Classical versus quantum dynamics of the atomic Josephson junction

We compare the classical (mean-field) dynamics with the quantum dynamics of atomic Bose-Einstein condensates in double-well potentials. The quantum dynamics are computed using a simple scheme based on the Raman-Nath equations. Two different methods for exciting a non-equilibrium state are considered: an asymmetry between the wells which is suddenly removed and a periodic time oscillating asymmetry. The first method generates wave packets that lead to collapses and revivals of the expectation values of the macroscopic variables, and we calculate the time scale for these revivals. The second method permits the excitation of a single energy eigenstate of the many-particle system, including Schrodinger cat states. We also discuss a band theory interpretation of the energy level structure of an asymmetric double well, thereby identifying analogies to Bloch oscillations and Bragg resonances. Both the Bloch and Bragg dynamics are purely quantum and are not contained in the mean-field treatment.