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86
Chapter1/chapter1.tex
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@ -83,41 +83,41 @@ imprinted in the scattered light \cite{klinder2015, landig2016}.
There are three prominent directions in which the field of quantum There are three prominent directions in which the field of quantum
optics of quantum gases has progressed in. First, the use of quantised optics of quantum gases has progressed in. First, the use of quantised
light enables direct coupling to the quantum properties of the atoms light enables direct coupling to the quantum properties of the atoms
\cite{mekhov2007prl, mekhov2007pra, mekhov2007NP, mekhov2012}. This \cite{mekhov2007prl, mekhov2007pra, mekhov2007NP, LP2009,
allows us to probe the many-body system in a nondestructive manner and mekhov2012}. This allows us to probe the many-body system in a
under certain conditions even perform quantum non-demolition (QND) nondestructive manner and under certain conditions even perform
measurements. QND measurements were originally developed in the quantum non-demolition (QND) measurements. QND measurements were
context of quantum optics as a tool to measure a quantum system originally developed in the context of quantum optics as a tool to
without significantly disturbing it \cite{braginsky1977, unruh1978, measure a quantum system without significantly disturbing it
brune1990, brune1992}. This has naturally been extended into the \cite{braginsky1977, unruh1978, brune1990, brune1992}. This has
realm of ultracold gases where such non-demolition schemes have been naturally been extended into the realm of ultracold gases where such
applied to both fermionic \cite{eckert2008qnd, roscilde2009} and non-demolition schemes have been applied to both fermionic
bosonic systems \cite{hauke2013, rogers2014}. In this thesis, we \cite{eckert2008qnd, roscilde2009} and bosonic systems
consider light scattering in free space from a bosonic ultracold gas \cite{hauke2013, rogers2014}. In this thesis, we consider light
and show that there are many prominent features that go beyond scattering in free space from a bosonic ultracold gas and show that
classical optics. Even the scattering angular distribution is there are many prominent features that go beyond classical
nontrivial with Bragg conditions that are significantly different from optics. Even the scattering angular distribution is nontrivial with
the classical case. Furthermore, we show that the direct coupling of Bragg conditions that are significantly different from the classical
quantised light to the atomic systems enables the nondestructive case. Furthermore, we show that the direct coupling of quantised light
probing beyond a standard mean-field description. We demonstrate this to the atomic systems enables the nondestructive probing beyond a
by showing that the whole phase diagram of a disordered standard mean-field description. We demonstrate this by showing that
one-dimensional Bose-Hubbard Hamiltonian, which consists of the the whole phase diagram of a disordered one-dimensional Bose-Hubbard
superfluid, Mott insulating, and Bose glass phases, can be mapped from Hamiltonian, which consists of the superfluid, Mott insulating, and
the properties of the scattered light. Additionally, we go beyond Bose glass phases, can be mapped from the properties of the scattered
standard QND approaches, which only consider coupling to density light. Additionally, we go beyond standard QND approaches, which only
observables, by also considering the direct coupling of the quantised consider coupling to density observables, by also considering the
light to the interference between neighbouring lattice sites. We show direct coupling of the quantised light to the interference between
that not only is this possible to achieve in a nondestructive manner, neighbouring lattice sites. We show that not only is this possible to
it is also achieved without the need for single-site resolution. This achieve in a nondestructive manner, it is also achieved without the
is in contrast to the standard destructive time-of-flight measurements need for single-site resolution. This is in contrast to the standard
currently used to perform these measurements \cite{miyake2011}. Within destructive time-of-flight measurements currently used to perform
a mean-field treatment this enables probing of the order parameter as these measurements \cite{miyake2011}. Within a mean-field treatment
well as matter-field quadratures and their squeezing. This can have an this enables probing of the order parameter as well as matter-field
impact on atom-wave metrology and information processing in areas quadratures and their squeezing. This can have an impact on atom-wave
where quantum optics has already made progress, e.g.,~quantum imaging metrology and information processing in areas where quantum optics has
with pixellized sources of non-classical light \cite{golubev2010, already made progress, e.g.,~quantum imaging with pixellized sources
kolobov1999}, as an optical lattice is a natural source of multimode of non-classical light \cite{golubev2010, kolobov1999}, as an optical
nonclassical matter waves. lattice is a natural source of multimode nonclassical matter waves.
Second, coupling a quantum gas to a cavity also enables us to study 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 open system many-body dynamics either via dissipation where we have no
@ -145,8 +145,9 @@ the first condenste was obtained that theoretical work on the effects
of measurement on BECs appeared \cite{cirac1996, castin1997, of measurement on BECs appeared \cite{cirac1996, castin1997,
ruostekoski1997}. Recently, work has also begun on combining weak ruostekoski1997}. Recently, work has also begun on combining weak
measurement with the strongly correlated dynamics of ultracold gases measurement with the strongly correlated dynamics of ultracold gases
in optical lattices \cite{mekhov2009prl, mekhov2009pra, mekhov2012, in optical lattices \cite{mekhov2009prl, mekhov2009pra, LP2010,
douglas2012, douglas2013, ashida2015, ashida2015a}. mekhov2012, douglas2012, LP2013, douglas2013, ashida2015,
ashida2015a}.
In this thesis we focus on the latter by considering a quantum gas in In this thesis we focus on the latter by considering a quantum gas in
an optical lattice coupled to a cavity \cite{mekhov2012}. This an optical lattice coupled to a cavity \cite{mekhov2012}. This
@ -220,7 +221,7 @@ of quantum gases is beyond the scope of this thesis.
\newpage \newpage
\section*{Publication List} \section*{List of Publications}
The work contained in this thesis is based on seven publications The work contained in this thesis is based on seven publications
\cite{kozlowski2015, elliott2015, atoms2015, mazzucchi2016, \cite{kozlowski2015, elliott2015, atoms2015, mazzucchi2016,
@ -248,19 +249,20 @@ The work contained in this thesis is based on seven publications
\cite{mazzucchi2016} & G. Mazzucchi$^*$, W. Kozlowski$^*$, \cite{mazzucchi2016} & G. Mazzucchi$^*$, W. Kozlowski$^*$,
S. F. Caballero-Benitez, T. J. Elliott, and S. F. Caballero-Benitez, T. J. Elliott, and
I. B. Mekhov. ``Quantum measurement-induced dynamics of many- body I. B. Mekhov. ``Quantum measurement-induced dynamics of many-body
ultracold bosonic and fermionic systems in optical ultracold bosonic and fermionic systems in optical
lattices''. \emph{Physical Review A}, 93:023632, lattices''. \emph{Physical Review A}, 93:023632,
2016. $^*$\emph{Equally contributing authors}. \\ \\ 2016. $^*$\emph{Equally contributing authors}. \\ \\
\cite{kozlowski2016zeno} & W. Kozlowski, S. F. Caballero-Benitez, \cite{kozlowski2016zeno} & W. Kozlowski, S. F. Caballero-Benitez,
and I. B. Mekhov. ``Non- hermitian dynamics in the quantum zeno and I. B. Mekhov. ``Non-Hermitian dynamics in the quantum Zeno
limit''. \emph{Physical Review A}, 94:012123, 2016. \\ \\ limit''. \emph{Physical Review A}, 94:012123, 2016. \\ \\
\cite{mazzucchi2016njp} & G. Mazzucchi, W. Kozlowski, \cite{mazzucchi2016njp} & G. Mazzucchi, W. Kozlowski,
S. F. Caballero-Benitez, and I. B Mekhov. ``Collective dynamics of S. F. Caballero-Benitez, and I. B Mekhov. ``Collective dynamics of
multimode bosonic systems induced by weak quan- tum multimode bosonic systems induced by weak quantum
measurement''. \emph{New Journal of Physics}, 18(7):073017, 2016. \\ \\ measurement''. \emph{New Journal of Physics}, 18(7):073017,
2016. \\ \\
\cite{kozlowski2016phase} & W. Kozlowski, S. F. Caballero-Benitez, \cite{kozlowski2016phase} & W. Kozlowski, S. F. Caballero-Benitez,
and I. B. Mekhov. ``Quantum state reduction by and I. B. Mekhov. ``Quantum state reduction by

27
Chapter2/chapter2.tex
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@ -1174,23 +1174,20 @@ provided a sufficient number of photons can be collected to calculate
reliable expectation values. The case of scattering into a cavity and reliable expectation values. The case of scattering into a cavity and
the effect of efficiency on the conditioned state was addressed in the effect of efficiency on the conditioned state was addressed in
Ref. \cite{mazzucchi2016njp} where it was shown that detector Ref. \cite{mazzucchi2016njp} where it was shown that detector
efficiencies as low as 1\% are still capable of resolving the dynamics efficiencies are not a problem provided that the photon scattering
to a good degree of accuracy and 10\% was sufficient for near unit pattern is periodic in some way, e.g.~oscillatory as was the case in
fidelity. However, this incredible result requires that the photon Ref. \cite{mazzucchi2016njp} or constant. This way it is only
scattering pattern is periodic in some way, e.g.~oscillatory as was necessary to detect a sufficient number of photons to deduce the
the case in Ref. \cite{mazzucchi2016njp} or constant. This way it is
only necessary to detect a sufficient number of photons to deduce the
correct phase of the oscillations or the rate for the case of a correct phase of the oscillations or the rate for the case of a
constant scattering rate. In this thesis we deal predominantly with constant scattering rate. In this thesis we deal predominantly with
these two cases so photodetector efficiency is not an issue. these two cases so photodetector efficiency is not an issue.
The other issue is the heating of the trapped gas which will limit the The other issue is the heating of the trapped gas which will limit the
lifetime of the experiment. For free space scattering imaging times of lifetime of the experiment. For free space scattering appropriate
several hundred milliseconds have been achieved by for example using conditions have been achieved by for example using molasses beams that
molasses beams that simultaneously cool and trap the atoms simultaneously cool and trap the atoms \cite{weitenberg2011,
\cite{weitenberg2011, weitenbergThesis}. Similar feats have been weitenbergThesis}. Similar feats have been achieved with atoms
achieved with atoms coupled to a leaky cavity where interogation times coupled to a leaky cavity in Ref. \cite{brennecke2013}. Crucially, the
of 0.8s have been achieved in Ref. \cite{brennecke2013}. Crucially, cavity in said experiment has a decay rate of the order of MHz which
the cavity in said experiment has a decay rate of the order of MHz is necessary to observe measurement backaction which we will consider
which is necessary to observe measurement backaction which we will in the subsequent chapters.
consider in the subsequent chapters.

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Chapter5/chapter5.tex
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@ -1743,11 +1743,11 @@ discussed.
To obtain a state with a specific value of $\Delta N$ postselection To obtain a state with a specific value of $\Delta N$ postselection
may be necessary, but otherwise it is not needed. The process can be may be necessary, but otherwise it is not needed. The process can be
optimised by feedback control since the state is monitored at all optimised by feedback control since the state is monitored at all
times \cite{ivanov2014, mazzucchi2016feedback}. Furthermore, the form times \cite{ivanov2014, mazzucchi2016feedback,
of the measurement operator is very flexible and it can easily be ivanonv2016}. Furthermore, the form of the measurement operator is
engineered by the geometry of the optical setup \cite{elliott2015, very flexible and it can easily be engineered by the geometry of the
mazzucchi2016} which can be used to design a state with desired optical setup \cite{elliott2015, mazzucchi2016} which can be used to
properties. design a state with desired properties.
\section{Conclusions} \section{Conclusions}

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Classes/PhDThesisPSnPDF.cls
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@ -1160,14 +1160,23 @@ wish to left align your text}
\thispagestyle{empty} \thispagestyle{empty}
\setsinglecolumn \setsinglecolumn
\begin{center} \begin{center}
{ \Large {\bfseries {\@title}} \par} { \Large \singlespacing {\bfseries {\@title}} \par}
{{\large \vspace*{1em} \@author} \par} { {\onehalfspacing \vspace*{1em} \@author, \@college \\
A thesis submitted for the degree of \@degreetitle \\
\@degreedate \\
{\Large \vspace*{1em} {\bfseries {Abstract}}}\par}}
\end{center} \end{center}
\else \else
% Normal abstract in the thesis % Normal abstract in the thesis
\cleardoublepage \cleardoublepage
\setsinglecolumn \setsinglecolumn
\chapter*{\centering \Large Abstract} \begin{center}
{ \Large \singlespacing {\bfseries {\@title}} \par}
{ {\onehalfspacing \vspace*{1em} \@author, \@college \\
A thesis submitted for the degree of \@degreetitle \\
\@degreedate \\
{\Large \vspace*{1em} {\bfseries {Abstract}}}\par}}
\end{center}
\thispagestyle{empty} \thispagestyle{empty}
\fi \fi
} }

12
References/references.bib
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@ -203,6 +203,12 @@ year = {2010}
year={2012}, year={2012},
publisher={IOP Publishing} publisher={IOP Publishing}
} }
@article{ivanov2016,
title={Incoherent quantum feedback control of collective light scattering by Bose-Einstein condensates},
author={Ivanov, Denis A and Ivanova, Tatiana Yu and Mekhov, Igor B},
journal={arXiv preprint arXiv:1601.02230},
year={2016}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Group papers %% Group papers
@ -223,8 +229,8 @@ year = {2010}
S. F. and Mekhov, I. B.}, S. F. and Mekhov, I. B.},
journal = {Physical Review Letters}, journal = {Physical Review Letters},
pages = {113604}, pages = {113604},
title = {{Multipartite Entangled Spatial Modes of Ultracold Atoms title = {Multipartite Entangled Spatial Modes of Ultracold Atoms
Generated and Controlled by Quantum Measurement}}, Generated and Controlled by Quantum Measurement},
volume = {114}, volume = {114},
year = {2015} year = {2015}
} }
@ -350,7 +356,7 @@ year = {2010}
@article{mazzucchi2016feedback, @article{mazzucchi2016feedback,
title={Quantum optical feedback control for creating strong correlations in many-body systems}, title={Quantum optical feedback control for creating strong correlations in many-body systems},
author={Mazzucchi, G. and Caballero-Benitez, S. F. and Ivanov, D. A. and Mekhov, I. B.}, author={Mazzucchi, G. and Caballero-Benitez, S. F. and Ivanov, D. A. and Mekhov, I. B.},
journal={arXiv preprint arXiv:1606.06022}, journal={arXiv preprint arXiv:1606.06022 (TBP in Optica)},
year={2016} year={2016}
} }

2
thesis-info.tex
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@ -52,7 +52,7 @@ Dynamics in Ultracold Bosonic Gases}
%% Submission date %% Submission date
% Default is set as {\monthname[\the\month]\space\the\year} % Default is set as {\monthname[\the\month]\space\the\year}
%\degreedate{September 2014} \degreedate{Trinity Term 2016}
%% Meta information %% Meta information
%\subject{LaTeX} \keywords{{LaTeX} {PhD Thesis} {Engineering} {University of %\subject{LaTeX} \keywords{{LaTeX} {PhD Thesis} {Engineering} {University of