Competition between Weak Quantum Measurement and Many-Body Dynamics in Ultracold Bosonic Gases
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A dissertation submitted for the degree of *Doctor of Philosophy* at
the University of Oxford.

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
matter. Here, we consider coupling these systems to quantised 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 matter. By considering a global measurement we show that it
is possible to distinguish a highly delocalised phase like a
superfluid from the Bose glass and Mott insulator. 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 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.

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.

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