Adiabatic and non-adiabatic merging of independent Bose condensates

Motivated by a recent experiment [Chikkatur, et al. Science, 296, 2193 (2002)] on the merging of atomic condensates, we investigate how two independent condensates with random initial phases can develop a unique relative phase when we move them together. In the adiabatic limit, the uniting of independent condensates can be understood from the eigenstate evolution of the governing Hamiltonian, which maps degenerate states (corresponding to fragmented condensates) to a single state (corresponding to a united condensate) . In the non-adiabatic limit corresponding to the practical experimental configurations, we give an explanation on why we can still get a large condensate fraction with a unique relative phase. Detailed numerical simulations are then performed for the non-adiabatic merging of the condensates, which confirm our explanation and qualitative estimation. The results may have interesting implications for realizing a continuous atom laser based on merging of condensates.