The Hyperfine Molecular Hubbard Hamiltonian

TL;DR

This paper derives the Hyperfine Molecular Hubbard Hamiltonian for ultracold heteronuclear alkali dimers in optical lattices, highlighting how external fields control internal states and correlations, with implications for quantum dynamics and phase behavior.

Contribution

The paper introduces a first-principles derivation of the HMHH, a novel effective Hamiltonian capturing hyperfine, rotational, and dipolar interactions in ultracold molecules.

Findings

Control of internal states via electric and magnetic fields

Prediction of quantum dephasing effects

Tunable complexity and phase diagram dependence

Abstract

An ultracold gas of heteronuclear alkali dimer molecules with hyperfine structure loaded into a one-dimensional optical lattice is investigated. The \emph{Hyperfine Molecular Hubbard Hamiltonian} (HMHH), an effective low-energy lattice Hamiltonian, is derived from first principles. The large permanent electric dipole moment of these molecules gives rise to long range dipole-dipole forces in a DC electric field and allows for transitions between rotational states in an AC microwave field. Additionally, a strong magnetic field can be used to control the hyperfine degrees of freedom independently of the rotational degrees of freedom. By tuning the angle between the DC electric and magnetic fields and the strength of the AC field it is possible to control the number of internal states involved in the dynamics as well as the degree of correlation between the spatial and internal degrees of freedom. The HMHH's unique features have direct experimental consequences such as quantum dephasing, tunable complexity, and the dependence of the phase diagram on the molecular state.