Generating macroscopic-quantum-superposition states in momentum and internal-state space from Bose-Einstein condensates with repulsive interactions

Resonant Raman coupling between internal levels can create double-well momentum-space potentials for multilevel ``periodically-dressed'' atoms. We develop a many-body formalism for a weakly interacting, trapped periodically dressed Bose gas which illustrates how a tunable exchange interaction yields correlated many-body ground states. In contrast to the case of a position-space double well, the ground state of stable periodically-dressed Bose gases with repulsive interactions tends toward a macroscopic superposition state in the regime where interactions dominate the momentum-space tunneling induced by the external trapping potential. We discuss how real-time control of experimental parameters can be used to create macroscopic quantum superpositions of either momentum or internal states, and how these states could be dynamically controlled, opening the way toward highly sensitive interferometry and frequency metrology.