Emergent Time Scale in Entangled Quantum Dynamics of Ultracold Molecules in Optical Lattices

TL;DR

This paper introduces a new time-dependent lattice Hamiltonian for ultracold molecules in optical lattices, revealing an emergent time scale in their entangled quantum dynamics and proposing experimental methods to measure molecular properties.

Contribution

The paper derives the Molecular Hubbard Hamiltonian (MHH), a novel time-dependent model capturing many-body physics of ultracold molecules, and studies its entangled dynamics using TEBD.

Findings

Identifies an emergent time scale for entanglement growth and order formation.

Shows the non-monotonic dependence of this time scale on system parameters.

Proposes using phase boundary measurements to determine molecular polarizability.

Abstract

We derive a novel lattice Hamiltonian, the \emph{Molecular Hubbard Hamiltonian} (MHH), 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 MHH is explicitly time-dependent, making a dynamic generalization of the concept of quantum phase transitions necessary. Using the Time-Evolving Block Decimation (TEBD) algorithm to study entangled dynamics, we demonstrate that, in the case of hard core bosonic molecules at half filling, the MHH exhibits an emergent time scale over which spatial entanglement grows, crystalline order appears, and oscillations between rotational states self-damp into an asymptotic superposition. We show that this time scale is a non-monotonic function of the physical parameters describing the lattice. We also point out that experimental mapping of the static phase boundaries of the MHH can be used to measure the molecular polarizability tensor.