Bifurcation effects in coupled Bose-Einstein condensates

When Bose-Einstein condensed ~BEC! systems are coupled, dramatic phenomena occur, owing to macroscopic phase coherence. Effective second-quantized Hamiltonians are often used as simple models @1–3,5–7# to bring out the characteristic behavior of these systems. Very similar Hamiltonians are used @8–10# to model striking effects in vibrational spectra of polyatomic molecules, related to classical nonlinearity and chaos. This paper explores bifurcation phenomena and their classification as phases of BEC systems, and describes additional BEC effects, possibly accessible to experiment. We start with a Hamiltonian for two states, e.g., two BEC traps or two vibrational degrees of freedom in a molecule: