Subhankar, SarthakThis dissertation is based on two independent projects and is therefore divided into two parts. The first half of this dissertation summarizes a series of investigations, both experimental and theoretical, that culminates in the realization of an optical lattice with a subwavelength spacing of $\lambda/4$, where $\lambda$ is the wavelength of light used to create the lattice. The second half of this thesis presents details on the design andconstruction of an apparatus for dual-species optical tweezer arrays of Rb and Yb for Rydberg-interaction-mediated quantum computation and simulation. Ultracold atoms trapped in optical lattices have proven to be a versatile, highly controllable, and pristine platform for studying quantum many-body physics. However, the characteristic single-particle energy scale in these systems is set by the recoil energy $E_R=h^2 /\left(8 m d^2\right)$. Here, $m$ is the mass of the atom, and $d$, the spatial period of the optical lattice, is limited by diffraction to ${\lambda}/{2}$, where $\lambda$ is the wavelength of light used to create the optical lattice. Although the temperatures in these systems can be exceedingly low, the energy scales relevant for investigating many-body physics phenomena, such as superexchange or magnetic dipole interactions, can be lower yet. This limitation can be overcome by raising the relevant energy scales of the system ($E_R^{\mathrm{eff}}=h^2 /\left(8 m d_{\mathrm{eff}}^2\right)$) by engineering optical lattices with spatial periodicities below the diffraction limit ($d_{\mathrm{eff}} < \lambda/2$). To realize this subwavelength-spaced lattice, we first generated a Kronig-Penney-like optical lattice using the nonlinear optical response of three-level atoms in spatially varying dark states. This conservative Kronig-Penney-like optical potential has strongly subwavelength barriers that can be less than 10 nm ($\equiv\lambda/50$) wide and are spaced $\lambda/2$ apart, where $\lambda$ is the wavelength of light used to generate the optical lattice. Using the same nonlinear optical response, we developed a microscopy technique that allowed the probability density of atoms in optical lattices to be measured with a subwavelength resolution of $\lambda/50$. We theoretically investigated the feasibility of stroboscopically pulsing spatially shifted 1D Kronig-Penney-like optical lattices to create lattices with subwavelength spacings. We applied the lattice pulsing techniques developed in this theoretical investigation to realize a $\lambda/4$-spaced optical lattice. We used the subwavelength resolution microscopy technique to confirm the existence of this $\lambda/4$-spaced optical lattice by measuring the probability density of the atoms in the ground band of the $\lambda/4$-spaced optical lattice. Single neutral atoms trapped in optical tweezer arrays with Rydberg interaction-mediated entangling gate operations have recently emerged as a promising platform for quantum computation and quantum simulation. These systems were first realized using atoms of a single species, with alkali atoms being the first to be trapped in optical tweezers, followed by alkaline-earth (like) atoms, and magnetic lanthanides. Recently, dual-species (alkali-alkali) optical tweezer arrays were also realized. Dual-species Rydberg arrays are a promising candidate for large-scale quantum computation due to their capability for multi-qubit gate operations and crosstalk-free measurements for mid-circuit readouts. However, a dual-species optical tweezer array of an alkali atom and an alkaline-earth (like) atom, which combines the beneficial properties of both types of atoms, has yet to be realized. In this half of the thesis, I present details on the design and construction of an apparatus for dual-species Rydberg tweezer arrays of Rb (alkali) and Yb (alkaline-earth like).enDissertationPhysicsQuantum physicsOpticsdiffraction limitdual speciesKronig-Penneyoptical tweezerRydbergsubwavelength