The primary objective of this proposal is to explore the physics of multi-component condensates containing both atomic and molecular species, one of the most rapidly evolving areas of physics research. Of particular interest is the two-color Raman photo-association model (or its Feshbach equivalence), also known as the nonlinear system, where a pair of stable atoms is either photo-associated (or magnetoassociated) into an unstable excited molecule, which is subsequently driven into a stable (ground) molecular state by a laser field. The nonlinear system supports a coherent population trapping (CPT) or dark state, which is a superposition of atomic and stable molecular states. Such a CPT state facilitates the stimulated Raman adiabatic passage (STIRAP), which utilizes a counterintuitive pulse sequence to coherently convert atoms into stable molecules while avoiding the decoherence associated with the particle loss in the excited state. The technique of STIRAP will be generalized from recent work [H. Y. Ling, H. Pu, and B. Seaman, Phys. Rev. Lett. 93, 250403 (2004)] to the nonlinear systems, where both particle collisions and trap potentials cannot be ignored. The adiabatic condition, which sets the limit to the powers and the widths of the laser pulses for an efficient STIRAP, will be studied in connection with the collective excitation modes of the CPT state. Also studied is the question of how to prepare the system, through quantum state engineering involving laser light, into the nonlinear CPT state in the presence of trap potentials, and the question of how to design more robust STIRAPs capable of efficiently converting atoms into molecules under quite relaxed CPT conditions. The possibility of creating, in the nonlinear system, a coherent superposition of an atomic condensate and a molecular vortex will also be studied - such a superposition represents a new and relatively unexplored quantum state of matter, unique of the coupled atomic-molecular condensate systems. In contrast to two bosonic atoms, which can only form a molecule tightly bound in real space, two fermionic atoms have the additional opportunity of forming a Bardeen-Cooper-Schrieffer (BCS) pair bound in momentum space. This leads to the final area of the proposal to explore the coupled fermionic atomic-molecular condensate systems for studies related to the formation of BCS atom pairs and to the BEC-BCS crossover - the transition from condensates of mainly bound BEC molecules to that of BCS pairs.
