Non-Hermitian Topology of Microcavity Exciton Polaritons
Date
2021
Authors
Hu, Yow-ming Robin
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Abstract
Topology in solid state physics gave a new way to classify
materials using quantities
called topological invariants. Phases with non-vanishing
topological invariants can exhibit
non-trivial dynamics of charge-carriers at the boundary which is
protected against
scattering with impurities and imperfections. The study of
topology has recently been
generalized to a new class of systems with dissipation, which can
be described by effective
non-Hermitian Hamiltonians and have complex-valued eigenenergies.
It has been
discovered that there are topological invariants unique to
non-Hermitian systems. One
of them—spectral winding arises near the exceptional points
(the non-Hermitian spectral
degeneracies). In this thesis, I investigated the non-Hermitian
topology of a mixed
light-matter system—microcavity exciton polaritons.
The exciton polaritons are composite particles created by
strongly coupling bound
electron-hole pairs (excitons) to photons in a microcavity. They
can be described by a
non-Hermitian Hamiltonian because both gain (via optical pumping)
and loss (radiative
decay) are always present in the system. The ANU Polariton BEC
group has previously
observed a non-Hermitian spectral degeneracy in this system and,
in a separate study,
detected the spectral winding around a pair of the exceptional
points. However, a comprehensive
theory of non-Hermitian topology for this system has not yet been
developed.
In this thesis, I took the first essential steps towards building
a theoretical framework for
studies of non-Hermitian topology in exciton-polariton systems.
In particular, I derived
quantities that characterise the global properties of the
eigenvalues that are analogous to
those used in Hermitian topological systems.
One important topological invariant in the solid state system is
the Chern number.
The Chern number is realted to a quantity called the Berry
curvature, which acts on
the electrons in the solid state system as an effective magnetic
field when an external
field is absent. The Berry curvature is part of a larger quantity
called the quantum
geometric tensor. The real part of quantum geometric tensor is a
metric that defines the
distance between two states in momentum space, while its
imaginary part is related to
the Berry curvature. In this thesis, I generalized the quantum
geometric tensor to non-
Hermitian systems using a recently developed formalism (Chapter
4). I then investigated
the properties of the components of the four quantum geometric
tensors and concluded
that two of them are the natural non-Hermitian generalizations,
while the remaining ones
are inconsistent (Chapter 5). This conclusion was further
supported by investigation
of exciton-polariton wavepacket dynamics (Chapter 6). The last
Chapter of this thesis
summarises conclusions drawn from my study and presents an
outlook on further research.
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non-Hermitian physics, topology, exciton polaritons, photonics, condensed matter
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Thesis (Honours)
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