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% ************************** Thesis Abstract *****************************
% Use `abstract' as an option in the document class to print only the titlepage and the abstract.
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\begin{abstract}
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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
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matter. Here, we consider coupling these systems to quantised light
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where the quantum nature of both the optical and matter fields play
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equally important roles in order to push the boundaries of what is
possible in ultracold atomic systems.
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We show that light can serve as a nondestructive probe of the
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quantum state of matter. By considering a global measurement we show
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that it is possible to distinguish a highly delocalised phase like a
superfluid from the Bose glass and Mott insulator. We also
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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
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multimode oscillations across the whole lattice when the measurement
is weak and correlated tunnelling, as well as selective suppression
and enhancement of dynamical processes beyond the projective limit
of the quantum Zeno effect in the strong measurement regime.
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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
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can lead to a new class of measurement projections thus extending
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the measurement postulate for the case of strong competition with
the systems own evolution.
\end{abstract}