Continuous Transition between Bosonic Fractional Chern Insulator and Superfluid.

The properties of fractional Chern insulator (FCI) phases and the phase transitions between FCIs and Mott insulators in bosonic systems are well studied. The continuous transitions between FCI and superfluids (SFs), however, despite the inspiring field theoretical predictions [M. Barkeshli and J.

Maximal Quantum Interaction between Free Electrons and Photons.

The emerging field of free-electron quantum optics enables electron-photon entanglement and holds the potential for generating nontrivial photon states for quantum information processing. Although recent experimental studies have entered the quantum regime, rapid theoretical developments predict that qualitatively unique phenomena only emerge beyond a certain interaction strength. It is thus pertinent to identify the maximal electron-photon interaction strength and the materials, geometries, and particle energies that enable one to approach it.

Superscattering of light: fundamentals and applications.

Superscattering, theoretically predicted in 2010 and experimentally observed in 2019, is an exotic scattering phenomenon of light from subwavelength nanostructures. In principle, superscattering allows for an arbitrarily large total scattering cross section, due to the degenerate resonance of eigenmodes or channels. Consequently, the total scattering cross section of a superscatterer can be significantly enhanced, far exceeding the so-called single-channel limit.

Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries.

We theoretically construct a higher-order topological insulator (HOTI) on a Brillouin real projective plane enabled by momentum-space nonsymmorphic (k-NS) symmetries from synthetic gauge fields. Two anicommutative k-NS glide reflections appear in a checkerboard Z_{2} flux model, impose nonsymmorphic constraints on Berry curvature, and quantize bulk and Wannier-sector polarization nonlocally across different momenta. The model's bulk exhibits an isotropic quadrupole phase diagram, where the transition appears intrinsically from bulk gap closure.

Synthetic Non-Abelian Gauge Fields for Non-Hermitian Systems.

Non-Abelian gauge fields are versatile tools for synthesizing topological phenomena, but have so far been mostly studied in Hermitian systems, where gauge flux has to be defined from a closed loop in order for vector potentials, whether Abelian or non-Abelian, to become physically meaningful. We show that this condition can be relaxed in non-Hermitian systems by proposing and studying a generalized Hatano-Nelson model with imbalanced non-Abelian hopping. Despite lacking gauge flux in one dimension, non-Abelian gauge fields create rich non-Hermitian topological consequences.