Ultra-cold atoms in optical lattices provide a versatile and robust platform to study fundamental condensed-matter physics problems and have applications in quantum optics as well as quantum information processing. For many of these applications, Rydberg atoms (atoms excited to large principal quantum numbers) are ideal due to its long coherence times and strong interactions. However, one of the pre-requisite for such applications is identical confinement of ground state atoms with Rydberg atoms. This is challenging for conventionally used alkali atoms. In this thesis, I discuss the potential of using alkaline-earth Rydberg atoms for many-body physics by implementing simultaneous trapping for the relevant internal states. In particular, I consider a scheme for generating multi-particle entanglement and explore charge transport in a one dimensional atomic lattice.
Charge dynamics in an ultracold setup involving a laser-dressed atom and an ion is studied here. This transfer of charge is enabled through molecular Rydberg states that are accessed via a laser. The character of the charge exchange crucially depends on the coupling between the electronic dynamics and the motional dynamics of the atoms and ion. The molecular Rydberg states are characterized and a criterion for distinguishing coherent and incoherent regimes is formulated. Furthermore the concept is generalized to the many-body setup as the ion effectively propagates through a chain of atoms. Aspects of the transport, such as its direction, can be controlled by the excitation laser. This leads to new directions in the investigation of hybrid atom-ion systems that can be experimentally explored using optically trapped strontium atoms.