120 lines
7.0 KiB
TeX
120 lines
7.0 KiB
TeX
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%*********************************** Seventh Chapter *****************************
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\chapter{Summary and Conclusions} %Title of the Seventh Chapter
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Quantum optics of quantum gases explores the ultimate quantum regime
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of light-matter interactions where both the optical and matter fields
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are fully quantised. It provides a very rich system in which new
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phenomena can be observed, engineered, and controlled beyond what
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would be possible in condensed matter. Combined with rapid and
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promising experimental progress in this field the theoretical
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proposals have the potential of directing the research in the
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foreseeable future \cite{baumann2010, wolke2012, schmidt2014,
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klinder2015, landig2016}.
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In this thesis we focused on the coupling between global quantised
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optical fields and an ultracold bosonic quantum gas. By considering
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global fields as opposed to localised light-matter interactions we
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were able to introduce several nonlocal properties to the Hamiltonian
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in a controllable manner which would otherwise be impossible to
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implement. We showed how this can be useful in the context of
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nondestructive probing by showing that it can easily distinguish
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between a highly delocalised quantum state such as a superfluid and
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insulating states such as the Mott insulator and the Bose glass phases
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which is currently a challenge \cite{derrico2014}. Furthermore, we
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have seen how the correlation length, which would be inaccessible in
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localised measurements, was immediately visible in our scheme and lead
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to an angular scattering pattern that was far richer than it was for
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the classical case. This is best highlighted by the fact that it would
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be visible even when classically no light would scatter coherently at
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all.
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More interestingly, the global nature of the measurement was also
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capable of creating such long-range correlations itself when we
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considered measurement backaction. This was most visible when we saw
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how weak measurement was capable of driving global macroscopic
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multimode oscillations between different spatial modes, such as odd
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and even sites, across the whole lattice which could be used for
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quantum information and metrology. Such dynamical states show spatial
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density-density correlations with nontrivial periods and long-range
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coherence, thus having supersolid properties, but as an essentially
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dynamical version. Furthermore, the tunability of the optical
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arrangement meant that we had extreme flexibility in choosing our
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observables, effectively tailoring the long-range entanglement and
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correlations in the system. We have also shown how global measurement
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when combined with both atomic tunnelling and interactions leads to
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highly nontrivial dynamics in which backaction can either compete or
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cooperate with on-site repulsion in squeezing the atomic variables.
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In the limit of strong measurement when quantum Zeno dynamics occurs
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we showed that these nonlocal spatial modes created by the global
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measurement lead to long-range correlated tunnelling events whilst
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suppressing any other dynamics between different spatial modes of the
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measurement. Such globally paired tunneling due to a fundamentally
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novel phenomenon can enrich physics of long-range correlated systems
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beyond relatively shortrange interactions expected from standard
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dipole-dipole interactions \cite{sowinski2012, omjyoti2015}. These
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nonlocal high-order processes entangle regions of the optical lattice
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that are disconnected by the measurement. Using different detection
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schemes, we showed how to tailor density-density correlations between
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distant lattice sites. Quantum optical engineering of nonlocal
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coupling to environment, combined with quantum measurement, can allow
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the design of nontrivial system-bath interactions, enabling new links
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to quantum simulations \cite{stannigel2013} and thermodynamics
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\cite{erez2008}. Interestingly, these dynamics also provide a link to
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non-Hermitian quantum mechanics as this regime of measurement can be
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accurately described with a non-Hermitian Hamiltonian. Furthermore, we
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show that this allows for a rather novel type of competition between
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measurement and tunnelling where both processes actually cooperate to
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produce a steady state in which tunnelling is suppressed by
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destructive matter-wave interference.
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A unique feature of our global measurement scheme meant that we could
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couple directly to the phase observables of the system by coupling to
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the interference between the lattice sites, which represents the
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shortest meaningful distance in an optical lattice, rather than their
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on-site density. This defines most processes in optical lattices. For
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example, matter-field phase changes may happen not only due to
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external gradients, but also due to intriguing effects such quantum
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jumps leading to phase flips at neighbouring sites and sudden
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cancellation of tunneling \cite{vukics2007}, which should be
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accessible by this method. Furthremore, in mean-field one can measure
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the matter-field amplitude (which is also the order parameter),
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quadratures and their squeezing. This can link atom optics to areas
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where quantum optics has already made progress, e.g., quantum imaging
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\cite{golubev2010, kolobov1999}, using an optical lattice as an array
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of multimode nonclassical matter- field sources with a high degree of
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entanglement for quantum information processing. We have also shown
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how this scheme of coupling to phase observables can be used in the
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context of quantum measurement backaction to achieve a new degree of
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control. We used this result to show a generalisation of weak
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measurement on dynamical systems by showing that there is now a new
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class of projections available even when the measurement is not a
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compatible observable of the Hamiltonian. This an interesting result
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as the projections themselves are unlike those postulated by the
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Copenhagen interpretation, those present in quantum Zeno dynamic, or
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even those possible to engineer using dissipative methods.
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In this thesis we have covered significant areas of the broad field
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that is quantum optics of quantum gases, but there is much more that
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has been left untouched. Here, we have only considered spinless
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bosons, but the theory can also been extended to fermions
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\cite{atoms2015, mazzucchi2016, mazzucchi2016af} and
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molecules \cite{LP2013} and potentially even photonic circuits
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\cite{mazzucchi2016njp}. Furthermore, the question of quantum
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measurement and its properties has been a subject of heated debate
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since the very origins of quantum theory yet it is still as mysterious
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as it was at the beginning of the $20^\mathrm{th}$ century. However,
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this work has hopefully demonstrated that coupling quantised light
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fields to many-body systems provides a very rich playground for
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exploring new quantum mechanical phenomena beyond what would otherwise
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be possible in other fields.
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