  We study the coherent atomic tunneling between two zero-temperature
Bose-Einstein condensates (BEC) confined in a double-well magnetic trap. Two
Gross-Pitaevskii equations for the self-interacting BEC amplitudes, coupled by
a transfer matrix element, describe the dynamics in terms of the inter-well
phase-difference and population imbalance. In addition to the anharmonic
generalization of the familiar $ac$ Josephson effect and plasma oscillations
occurring in superconductor junctions, the non-linear BEC tunneling dynamics
sustains a self-maintained population imbalance: a novel "macroscopic quantum
self-trapping effect".
