The Molecular Hubbard Hamiltonian

We present the Molecular Hubbard Hamiltonian [1], which describes ultracold heteronuclear diatomic molecules in an optical lattice in a strong DC electric field. Using time-evolving block decimation, we describe the quantum dephasing and entangled many body dynamics of the molecules due to an additional AC electric field driving rotational state transitions. We also discuss the effect of nuclear hyperfine structure and strong magnetic fields. [1] M. L. Wall and L. D. Carr, ``Emergent Time Scales in Entangled Quantum Dynamics of Ultracold Molecules in Optical Lattices,'' New Journal of Physics {\bf 11}, 055027 (2009).