Quantum dynamics in low-dimensional topological systems
- URL: http://arxiv.org/abs/2008.02044v2
- Date: Thu, 3 Sep 2020 12:17:21 GMT
- Title: Quantum dynamics in low-dimensional topological systems
- Authors: Miguel Bello
- Abstract summary: We study the quantum dynamics that take place in low dimensional topological systems, specifically 1D and 2D lattices.
We find that the topological nature of the bath reflects itself in the photon bound states and the effective dipolar interactions between the emitters.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The discovery of topological matter has revolutionized the field of condensed
matter physics giving rise to many interesting phenomena, and fostering the
development of new quantum technologies. In this thesis we study the quantum
dynamics that take place in low dimensional topological systems, specifically
1D and 2D lattices that are instances of topological insulators. First, we
study the dynamics of doublons, bound states of two fermions that appear in
systems with strong Hubbard-like interactions. We also include the effect of
periodic drivings and investigate how the interplay between interaction and
driving produces novel phenomena. Prominent among these are the disappearance
of topological edge states in the SSH-Hubbard model, the sublattice confinement
of doublons in certain 2D lattices, and the long-range transfer of doublons
between the edges of any finite lattice. Then, we apply our insights about
topological insulators to a rather different setup: quantum emitters coupled to
the photonic analogue of the SSH model. In this setup we compute the dynamics
of the emitters, regarding the photonic SSH model as a collective structured
bath. We find that the topological nature of the bath reflects itself in the
photon bound states and the effective dipolar interactions between the
emitters. Also, the topology of the bath affects the single-photon scattering
properties. Finally, we peek into the possibility of using these kind of setups
for the simulation of spin Hamiltonians and discuss the different ground states
that the system supports.
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