Related papers: Creating high-dimensional topological physics usin…
We study the differential polynomial rings which are defined using the special geometry of the moduli spaces of Calabi-Yau threefolds. The higher genus topological string amplitudes are expressed as polynomials in the generators of these…
Topological plasmonics offers new ways to manipulate light by combining concepts from topology and plasmonics, similar to topological edge states in photonics. However, designing such topological states remains challenging due to the…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…
The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid…
A one-dimensional metamaterial with parity-time (${\cal PT}$) symmetry that relies on balanced gain and loss is introduced, comprising of magnetically coupled split-ring resonators (SRRs). A particular topology that combines a non-trivial…
We propose two kinds of distinguishing parameter regimes to induce topological Su-Schrieffer-Heeger (SSH) phase in a one dimensional (1D) multi-resonator cavity optomechanical system via modulating the frequencies of both cavity fields and…
The interplay between ferroelectricity and band topology can give rise to a wide range of both fundamental and applied research. Here, we map out the emergence of nontrivial corner states in two-dimensional ferroelectrics, and remarkably…
Research on high-$T_c$ superconductors has generally not focused on analysis of the topological structure of electronic bands in these materials. In this article we collate and discuss several well-known experimental observables that signal…
Topological photonics aims to utilize topological photonic bands and corresponding edge modes to implement robust light manipulation, which can be readily achieved in the linear regime of light-matter interaction. Importantly, unlike solid…
Arbitrary linear transformations are of crucial importance in a plethora of photonic applications spanning classical signal processing, communication systems, quantum information processing and machine learning. Here, we present a new…
The concepts of Weyl fermions and topological semimetals emerging in three-dimensional momentum space are extensively explored owing to the vast variety of exotic properties that they give rise to. On the other hand, very little is known…
We demonstrate the possibility of using time-space crystalline structures to simulate eight-dimensional systems based on only two physical dimensions. A suitable choice of system parameters allows us to obtain a gapped energy spectrum,…
We bound the number of electromagnetic signals which may be observed over a frequency range $2W$ for a time $T$ within a region of space enclosed by a radius $R$. Our result implies that broadband fields in space cannot be arbitrarily…
Entanglement in high-dimensional quantum systems, where one or more degrees of freedom of light are involved, offers increased information capacities and enables new quantum protocols. Here, we demonstrate a functional source of…
Topological phases based on tight-binding models have been extensively studied in recent decades. By mimicking the linear combination of atomic orbitals in tight-binding models based on the evanescent couplings between resonators in…
Frequency multiplication involves generating harmonics from an input frequency, a technique particularly useful for integrating spin-wave devices operating at different frequencies. While topological magnetic textures offer distinct…
We present a novel multipole formulation for computing the band structures of two-dimensional arrays of cylindrical Helmholtz resonators. This formulation is derived by combining existing multipole methods for arrays of ideal cylinders with…
We investigate the dynamics and topology of metastructures with quasiperiodically modulated local resonances. The concept is implemented on a LEGO beam featuring an array of tunable pillar-cone resonators. The versatility of the platform…
We describe recent nonlinear analytic approximation tools in the classical setting of Hardy spaces in the upper half plane and show how to transfer them to the higher dimensional real setting of harmonic functions in upper half spaces. It…
We introduce higher-order topological Dirac superconductor (HOTDSC) as a new gapless topological phase of matter in three dimensions, which extends the notion of Dirac phase to a higher-order topological version. Topologically distinct from…