In this thesis, I describe the development of and scientific results from a new platform for creating ultracold atoms via single-atom control. We employ Raman-sideband cooling to isolated bosonic ⁸⁷Rb atoms confined within sub-micron optical tweezers, yielding single particle three dimensional ground-state fractions of 90%. We create multiple, independent, mobile optical tweezers, which simultaneously allows multi-particle studies with single-atom microscopy and highly tunable length-scales. We employ this toolset in both of the main experiments discussed in this thesis. In one experiment, we observe Hong-Ou-Mandel interference of two bosonic atoms, each of which is independently prepared in spatially separated optical tweezers. The interference we observe is a direct consequence of the purity of the single particle quantum states produced, and the indistinguishability of the atoms. In a second experiment, we introduce a spin-degree of freedom and exploit spin-exchange dynamics, driven by the quantum-statistics of the particles, to create a spin-entangled pair of spatially separated atoms.