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978-3-8439-1337-9, Reihe Physik
Majorana Modes and Topological States in Realistic Driven-Dissipative Quantum Systems
170 Seiten, Dissertation Eidgenössische Technische Hochschule (ETH) Zürich (2013), Softcover, A5
Since the discovery, more than two decades ago, of phases of matter with topological properties, most theoretical studies of topological order have focused on closed quantum systems, i.e., on systems "enclosed in an imaginary box" preventing them from interacting with their environment. Closed quantum systems have served as a paradigm for understanding and even defining topological properties. In nature, however, quantum systems are never truly isolated, and their open nature often brings about more complexity and more richness in phenomena.
The first part of this thesis explores the concept of topological order in open quantum many-body systems from the point of view of purely dissipative free-fermion systems. A symmetry-based topological classification of such systems is constructed in a general theoretical framework based on the density matrix of the system, and a connection between bulk and edge topological properties (or "bulk-edge correspondence") is established in this context. Surprising phenomena with no counterpart in closed systems are identified and illustrated in experimentally realistic models. In particular, the emergence of unpaired Majorana modes in a non-equilibrium symmetry-protected topological phase characterized by a vanishing Chern number is demonstrated, providing a proof of principle that—challenging conventional wisdom—dissipation need not have destructive effects, but may rather give rise to intriguing novel topological phenomena.
In recent years, hybrid light-matter quantum many-body systems have been established as a rich platform for investigating phenomena traditionally regarded as pertaining to the realm of condensed matter physics. In the second part of this thesis, a theoretical model is developed for simulating the physics of Majorana modes in such intrinsically open quantum systems. Majorana-like modes are realized in a driven-dissipative system of strongly correlated photons consisting of a chain of tunnel-coupled cavities, where the optical counterpart of p-wave pairing arises from the interplay between strong on-site interactions and parametric amplification. An optical detection scheme is proposed, along with a potential implementation based on state-of-the-art circuit-QED technologies.