Some minor changes
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Wojciech Kozlowski
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@ -83,41 +83,41 @@ imprinted in the scattered light \cite{klinder2015, landig2016}.
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There are three prominent directions in which the field of quantum
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optics of quantum gases has progressed in. First, the use of quantised
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light enables direct coupling to the quantum properties of the atoms
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\cite{mekhov2007prl, mekhov2007pra, mekhov2007NP, mekhov2012}. This
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allows us to probe the many-body system in a nondestructive manner and
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under certain conditions even perform quantum non-demolition (QND)
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measurements. QND measurements were originally developed in the
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context of quantum optics as a tool to measure a quantum system
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without significantly disturbing it \cite{braginsky1977, unruh1978,
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brune1990, brune1992}. This has naturally been extended into the
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realm of ultracold gases where such non-demolition schemes have been
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applied to both fermionic \cite{eckert2008qnd, roscilde2009} and
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bosonic systems \cite{hauke2013, rogers2014}. In this thesis, we
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consider light scattering in free space from a bosonic ultracold gas
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and show that there are many prominent features that go beyond
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classical optics. Even the scattering angular distribution is
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nontrivial with Bragg conditions that are significantly different from
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the classical case. Furthermore, we show that the direct coupling of
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quantised light to the atomic systems enables the nondestructive
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probing beyond a standard mean-field description. We demonstrate this
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by showing that the whole phase diagram of a disordered
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one-dimensional Bose-Hubbard Hamiltonian, which consists of the
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superfluid, Mott insulating, and Bose glass phases, can be mapped from
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the properties of the scattered light. Additionally, we go beyond
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standard QND approaches, which only consider coupling to density
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observables, by also considering the direct coupling of the quantised
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light to the interference between neighbouring lattice sites. We show
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that not only is this possible to achieve in a nondestructive manner,
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it is also achieved without the need for single-site resolution. This
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is in contrast to the standard destructive time-of-flight measurements
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currently used to perform these measurements \cite{miyake2011}. Within
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a mean-field treatment this enables probing of the order parameter as
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well as matter-field quadratures and their squeezing. This can have an
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impact on atom-wave metrology and information processing in areas
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where quantum optics has already made progress, e.g.,~quantum imaging
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with pixellized sources of non-classical light \cite{golubev2010,
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kolobov1999}, as an optical lattice is a natural source of multimode
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nonclassical matter waves.
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\cite{mekhov2007prl, mekhov2007pra, mekhov2007NP, LP2009,
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mekhov2012}. This allows us to probe the many-body system in a
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nondestructive manner and under certain conditions even perform
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quantum non-demolition (QND) measurements. QND measurements were
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originally developed in the context of quantum optics as a tool to
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measure a quantum system without significantly disturbing it
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\cite{braginsky1977, unruh1978, brune1990, brune1992}. This has
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naturally been extended into the realm of ultracold gases where such
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non-demolition schemes have been applied to both fermionic
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\cite{eckert2008qnd, roscilde2009} and bosonic systems
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\cite{hauke2013, rogers2014}. In this thesis, we consider light
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scattering in free space from a bosonic ultracold gas and show that
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there are many prominent features that go beyond classical
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optics. Even the scattering angular distribution is nontrivial with
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Bragg conditions that are significantly different from the classical
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case. Furthermore, we show that the direct coupling of quantised light
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to the atomic systems enables the nondestructive probing beyond a
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standard mean-field description. We demonstrate this by showing that
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the whole phase diagram of a disordered one-dimensional Bose-Hubbard
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Hamiltonian, which consists of the superfluid, Mott insulating, and
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Bose glass phases, can be mapped from the properties of the scattered
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light. Additionally, we go beyond standard QND approaches, which only
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consider coupling to density observables, by also considering the
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direct coupling of the quantised light to the interference between
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neighbouring lattice sites. We show that not only is this possible to
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achieve in a nondestructive manner, it is also achieved without the
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need for single-site resolution. This is in contrast to the standard
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destructive time-of-flight measurements currently used to perform
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these measurements \cite{miyake2011}. Within a mean-field treatment
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this enables probing of the order parameter as well as matter-field
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quadratures and their squeezing. This can have an impact on atom-wave
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metrology and information processing in areas where quantum optics has
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already made progress, e.g.,~quantum imaging with pixellized sources
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of non-classical light \cite{golubev2010, kolobov1999}, as an optical
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lattice is a natural source of multimode nonclassical matter waves.
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Second, coupling a quantum gas to a cavity also enables us to study
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open system many-body dynamics either via dissipation where we have no
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@ -145,8 +145,9 @@ the first condenste was obtained that theoretical work on the effects
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of measurement on BECs appeared \cite{cirac1996, castin1997,
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ruostekoski1997}. Recently, work has also begun on combining weak
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measurement with the strongly correlated dynamics of ultracold gases
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in optical lattices \cite{mekhov2009prl, mekhov2009pra, mekhov2012,
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douglas2012, douglas2013, ashida2015, ashida2015a}.
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in optical lattices \cite{mekhov2009prl, mekhov2009pra, LP2010,
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mekhov2012, douglas2012, LP2013, douglas2013, ashida2015,
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ashida2015a}.
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In this thesis we focus on the latter by considering a quantum gas in
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an optical lattice coupled to a cavity \cite{mekhov2012}. This
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@ -220,7 +221,7 @@ of quantum gases is beyond the scope of this thesis.
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\newpage
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\section*{Publication List}
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\section*{List of Publications}
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The work contained in this thesis is based on seven publications
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\cite{kozlowski2015, elliott2015, atoms2015, mazzucchi2016,
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@ -248,19 +249,20 @@ The work contained in this thesis is based on seven publications
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\cite{mazzucchi2016} & G. Mazzucchi$^*$, W. Kozlowski$^*$,
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S. F. Caballero-Benitez, T. J. Elliott, and
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I. B. Mekhov. ``Quantum measurement-induced dynamics of many- body
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I. B. Mekhov. ``Quantum measurement-induced dynamics of many-body
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ultracold bosonic and fermionic systems in optical
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lattices''. \emph{Physical Review A}, 93:023632,
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2016. $^*$\emph{Equally contributing authors}. \\ \\
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\cite{kozlowski2016zeno} & W. Kozlowski, S. F. Caballero-Benitez,
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and I. B. Mekhov. ``Non- hermitian dynamics in the quantum zeno
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and I. B. Mekhov. ``Non-Hermitian dynamics in the quantum Zeno
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limit''. \emph{Physical Review A}, 94:012123, 2016. \\ \\
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\cite{mazzucchi2016njp} & G. Mazzucchi, W. Kozlowski,
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S. F. Caballero-Benitez, and I. B Mekhov. ``Collective dynamics of
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multimode bosonic systems induced by weak quan- tum
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measurement''. \emph{New Journal of Physics}, 18(7):073017, 2016. \\ \\
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multimode bosonic systems induced by weak quantum
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measurement''. \emph{New Journal of Physics}, 18(7):073017,
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2016. \\ \\
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\cite{kozlowski2016phase} & W. Kozlowski, S. F. Caballero-Benitez,
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and I. B. Mekhov. ``Quantum state reduction by
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@ -1174,23 +1174,20 @@ provided a sufficient number of photons can be collected to calculate
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reliable expectation values. The case of scattering into a cavity and
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the effect of efficiency on the conditioned state was addressed in
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Ref. \cite{mazzucchi2016njp} where it was shown that detector
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efficiencies as low as 1\% are still capable of resolving the dynamics
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to a good degree of accuracy and 10\% was sufficient for near unit
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fidelity. However, this incredible result requires that the photon
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scattering pattern is periodic in some way, e.g.~oscillatory as was
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the case in Ref. \cite{mazzucchi2016njp} or constant. This way it is
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only necessary to detect a sufficient number of photons to deduce the
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efficiencies are not a problem provided that the photon scattering
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pattern is periodic in some way, e.g.~oscillatory as was the case in
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Ref. \cite{mazzucchi2016njp} or constant. This way it is only
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necessary to detect a sufficient number of photons to deduce the
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correct phase of the oscillations or the rate for the case of a
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constant scattering rate. In this thesis we deal predominantly with
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these two cases so photodetector efficiency is not an issue.
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The other issue is the heating of the trapped gas which will limit the
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lifetime of the experiment. For free space scattering imaging times of
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several hundred milliseconds have been achieved by for example using
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molasses beams that simultaneously cool and trap the atoms
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\cite{weitenberg2011, weitenbergThesis}. Similar feats have been
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achieved with atoms coupled to a leaky cavity where interogation times
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of 0.8s have been achieved in Ref. \cite{brennecke2013}. Crucially,
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the cavity in said experiment has a decay rate of the order of MHz
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which is necessary to observe measurement backaction which we will
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consider in the subsequent chapters.
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lifetime of the experiment. For free space scattering appropriate
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conditions have been achieved by for example using molasses beams that
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simultaneously cool and trap the atoms \cite{weitenberg2011,
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weitenbergThesis}. Similar feats have been achieved with atoms
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coupled to a leaky cavity in Ref. \cite{brennecke2013}. Crucially, the
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cavity in said experiment has a decay rate of the order of MHz which
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is necessary to observe measurement backaction which we will consider
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in the subsequent chapters.
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@ -1743,11 +1743,11 @@ discussed.
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To obtain a state with a specific value of $\Delta N$ postselection
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may be necessary, but otherwise it is not needed. The process can be
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optimised by feedback control since the state is monitored at all
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times \cite{ivanov2014, mazzucchi2016feedback}. Furthermore, the form
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of the measurement operator is very flexible and it can easily be
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engineered by the geometry of the optical setup \cite{elliott2015,
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mazzucchi2016} which can be used to design a state with desired
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properties.
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times \cite{ivanov2014, mazzucchi2016feedback,
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ivanonv2016}. Furthermore, the form of the measurement operator is
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very flexible and it can easily be engineered by the geometry of the
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optical setup \cite{elliott2015, mazzucchi2016} which can be used to
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design a state with desired properties.
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\section{Conclusions}
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@ -1160,14 +1160,23 @@ wish to left align your text}
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\thispagestyle{empty}
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\setsinglecolumn
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\begin{center}
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{ \Large {\bfseries {\@title}} \par}
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{{\large \vspace*{1em} \@author} \par}
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{ \Large \singlespacing {\bfseries {\@title}} \par}
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{ {\onehalfspacing \vspace*{1em} \@author, \@college \\
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A thesis submitted for the degree of \@degreetitle \\
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\@degreedate \\
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{\Large \vspace*{1em} {\bfseries {Abstract}}}\par}}
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\end{center}
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\else
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% Normal abstract in the thesis
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\cleardoublepage
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\setsinglecolumn
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\chapter*{\centering \Large Abstract}
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\begin{center}
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{ \Large \singlespacing {\bfseries {\@title}} \par}
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{ {\onehalfspacing \vspace*{1em} \@author, \@college \\
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A thesis submitted for the degree of \@degreetitle \\
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\@degreedate \\
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{\Large \vspace*{1em} {\bfseries {Abstract}}}\par}}
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\end{center}
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\thispagestyle{empty}
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\fi
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}
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@ -203,6 +203,12 @@ year = {2010}
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year={2012},
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publisher={IOP Publishing}
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}
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@article{ivanov2016,
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title={Incoherent quantum feedback control of collective light scattering by Bose-Einstein condensates},
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author={Ivanov, Denis A and Ivanova, Tatiana Yu and Mekhov, Igor B},
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journal={arXiv preprint arXiv:1601.02230},
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year={2016}
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% Group papers
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@ -223,8 +229,8 @@ year = {2010}
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S. F. and Mekhov, I. B.},
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journal = {Physical Review Letters},
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pages = {113604},
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title = {{Multipartite Entangled Spatial Modes of Ultracold Atoms
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Generated and Controlled by Quantum Measurement}},
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title = {Multipartite Entangled Spatial Modes of Ultracold Atoms
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Generated and Controlled by Quantum Measurement},
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volume = {114},
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year = {2015}
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}
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@ -350,7 +356,7 @@ year = {2010}
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@article{mazzucchi2016feedback,
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title={Quantum optical feedback control for creating strong correlations in many-body systems},
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author={Mazzucchi, G. and Caballero-Benitez, S. F. and Ivanov, D. A. and Mekhov, I. B.},
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journal={arXiv preprint arXiv:1606.06022},
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journal={arXiv preprint arXiv:1606.06022 (TBP in Optica)},
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year={2016}
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}
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@ -52,7 +52,7 @@ Dynamics in Ultracold Bosonic Gases}
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%% Submission date
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% Default is set as {\monthname[\the\month]\space\the\year}
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%\degreedate{September 2014}
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\degreedate{Trinity Term 2016}
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%% Meta information
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%\subject{LaTeX} \keywords{{LaTeX} {PhD Thesis} {Engineering} {University of
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