From 0816fa714ff559a2a258a4dcbcddfe8cebdeece4 Mon Sep 17 00:00:00 2001 From: Wojciech Kozlowski Date: Wed, 28 Sep 2016 19:10:50 +0100 Subject: [PATCH] Some minor changes --- Chapter1/chapter1.tex | 88 +++++++++++++++++++------------------ Chapter2/chapter2.tex | 27 +++++------- Chapter5/chapter5.tex | 10 ++--- Classes/PhDThesisPSnPDF.cls | 15 +++++-- References/references.bib | 12 +++-- thesis-info.tex | 2 +- 6 files changed, 84 insertions(+), 70 deletions(-) diff --git a/Chapter1/chapter1.tex b/Chapter1/chapter1.tex index 8b53e8e..f24e5fd 100644 --- a/Chapter1/chapter1.tex +++ b/Chapter1/chapter1.tex @@ -83,41 +83,41 @@ 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, mekhov2007pra, mekhov2007NP, 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 systems \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. +\cite{mekhov2007prl, mekhov2007pra, mekhov2007NP, LP2009, + 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 systems +\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 @@ -145,8 +145,9 @@ 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 optical lattices \cite{mekhov2009prl, mekhov2009pra, LP2010, + mekhov2012, douglas2012, LP2013, 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 @@ -220,7 +221,7 @@ of quantum gases is beyond the scope of this thesis. \newpage -\section*{Publication List} +\section*{List of Publications} The work contained in this thesis is based on seven publications \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$^*$, 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 lattices''. \emph{Physical Review A}, 93:023632, 2016. $^*$\emph{Equally contributing authors}. \\ \\ \cite{kozlowski2016zeno} & W. Kozlowski, S. F. Caballero-Benitez, - and I. B. Mekhov. ``Non- hermitian dynamics in the quantum zeno - limit''. \emph{Physical Review A}, 94:012123, 2016. \\ \\ + and I. B. Mekhov. ``Non-Hermitian dynamics in the quantum Zeno + limit''. \emph{Physical Review A}, 94:012123, 2016. \\ \\ \cite{mazzucchi2016njp} & G. Mazzucchi, W. Kozlowski, S. F. Caballero-Benitez, and I. B Mekhov. ``Collective dynamics of - multimode bosonic systems induced by weak quan- tum - measurement''. \emph{New Journal of Physics}, 18(7):073017, 2016. \\ \\ + multimode bosonic systems induced by weak quantum + measurement''. \emph{New Journal of Physics}, 18(7):073017, + 2016. \\ \\ \cite{kozlowski2016phase} & W. Kozlowski, S. F. Caballero-Benitez, and I. B. Mekhov. ``Quantum state reduction by diff --git a/Chapter2/chapter2.tex b/Chapter2/chapter2.tex index a3a8972..4d47f08 100644 --- a/Chapter2/chapter2.tex +++ b/Chapter2/chapter2.tex @@ -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 the effect of efficiency on the conditioned state was addressed in Ref. \cite{mazzucchi2016njp} where it was shown that detector -efficiencies as low as 1\% are still capable of resolving the dynamics -to a good degree of accuracy and 10\% was sufficient for near unit -fidelity. However, this incredible result requires that the photon -scattering pattern is periodic in some way, e.g.~oscillatory as was -the case in Ref. \cite{mazzucchi2016njp} or constant. This way it is -only necessary to detect a sufficient number of photons to deduce the +efficiencies are not a problem provided that the photon scattering +pattern is periodic in some way, e.g.~oscillatory as was 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 constant scattering rate. In this thesis we deal predominantly with these two cases so photodetector efficiency is not an issue. 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 -several hundred milliseconds have been achieved by for example using -molasses beams that simultaneously cool and trap the atoms -\cite{weitenberg2011, weitenbergThesis}. Similar feats have been -achieved with atoms coupled to a leaky cavity where interogation times -of 0.8s have been achieved in Ref. \cite{brennecke2013}. Crucially, -the cavity in said experiment has a decay rate of the order of MHz -which is necessary to observe measurement backaction which we will -consider in the subsequent chapters. +lifetime of the experiment. For free space scattering appropriate +conditions have been achieved by for example using molasses beams that +simultaneously cool and trap the atoms \cite{weitenberg2011, + weitenbergThesis}. Similar feats have been achieved with atoms +coupled to a leaky cavity in Ref. \cite{brennecke2013}. Crucially, the +cavity in said experiment has a decay rate of the order of MHz which +is necessary to observe measurement backaction which we will consider +in the subsequent chapters. diff --git a/Chapter5/chapter5.tex b/Chapter5/chapter5.tex index 389c98d..f8f2c65 100644 --- a/Chapter5/chapter5.tex +++ b/Chapter5/chapter5.tex @@ -1743,11 +1743,11 @@ discussed. 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 optimised by feedback control since the state is monitored at all -times \cite{ivanov2014, mazzucchi2016feedback}. Furthermore, the form -of the measurement operator is very flexible and it can easily be -engineered by the geometry of the optical setup \cite{elliott2015, - mazzucchi2016} which can be used to design a state with desired -properties. +times \cite{ivanov2014, mazzucchi2016feedback, + ivanonv2016}. Furthermore, the form of the measurement operator is +very flexible and it can easily be engineered by the geometry of the +optical setup \cite{elliott2015, mazzucchi2016} which can be used to +design a state with desired properties. \section{Conclusions} diff --git a/Classes/PhDThesisPSnPDF.cls b/Classes/PhDThesisPSnPDF.cls index e3c9f03..d011f26 100644 --- a/Classes/PhDThesisPSnPDF.cls +++ b/Classes/PhDThesisPSnPDF.cls @@ -1160,14 +1160,23 @@ wish to left align your text} \thispagestyle{empty} \setsinglecolumn \begin{center} - { \Large {\bfseries {\@title}} \par} - {{\large \vspace*{1em} \@author} \par} + { \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} \else % Normal abstract in the thesis \cleardoublepage \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} \fi } diff --git a/References/references.bib b/References/references.bib index 559b98c..1215df9 100644 --- a/References/references.bib +++ b/References/references.bib @@ -203,6 +203,12 @@ year = {2010} year={2012}, 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 @@ -223,8 +229,8 @@ year = {2010} S. F. and Mekhov, I. B.}, journal = {Physical Review Letters}, pages = {113604}, - title = {{Multipartite Entangled Spatial Modes of Ultracold Atoms - Generated and Controlled by Quantum Measurement}}, + title = {Multipartite Entangled Spatial Modes of Ultracold Atoms + Generated and Controlled by Quantum Measurement}, volume = {114}, year = {2015} } @@ -350,7 +356,7 @@ year = {2010} @article{mazzucchi2016feedback, 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.}, - journal={arXiv preprint arXiv:1606.06022}, + journal={arXiv preprint arXiv:1606.06022 (TBP in Optica)}, year={2016} } diff --git a/thesis-info.tex b/thesis-info.tex index ac6a79c..16b469a 100644 --- a/thesis-info.tex +++ b/thesis-info.tex @@ -52,7 +52,7 @@ Dynamics in Ultracold Bosonic Gases} %% Submission date % Default is set as {\monthname[\the\month]\space\the\year} -%\degreedate{September 2014} +\degreedate{Trinity Term 2016} %% Meta information %\subject{LaTeX} \keywords{{LaTeX} {PhD Thesis} {Engineering} {University of