Coherent control of the self-trapping transition

We discuss the dynamics of two weakly coupled Bose-Einstein condensates in a double-well potential, contrasting the mean-field picture to the exact N- particle evolution. On the mean-field level, a self-trapping transition occ urs when the scaled interaction strength exceeds a critical value; this tra nsition essentially persists in small condensates comprising about 1000 ato ms. When the double-well is modulated periodically in time, Floquet-type so lutions to the nonlinear Schrodinger equation take over the role of the sta tionary mean-field states. These nonlinear Floquet states can be classified as "unbalanced" or "balanced", depending on whether or not they entail lon g-time confinement of most particles to one well. Since the emergence of un balanced Floquet states depends on the amplitude and frequency of the modul ating force, we predict that the onset of self-trapping can efficiently be controlled by varying these parameters. This prediction is verified numeric ally by both mean-field and N-particle calculations.