Quantum simulation beyond periodicity: A theoretical study of the many-body and topological properties of quasiperiodic systems

Quasicrystals are intriguing materials that lie at the border between periodic and disordered matter. Their atomic structure exhibits fully long-range ordered, yet never-repeating structures. As such, they inherit properties from both periodic and disordered materials, and are for instance suspected of hosting novel quantum phases of matter that could evade thermalisation. Solid-state quasicrystalline samples are inherently subject to defects, finite grain size, and constantly subject to atomic vibrations. Together, these effects hamper the observation of truly quantum properties caused by their quasiperiodic atomic structure. In contrast, by shining intense laser light at specific angles onto ultracold atomic clouds, physicists are now able to create synthetic, defect-free, optical quasicrystalline lattices. These optical quasicrystals constitute highly tunable quantum simulators for investigating coherent quantum effects in quasicrystals. To study the physical properties of non-periodic quantum systems, and quasiperiodic ones in particular, it is necessary to consider systems of large system sizes to obtain reliable and converged results. In particular, the study of quantum phase transitions in periodic systems is often realised using a Hubbard model description of the system, where system is re-expressed as a collection of localised sites, corresponding to localised orbitals (Wannier functions), which are typically constructed using the periodicity of the system. These technique can therefore not apply to the context of non-periodic quantum systems in general, and optical quasicrystals in particular. First, we address the challenge of constructing Wannier functions for non-periodic potentials, for which Bloch's theorem by necessity does not apply. We develop a general numerical framework for constructing the Wannier functions and Hubbard models of non-periodic potentials, which allows the exploration of a wide range of previously inaccessible non-periodic systems at large system size. Second, we turn more specifically towards optical quasicrystals and the study of their infinite-size limit. We introduce the notion of configuration-space representation for describing the Hubbard models of quasiperiodic potentials. By organising lattice sites based on their local surroundings, we find that the Hubbard model of several quasiperiodic potentials can be re-expressed in terms of smooth functions on a compact, uniformly dense, parameter space. This representation allows for describing the infinite-size limit of the system, and provides crucial insights into their physical properties in the thermodynamic limit. Third, we apply the developed techniques to three experimentally relevant systems: the eightfold optical quasicrystal (8QC), the optical two-dimensional Aubry-André potential (O2DAA), and the fivefold optical quasicrystal (5QC). Our analysis reveals the distinct characteristics of each system, from the distribution of their Hubbard parameters to the localisation properties of their non-interacting eigenstates. In particular, we find that the configuration-space representation allows us to elucidate the origin of the energy gaps in the spectrum of the 8QC, and to show that the associated integrated density of states corresponds to irrational areas in configuration-space. Further, we turn to the topological properties of quasiperiodic systems and use the configuration space representation to uncover an intriguing robustness of Thouless pumping in the one-dimensional Aubry-André-Harper model to bounded onsite disorder. We explain the stability using a perturbative argument in the language of configuration space and find the persistence of quantised currents beyond the disorder-induced closing of energy gaps. Finally, we use the developed Hubbard models of the 8QC to test predictions made with the developed Hubbard model against recent experimental results performed with ultracold atoms. We investigate the system's ground state phase diagram in the regime of strong interactions using Quantum Monte Carlo (QMC) techniques and find superfluid, Bose glass, and Mott insulating phases in qualitative agreement with experimental data, as well as uncover the necessary ingredients for the formation of the Mott insulating phase. After focusing on the ground state, static properties of the 8QC, we investigate its dynamical properties by studying the quantum quench dynamics across the superfluid to Bose glass transition in the 8QC, and find excellent agreement with experimental data. Specifically, we find that the quench from the superfluid to Bose glass regime causes a gradual oscillating decay of the state's coherence, whose frequency is dominated by the bandwidth of the onsite energy distribution. Conversely, we find that the quench from the Bose glass to the superfluid regime exhibits light-cone-like correlation patterns, characteristic of ballistic dynamics compatible with an effective group velocity dictated by the strength of the tunneling terms.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2024

Author dc:creator

• Gottlob, Emmanuel

Advisor dc:contributor.advisor

• Schneider, Ulrich

• Cold Atoms
• Condensed Matter Physics
• Disordered Systems
• Quantum Simulation
• Quasicrystals
• Topological Phases of Matter

Licence

• https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/7e6f2868-b155-41a3-b656-60927535a13f/download
• https://creativecommons.org/licenses/by/4.0/

Language dc:language

eng

Author Identifier

0000-0003-3166-5497

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/375378