Quantum dynamics in low-dimensional topological systems

TL;DR

This thesis explores quantum dynamics in low-dimensional topological systems, revealing how interactions, periodic driving, and topology influence phenomena like edge states, doublon behavior, and emitter-photon interactions, with implications for quantum technologies.

Contribution

It provides new insights into the interplay of interactions, driving, and topology in 1D and 2D topological insulators, including effects on edge states and photon-emitter dynamics.

Findings

Disappearance of topological edge states in the SSH-Hubbard model.

Sublattice confinement and long-range transfer of doublons.

Topological effects on photon bound states and emitter interactions.

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.