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Topological Properties of Degenerate Quantum Gases in Kronig-Penney Like Potentials

Year: 2025
Type: dissertation
Abstract: In this thesis I study the topological properties exhibited in cold atom systems trapped in periodic and finite-size one-dimensional potentials. Ultracold atoms provide an excellent platform for exploring various many-body quantum models that are challenging to identify in traditional condensed matter systems. In particular, recent advancements in experimental cold atom physics have enabled the creation of subwavelength nanoscale potentials, making it possible to realize the Kronig-Penney model and its variations. One of these considers shifting a regular lattice of point-like barriers within a finite-sized box, which allows topologically protected edge states to emerge as a function of the shift parameter. The continuous shift parameter then provides a virtual dimension and the system becomes effectively two-dimensional, allowing topological states to be explored over a large and flexible parameter space. In my work I go beyond the standard singleparticle treatment of topological system and analyze the equilibrium and non-equilibrium physics of fermionic and bosonic many-body systems. The first project I present focuses on the non-equilibrium dynamics of a ground-state fermionic many-body gas following a quench between different lattice shift parameters that allow for edge states with different chirality. I examine the role of the single-particle chiral edge states in the non-equilibrium dynamics of the system and demonstrate that the usual monotonic decay associated with the orthogonality catastrophe, typically observed with increasing system size, is significantly altered. The second study explores the topological characteristics of a system of two interacting particles in the Kronig-Penney-type nanoscale potential and examines the appearance of two-particle topological states within the spectrum. This investigation is extended to the Rice-Mele model, where similar topological features are observed. Finally, the third study considers the optical realization of a height-modulated nanoscale potential, which generates a complex potential landscape. To probe the many-body properties of such a system, I examined the spectral function of a Tonks–Girardeau gas in a quasiperiodically modulated KP potential. By varying the modulation amplitude and frequency, I identified a transition between delocalized and localized single-particle eigenstates. In the localized regime, the spectral function shows flat, non-dispersive modes that reflect localized states, whereas in the delocalized regime it becomes continuous and dispersive.
DOI: 10.15102/0002001062
Language: English
Open Access status: green
OpenAlex ID: W7120082757
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