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Resonant Raman coupling between internal levels induced by continuousillumination of non-collinear laser beams can create double-well momentum-spacepotentials for multi-level ``periodically-dressed'' atoms. We develop anapproximate many-body formalism for a weakly interacting, trappedperiodically-dressed Bose gas which illustrates how a tunable exchangeinteraction yields correlated many-body ground states. In contrast to the caseof a position-space double well, the ground state of stableperiodically-dressed Bose gases with repulsive interactions tends toward aSchr\"{o}dinger cat state in the regime where interactions dominate themomentum-space tunnelling induced by the external trapping potential. Thedependence of the momentum-space tunnelling and exchange interaction onexperimental parameters is derived. We discuss how real-time control ofexperimental parameters can be used to create Schr\"{o}dinger cat states eitherbetween momentum or internal states, and how these states could be dynamicallycontrolled towards highly sensitive interferometry and frequency metrology.Comment: 7 pages, 3 figures. Submitted to PR

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