Davis, Kendall B and Mewes, M-O and Andrews, Michael R and
+                  Van Druten, NJ and Durfee, DS and Kurn, DM and
+                  Ketterle, Wolfgang},
+  journal={Physical review letters},
+  volume={75},
+  number={22},
+  pages={3969},
+  year={1995},
+  publisher={APS}
+}
+@article{bloch2008,
+  title={Many-body physics with ultracold gases},
+  author={Bloch, Immanuel and Dalibard, Jean and Zwerger, Wilhelm},
+  journal={Reviews of Modern Physics},
+  volume={80},
+  number={3},
+  pages={885},
+  year={2008},
+  publisher={APS}
+}
+@article{lewenstein2007,
+  title={Ultracold atomic gases in optical lattices: mimicking
+                  condensed matter physics and beyond},
+  author={Lewenstein, Maciej and Sanpera, Anna and Ahufinger, Veronica
+                  and Damski, Bogdan and Sen, Aditi and Sen, Ujjwal},
+  journal={Advances in Physics},
+  volume={56},
+  number={2},
+  pages={243--379},
+  year={2007},
+  publisher={Taylor \& Francis}
+}
+@article{andrews1997,
+  title={Observation of interference between two Bose condensates},
+  author={Andrews, MR and Townsend, CG and Miesner, H-J and Durfee, DS
+                  and Kurn, DM and Ketterle, W},
+  journal={Science},
+  volume={275},
+  number={5300},
+  pages={637--641},
+  year={1997},
+  publisher={American Association for the Advancement of Science}
+}
+@article{bloch2000,
+  title={Measurement of the spatial coherence of a trapped Bose gas at
+                  the phase transition},
+  author={Bloch, I and H{\"a}nsch, Th W and Esslinger, T},
+  journal={Nature},
+  volume={403},
+  number={6766},
+  pages={166--170},
+  year={2000},
+  publisher={Nature Publishing Group}
+}
+@article{matthews1999,
+  title={Vortices in a Bose-Einstein condensate},
+  author={Matthews, Michael Robin and Anderson, Brian P and Haljan, PC
+                  and Hall, DS and Wieman, CE and Cornell, EA},
+  journal={Physical Review Letters},
+  volume={83},
+  number={13},
+  pages={2498},
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thesis.tex

@@ -1,7 +1,7 @@
 % ******************************* PhD Thesis Template **************************
 % Please have a look at the README.md file for info on how to use the template
 
-\documentclass[a4paper,12pt,times,numbered,print,chapter]{Classes/PhDThesisPSnPDF}
+\documentclass[a4paper,12pt,times,numbered,print]{Classes/PhDThesisPSnPDF}
 
 % ******************************************************************************
 % ******************************* Class Options ********************************
@@ -101,7 +101,7 @@
 % To use choose `chapter' option in the document class
 
 \ifdefineChapter
- \includeonly{Chapter1/chapter1}
+ \includeonly{Abstract/Abstract}
 \fi
 
 % ******************************** Front Matter ********************************