The Molecular Hubbard Hamiltonian: Field Regimes and Molecular Species

TL;DR

This paper introduces the molecular Hubbard Hamiltonian for ultracold polar molecules, demonstrating how molecular structure and external fields influence many-body phases and quantum phase transitions, with detailed numerical analysis for various molecules.

Contribution

It provides explicit parameters for the MHH across different molecules and explores many-body phases using advanced numerical methods, highlighting differences from atomic systems.

Findings

Different molecules exhibit distinct many-body phases due to their structure.

External fields enable diverse control over molecular states and interactions.

Quantum phase transitions from superfluid to crystalline phases are demonstrated.

Abstract

The molecular Hubbard Hamiltonian (MHH) naturally arises for ultracold ground state polar alkali dimer molecules in optical lattices. We show that, unlike ultracold atoms, different molecules display different many-body phases due to intrinsic variances in molecular structure even when the molecular symmetry is the same. We also demonstrate a wide variety of experimental controls on $^1\Sigma$ molecules via external fields, including applied static electric and magnetic fields, an AC microwave field, and the polarization and strength of optical lattice beams. We provide explicit numerical calculations of the parameters of the MHH, including tunneling and direct and exchange dipole-dipole interaction energies, for the molecules {$^{6}$Li$^{133}$Cs}, $^{23}$Na$^{40}$K, $^{87}$Rb$^{133}$Cs, $^{40}$K$^{87}$Rb, and {$^{6}$Li$^{23}$Na} in weak and strong applied electric fields. As case studies of many-body physics, we use infinite-size matrix product state methods to explore the quantum phase transitions from the superfluid phase to half-filled and third-filled crystalline phases in one dimension.