In this thesis, I describe early experiments with a new platform that harnesses control over the full quantum state of individual 87Rb atoms to study out-of-equilibrium states of a few atoms placed in tailored optical potentials. We employ an enhanced loading technique that fills each well in 90% of loading attempts, image the configuration of the atoms, and then perform Raman sideband cooling that results in a 90% three-dimensional ground state fraction. Then, after initializing the spin of each atom, we can reconfigure the traps to initialize dynamics in a final optical potential of interest. For example, we can form a double well potential and observe the quantum interference of two atoms tunneling between the wells. Additionally, we have demonstrated the ability to coherently transfer atoms between wells and, by preparing two atoms in opposite spin states, have observed spin-exchange oscillations that periodically entangle the two atoms. I will also discuss plans and ongoing work to combine these capabilities with new techniques to gain more information from systems containing more atoms. In such systems, we wish to study how the spin-motional coupling of independently prepared atoms will lead to complex dynamics, such as in the Kondo lattice model.