The Hubbard model is an essential tool for understanding many-body physics in condensed matter systems. Artificial lattices of dopants in silicon are a promising method for the analog quantum simulation of extended Fermi-Hubbard Hamiltonians in the strong interaction regime. However, complex atom-based device fabrication requirements have meant emulating a tunable two-dimensional Fermi-Hubbard Hamiltonian in silicon has not been achieved. Here, we fabricate 3 × 3 arrays of single/few-dopant quantum dots with finite disorder and demonstrate tuning of the electron ensemble using gates and probe the many-body states using quantum transport measurements. By controlling the lattice constants, we tune the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from metallic to Mott insulating behavior. We simulate thermally activated hopping and Hubbard band formation using increased temperatures. As atomically precise fabrication continues to improve, these results enable a new class of engineered artificial lattices to simulate interactive fermionic models.

Metallic transition metal dichalcogenides, such as tantalum diselenide $\left(\mathrm{TaS}{\mathrm{e}}_2\right)$, display quantum correlated phenomena of superconductivity and charge density waves (CDWs) at low temperatures. Here, the photophysics of 2H-$\mathrm{TaS}{\mathrm{e}}_2$ during CDW transitions is revealed by combining temperature-dependent, low-frequency Raman spectroscopy and density functional theory (DFT). The spectra contain amplitude, phase, and zone-folded modes that are assigned to specific phonons and lattice restructuring predicted by DFT calculations with superb agreement. The noninvasive and efficient optical methodology detailed here demonstrates an essential link between atomic-scale and microscopic quantum phenomena.

In this paper, we show that quantum Hall resistance measurements using two terminals may be as precise as four-terminal measurements when applying superconducting split contacts. The described sample designs eliminate resistance contributions of terminals and contacts such that the size and complexity of next-generation quantized Hall resistance devices can be significantly improved.

The quantum Hall effect (QHE), and devices reliant on it, will continue to serve as the foundation of the ohm while also expanding its territory into other SI derived units. The foundation, evolution, and significance of all of these devices exhibiting some form of the QHE will be described in the context of optimizing future electrical resistance standards. As the world adapts to using the quantum SI, it remains essential that the global metrology community pushes forth and continues to innovate and produce new technologies for disseminating the ohm and other electrical units.

Transition-metal dichalcogenides (TMDCs) have offered experimental access to quantum confinement in one dimension. In recent years, metallic TMDCs like ${\mathrm{NbSe}}_2$ have taken center stage with many of them exhibiting interesting temperature-dependent properties such as charge density waves and superconductivity. In this paper, we perform a comprehensive optical analysis of ${\mathrm{NbSe}}_2$ by utilizing Raman spectroscopy, differential reflectance contrast, and spectroscopic ellipsometry. These analyses, when coupled with Kramers-Kronig analysis, allow us to extract the dielectric functions of bulk and atomically thin ${\mathrm{NbSe}}_2$ and relate them to the resonant behavior of the Raman spectra.