ABSTRACT In recent years, quantum simulators of topological models have been extensively studied across a variety of platforms and regimes. A new promising research direction makes use of meta‐atoms with multiple intrinsic degrees of freedom, which to date have been predominantly studied in the classical regime. Here, we propose a superconducting quantum simulator to study an extension of the well‐known “Zig‐Zag” model with long‐range cross‐polarization couplings using polarization transmons hosting degenerate dipole orbitals. We map the phase transitions of the extended “Zig‐Zag” model both numerically and analytically using inverse participation ratios and topological invariants. We demonstrate the existence of in‐gap localized non‐trivial and Tamm edge states. With linearized meta‐atoms, we show via electromagnetic modeling that the proposed arrangement closely reproduces the extended “Zig‐Zag” model. This work paves the way toward experimental investigation of the previously inaccessible topological quantum many‐body phenomena.
ABSTRACT In recent years, quantum simulators of topological models have been extensively studied across a variety of platforms and regimes. A new promising research direction makes use of meta‐atoms with multiple intrinsic degrees of freedom, which to date have been predominantly studied in the classical regime. Here, we propose a superconducting quantum simulator to study an extension of the well‐known “Zig‐Zag” model with long‐range cross‐polarization couplings using polarization transmons hosting degenerate dipole orbitals. We map the phase transitions of the extended “Zig‐Zag” model both numerically and analytically using inverse participation ratios and topological invariants. We demonstrate the existence of in‐gap localized non‐trivial and Tamm edge states. With linearized meta‐atoms, we show via electromagnetic modeling that the proposed arrangement closely reproduces the extended “Zig‐Zag” model. This work paves the way toward experimental investigation of the previously inaccessible topological quantum many‐body phenomena.
In recent years, quantum simulators of topological models have been extensively studied across a variety of platforms and regimes. A new promising research direction makes use of meta-atoms with multiple intrinsic degrees of freedom, which to date have been predominantly studied in the classical regime. Here, we propose a superconducting quantum simulator to study an extension of the well-known "Zig-Zag" model with long-range cross-polarization couplings using polarization transmons hosting degenerate dipole orbitals. We map the phase transitions of the extended "Zig-Zag" model both numerically and analytically using inverse participation ratios and topological invariants. We demonstrate the existence of in-gap localized trivial and Tamm edge states. With linearized meta-atoms, we show via electromagnetic modeling that the proposed arrangement closely reproduces the extended "Zig-Zag" model. This work paves the way towards experimental investigation of the previously inaccessible topological quantum many-body phenomena.
State-of-the-art quantum simulators -- ranging from ultracold atoms and trapped ions to Rydberg arrays and superconducting qubits -- have rapidly evolved into powerful platforms for investigating complex quantum many-body phenomena. In this thesis, we discuss various models and their static and non-equilibrium properties that can be realized on near-term quantum devices. We conduct comprehensive studies on the phases of these models, spanning novel symmetry-protected topological and critical gapless phases in one dimension to the non-equilibrium behavior of localized excitations in one-dimensional quantum chains and extended one-dimensional quantum objects embedded in a two-dimensional quantum magnet. On the technical side, we employ extensive tensor network simulations to validate our findings and introduce new algorithms to determine the lifetime of edge excitations emerging in the symmetry-protected topological phase of fermionic chains. Furthermore, we propose a new variational ansatz to directly search for these novel edge modes in the topological phase. By integrating analytical tools and tensor network simulations, this thesis contributes to the roadmap for establishing quantum simulators as promising tools for investigating complex quantum systems.
(English) In recent years, the evolution of quantum technologies has resulted in an unprecedented control over individual quantum particles and many-body systems. This remarkable progress has given rise to a new era, marked by the convergence of classical and quantum methodologies to investigate fundamental questions concerning the nature of quantum matter, improving our understanding of the role of entanglement in solid-state systems or the mechanisms behind high-energy physics. From analog quantum simulators to digital quantum computers, these advancements hold potential across diverse domains. This thesis explores the interplay between classical and quantum methods in understanding topological phases of matter. We concentrate on three distinct directions: non-conventional topological superconductors, interaction-induced topological phases in ultracold atom quantum simulators, and applications of variational quantum algorithms. Each trajectory relies on the combination of different techniques with the aim of understanding and characterizing topological phenomena in different settings. Exploring non-conventional topological superconductors involves extending the paradigmatic Kitaev chain model by incorporating additional terms in the Hamiltonian such as long-range interactions and quasi-periodic potentials. This investigation is relevant to better understand the impact of real-world conditions on the both the topological and localization properties of systems hosting non-local Majorana modes, which are promising candidates for topological quantum computation. In the realm of interacting systems, we explore the realization of interaction-induced topological phases in systems of ultracold atoms in optical lattices, both in one and two dimensions. The remarkable control and versatility of such platforms enable the simulation of both theoretical topological models and strongly correlated physics. Notably, the interplay between interactions and topology can give rise to intriguing phenomena, such as delocalized fractional charges and gapless topological phases,challenging existing intuition. We employ advanced numerical methods based on tensor networks to benchmark the experimental proposals that open the door to the realization and detection of novel many-body phases of matter, including topological quantum critical points and a higher-order topological Peierls insulator in Bose-Hubbard models with long-range interactions. Variational quantum algorithms, conversely, have the potential to efficiently tackle a wide range of problems, including ground state search, phase classification or accessing topological invariants. Despite current limitations in trainability and scalability, these hybrid classical-quantum algorithms provide practical insights into current quantum hardware capabilities and can inspire future architectures. We explore the application of variational quantum algorithms to shed light on topological phenomena, raising questions about their ability to discern topological phase transitions and compute topological invariants in situations where classical approaches fail. This thesis presents a comprehensive exploration of distinct approaches to topological quantum matter by leveraging quantum technologies and quantum-inspired classical algorithms. Our results not only advance our understanding of quantum systems but also pave the way for the realization and discovery of novel physics extending to quantum information processing, materials science, and beyond.
A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to reach parameter regions not studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wave function can be obtained exactly along a line and at a special point, for these two phases, respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation and discuss the phase transitions between the two SPT phases and their experimental signatures.
Symmetry plays a crucial role in understanding topological phases in materials. In one-dimensional systems, such as the Su-Schrieffer-Heeger (SSH) model, chiral symmetry is thought to ensure the quantization of the Zak phase and the nontrivial topological phase. However, our work demonstrates that the one-dimensional lattice system with broken chiral symmetry can still possess quantized Zak phase and nontrivial topological phase. Specifically, we use a Bose-Einstein condensate of 87Rb atoms in a momentum space lattice of ultracold atoms to effectively simulate a one-dimensional Zigzag model of 26 sites, which intrinsically breaks the chiral symmetry by additional next-nearest-neighbor coupling. To ensure the existence of the nontrivial topological phase, where the Zak phase can be measured from the time-averaged displacement during the system’s evolution, we need to preserve the inversion symmetry by modulating laser power so that all next-nearest-neighbor coupling strengths are equal. Furthermore, by changing the ratio of nearest-neighbor coupling strengths, we observe a topological phase transition from a nontrivial topological phase to a trivial topological phase at the point where the ratio equals 1. Our work demonstrates that the ultracold atom system provides a controllable platform for studying the symmetrical phase and topological phase, with the potential to explore nonlinear topological phenomena by increasing the interactions among atoms. In addition, our system can be used to investigate other interesting topological phenomena with more complex models, such as critical phenomena at the phase transitions and flat band structures in the extended SSH model with long-range coupling. By controlling the coupling strengths, we can also explore the influence of different symmetries on the topological properties of extended SSH models in the future. Moreover, our platform makes it possible to studythe models with more energy bands, such as the Aharonov-Bohm caging model with a three-level structure, which shows peculiar flat-band properties. This work provides opportunities for various studies in the fields of symmetry, topology, and the interaction of controllable quantum systems.
ABSTRACT The phenomenon of quantum walks of quasiparticles under nonreciprocal coupling is not only pivotal for investigating a myriad of novel quantum phenomena in nonreciprocal many‐body quantum systems, but also holds promise for the construction of nonreciprocal quantum devices. To date, manipulating the dynamical behavior of quasiparticles in such systems remains a significant challenge. Leveraging the quantum interference effect between coherent and dissipative coupling channels, we propose an effective scheme for realizing nonreciprocal coupling between superconducting qubits, and based on this scheme, we present a one‐dimensional nonreciprocal quantum simulator. Through numerical simulations, we demonstrate that this quantum simulator is capable of precisely manipulating a variety of exotic quantum phenomena, including the non‐Hermitian skin effect, chiral currents, and chiral spin waves. Furthermore, we simulate the propagation dynamics of entangled states under nonreciprocal coupling; the results indicate that nonreciprocity significantly suppresses the propagation of entanglement. Moreover, we provide a phenomenological interpretation of these exotic physical phenomena emerging in the non‐Hermitian regime. The nonreciprocal coupling mechanism and the quantum simulator presented in this work provide a highly coherent, scalable, and controllable platform for the quantum simulation of nonreciprocal many‐body systems, paving the way for the design of nonreciprocal quantum devices.