Abstract
We derive a novel lattice Hamiltonian, the molecular Hubbard Hamiltonian, which describes the essential many-body physics of closed-shell ultracold heteronuclear molecules in their absolute ground state in a quasi-one-dimensional optical lattice. The molecular Hubbard Hamiltonian is explicitly time dependent, making a dynamic generalization of the concept of quantum phase transitions necessary. Using the time-evolving block decimation algorithm to study entangled dynamics, we demonstrate that, in the case of hard-core bosonic molecules at half-filling, the molecular Hubbard Hamiltonian exhibits emergent timescales over which spatial entanglement grows, crystalline order appears and oscillations between rotational states self-damp into an asymptotic superposition. We show that these timescales are non-monotonic functions of the physical parameters describing the lattice.
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