  Double-well systems loaded with one, two, or many quantum particles give rise
to intriguing dynamics, ranging from Josephson oscillation to self-trapping.
This work presents theoretical and experimental results for two distinct
double-well systems, both created using dilute rubidium Bose-Einstein
condensates with particular emphasis placed on the role of interaction in the
systems. The first is realized by creating an effective two-level system
through Raman coupling of hyperfine states. The second is an effective
two-level system in momentum space generated through the coupling by an optical
lattice. Even though the non-interacting systems can, for a wide parameter
range, be described by the same model Hamiltonian, the dynamics for these two
realizations differ in the presence of interactions. The difference is
attributed to scattering diagrams that contribute in the lattice coupled system
but vanish in the Raman coupled system. The internal dynamics of the
Bose-Einstein condensates for both coupling scenarios is probed through a
Ramsey-type interference pulse sequence, which constitutes a key building block
of atom interferometers. These results have important implications in a variety
of contexts including lattice calibration experiments and momentum space
lattices used for quantum analog simulations.
