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Quantum particles on a lattice with competing long-range interactions are ubiquitous in physics. Transition metal oxides, layered molecular crystals and trapped ion arrays are a few examples out of many. In the strongly interacting regime,…
Conventional photonic lattices, such as metamaterials and photonic crystals, exhibit various interesting physical properties that are attributed to periodic modulations in lattice parameters. In this study, we introduce novel types of…
Controlling the electronic properties of interfaces has enormous scientific and technological implications and has been recently extended from semiconductors to complex oxides which host emergent ground states not present in the parent…
Understanding quantum many-body systems is at the heart of condensed matter physics. The ability to control the underlying lattice geometry of a system, and thus its many-body interactions, would enable the realization of and transition…
Solid-state platforms are particularly attractive for quantum optics because they facilitate on-chip integration and are compatible with established semiconductor and photonic technologies. However, a major challenge in solid-state quantum…
Moir\'e superlattices in two-dimensional materials provide a versatile platform to explore strongly correlated and topological phases. This work presents a practical theoretical workflow for studying the correlated and topological states in…
Concepts from quantum topological states of matter have been extensively utilized in the past decade in creating mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized…
Metasurfaces (MSs) have been utilized to manipulate different properties of electromagnetic waves. By combining local control over the wave amplitude, phase, and polarization into a single tunable structure, a multi-functional and…
We prepare and study a metastable attractive Mott insulator state formed with bosonic atoms in a three-dimensional optical lattice. Starting from a Mott insulator with Cs atoms at weak repulsive interactions, we use a magnetic Feshbach…
As a novel platform for exploring exotic quantum phenomena, the moir\'e lattice has garnered significant interest in solid-state physics, photonics, and cold atom physics. While moir\'e lattices in two- and three-dimensional systems have…
Moir\'{e} superlattices in transition metal dichalcogenide heterostructures provide a platform to engineer many-body interactions. Here, we realize a bichromatic moir\'{e} superlattice in an asymmetric WSe$_2$/WS$_2$/WSe$_2$ heterotrilayer…
We consider bosonic dipolar molecules in an optical lattice prepared in a mixture of different rotational states. The 1/r^3 interaction between molecules for this system is produced by exchanging a quantum of angular momentum between two…
An effective way to design structured coherent wave interference patterns that builds on the theory of coherent lattices, is presented. The technique combines prime number factorization in the complex plane with moir\'e theory to provide a…
We study localization driven solely by interparticle interactions in moir\'e lattice systems without intrinsic disorder or externally imposed quasiperiodic potentials. We consider a one-dimensional bilayer with incommensurate lattice…
The rapid progress in quantum technology enables the implementation of artificial many-body systems with correlated photons and polaritons. A multiconnected Jaynes-Cummings (MCJC) lattice can be constructed by connecting qubits and cavities…
The recent proposal of Romero-Isart {\em et al.}~\cite{romero-isart_superconducting_2013} to utilize the vortex lattice phases of superconducting materials to prepare a lattice for ultra-cold atoms-based quantum emulators, raises the need…
In multilayer moir\'e heterostructures, the interference of multiple twist angles ubiquitously leads to tunable ultra-long-wavelength patterns known as supermoir\'e lattices. However, their impact on the system's many-body electronic phase…
Moir{\'e} heterostructures, created by stacking two-dimensional (2D) materials together with a finite lattice mismatch or rotational twist, represent a new frontier of designer quantum materials. Typically, however, this requires the…
Metasurfaces mold the flow of classical light waves by engineering sub-wavelength patterns from dielectric or metallic thin films. We describe and analyze a method in which quantum operator-valued reflectivity can be used to control both…
Resonances in optical systems are useful for many applications, such as frequency comb generation, optical filtering, and biosensing. However, many of these applications are difficult to implement in optical metasurfaces because traditional…