The mutual feedback between quantum condensed matter and cold atom physics has been quite fruitful throughout history and continues to inspire ongoing research. Motivated by the recent activities on the quantum simulation of topological orders among the ultracold Rydberg atom arrays, we consider the possibility of searching for topological orders among the dipolar quantum magnets and polar molecules with a kagome lattice geometry. Together with other quantum interactions such as the transverse field, the dipolar interaction endows the kagome system with a similar structure as the Balents-Fisher-Girvin model and thus fosters the emergence of the \mathbb{Z}_2 ℤ 2 topological orders. We construct a \mathbb{Z}_2 ℤ 2 lattice gauge theory to access the topological ordered phase and describe the spinon and vison excitations for the \mathbb{Z}_2 ℤ 2 topological orders. We explain the spectroscopic consequences for various quantum phases as well as the experimental detection. We further discuss the rare-earth kagome magnets, ultracold polar molecules, and cluster Mott insulators for the physical realization.
The mutual feedback between quantum condensed matter and cold atom physics has been quite fruitful throughout history and continues to inspire ongoing research. Motivated by the recent activities on the quantum simulation of topological orders among the ultracold Rydberg atom arrays, we consider the possibility of searching for topological orders among the dipolar quantum magnets and polar molecules with a kagome lattice geometry. Together with other quantum interactions such as the transverse field, the dipolar interaction endows the kagome system with a similar structure as the Balents-Fisher-Girvin model and thus fosters the emergence of the \mathbb{Z}_2 ℤ 2 topological orders. We construct a \mathbb{Z}_2 ℤ 2 lattice gauge theory to access the topological ordered phase and describe the spinon and vison excitations for the \mathbb{Z}_2 ℤ 2 topological orders. We explain the spectroscopic consequences for various quantum phases as well as the experimental detection. We further discuss the rare-earth kagome magnets, ultracold polar molecules, and cluster Mott insulators for the physical realization.
Ultracold atomic and molecular systems in the past years have significantly advanced the exploration of topological phases of matter. Notably, the recent experimental progress achieved in ultracold molecules, particularly within optical-tweezer lattices and leveraging long-range dipolar interactions, has opened up new avenues for this prospect. Here, we propose the creation of an ultracold-molecule trimerized Kagome optical-tweezer lattice to examine the topological phases induced by long-range dipolar interactions. Through a comparison of topological features in scenarios with and without long-range couplings, we find that the long-range interactions can induce higher-order topological phases with diverse topological corner modes at each corner, a phenomenon that can even emerge in nonstandard trimerized Kagome lattices. Furthermore, we develop a dynamic method to spectrally and spatially detect these topological corner modes. Our research not only underscores that long-range interactions can engender much richer topological phases but also suggests exciting possibilities for designing reconfigurable topological lattices.
Interactions among atoms can lead to emergent phenomena, one of the most fascinating being topological order. Topological phases are important in understanding high-temperature superconductors and fault-tolerant quantum computing. Quantum spin liquids, a key example of topologically ordered phases, exhibit unique properties such as long-range entanglement in the ground state and support of anyonic excitations, making them an exciting focus in the study of strongly correlated systems. This thesis explores the detection and learning of topological phases in quantum many-body systems, including quantum spin models, cuprate superconductors and ultracold atomic platform of Rydberg atom arrays. Guided by the experiments on Kitaev materials, we begin by using spinon mean-field theory of quantum spin liquids to explain the transition from a quantized thermal Hall effect to an unquantized values. Making closer connections to experiments in cuprates, we include additional interactions with phonons present in the system. We examine how spinon-phonon interactions, characterized by symmetry analysis, give rise to a chiral phonon Hall viscosity and can also contribute to the thermal Hall effect. In the second part, we turn to Rydberg atom arrays, which have recently been shown to realize a Z2 quantum spin liquid phase—an elusive state in conventional solid-state materials. We study how Rydberg interactions and lattice geometries lead to the emergence of Z2 gauge theories and distinct classes of topological quantum spin liquids. Finally, we study a variational tensor network tomography method for learning topological states from randomized measurements on Rydberg atom arrays. We demonstrate its efficiency in characterizing complex two-dimensional states that could be realized in future experiments.
Dual-species arrays of ultracold neutral atoms have recently attracted increased interest due to the ability to independently control different atomic species and tune the interatomic interactions. This capability provides additional flexibility essential for both quantum computing and quantum simulation. In this work we theoretically investigate a quantum spin liquid (QSL) state to be simulated on a programmable quantum simulator based on a dual-species atomic array, arranged on a Kagome lattice. The Kagome lattice is formed by corner sharing triangles. This specific spatial arrangement enhances the competing interactions between atoms and is often considered as a model for realizing QSL states. When the atoms are excited into Rydberg states, long-range interactions result in Rydberg blockade. The geometric frustration of the Kagome lattice, combined with the Rydberg blockade, drives the system into exotic phases with topological order and long-range entanglement. To drive an array into the QSL state, we use a sweep-hold-sweep protocol, when the atoms are quasi-adiabatically excited into Rydberg state with individually controlled detuning from the resonance for each atomic species. The filling fraction, indicating emergence of a QSL state, is represented by a density of Rydberg excitations. We identified the conditions required for QSL state in a dual-species array with non-uniform interaction energies. We calculated the correlation length and studied the mutual information as a function of the size of the subset of the system. The existence of a topological order was proved by estimating the Kitaev-Preskill topological quantum entanglement entropy, and further confirmed by evaluating diagonal and off-diagonal topological string operators, which respectively probe the classical dimer-covering structure and the quantum coherence between distinct dimer configurations.
The physical realization of Z 2 topological order as encountered in the paradigmatic toric code has proven to be an elusive goal.We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius.First, we show that the blockade model-also known as a "PXP" model-realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term.This model can be interpreted as a Z 2 gauge theory whose dynamics is generated by monomer fluctuations.We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of ln 2 as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap.Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactions VðrÞ ∼ 1=r 6 for a choice of lattice parameters.Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter.We show how these can be measured experimentally using a dynamic protocol, providing a "smoking gun" experimental signature of the TQL phase.Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.
Continuous control over lattice geometry, when combined with long-range interactions, offers a powerful yet underexplored tool to generate highly frustrated quantum spin systems. By considering long-range dipolar antiferromagnetic interactions on a breathed Kagome lattice, we demonstrate how these tools can be leveraged to stabilize a chiral spin liquid. We support this prediction with large-scale density-matrix renormalization group calculations and explore the surrounding phase diagram, identifying a route to adiabatic preparation via a locally varying magnetic field. At the same time, we identify the relevant low-energy degrees of freedom in each unit cell, providing a complementary language to study the chiral spin liquid. Finally, we carefully analyze its stability and signatures in finite-sized clusters, proposing direct, experimentally viable measurements of the chiral edge mode in both Rydberg atom and ultracold polar molecule arrays.
Long-range interactions are important to complex physical systems. Specifically in quantum mechanical many-body systems, long-range interactions promote spatial structures, give rise to quantum frustration, and generate quantum entanglement. Nevertheless, quantum simulations of lattice systems have largely not been able to realize long-range interactions. Many efforts are underway to explore long-range interacting lattice systems using polar molecules, Rydberg atoms, and magnetic atoms. In this thesis, I present the realization of long-range interacting itinerant systems using magnetic erbium atoms. I start by discussing the construction of the Erbium quantum gas microscope, including the installation of an in-vacuum high-numerical-aperture objective, various optical lattices, and potential projection through the objective. Then, I present emerging quantum phases with half-filling and directly probe the spatial structures of dipolar quantum solids using site-resolved imaging. A kaleidoscope of phases emerges as we tune the dipolar interaction, demonstrating the great tunability of this experimental platform. The dipolar interactions can be tuned slowly to study first-order quantum phase transitions between different solids. Next, I discuss topological phases that emerge with unity filling. With a zoo of Fano-Feshbach resonances, erbium atoms are gifted with the flexibility of widely tunable on-site interaction, allowing continuous probing of the quantum phase transitions between topologically trivial and non-trivial phases. We explore average symmetry protected topological phases as an instance of the mixed state quantum order. Finally, I briefly discuss the observation of spin squeezing with itinerant systems and super- and sub-radiance in a sub-wavelength optical lattice.