Macroscopic Quantum Tunneling and Entangled States in Bose-Einstein Condensates

We use a multi-band Bose-Hubbard model to study the quantum dynamics of ultracold bosons in a two-well potential. We describe the energy eigenstates in detail. These consist of oscillator-like solutions, non-degenerate entangled states, and degenerate entangled states which include extreme cat-states. The ground state ranges from a single number state to a coherent, or superfluid, state. In the dynamics we find harmonic breathing and quantum revivals. Finally, we describe the macroscopic quantum tunneling of a dark soliton between two wells. We show how the oscillation frequency depends on the band spacing and the ratio of the tunneling energy to the interaction potential.