Molecular Hubbard Hamiltonian: Field regimes and molecular species

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 Σ 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 dipoledipole 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.

A versatile dual-species Zeeman slower for caesium and ytterbium

“…However, the variety of diatomic molecules that are potentially realisable using laser-cooling methods will each o↵er unique properties for experimental study. 11 Accordingly, we have chosen to investigate the previously untried mixture of Cs and Yb for three main reasons: Firstly, routes to quantum degeneracy have been established for both species individually. 33,34 Secondly, natural Yb consists a) Electronic mail: s.a.hopkins@durham.ac.uk of seven isotopes including five bosons and two fermions, thus allowing production of either bosonic or fermionic molecules with caesium and expanding the opportunities for finding a molecule with favourable properties.…”

“…The production of ultracold, heteronuclear, diatomic molecules in their ground state by coherently combining two di↵erent laser-cooled atomic species is currently an active research area [1][2][3][4] because of the potential for quantum information processing, [5][6][7][8][9][10][11] for cold chemistry, [12][13][14][15][16] the exploration of strongly interacting quantum systems [17][18][19][20] and precision measurement. [21][22][23][24] Heteronuclear molecules manifest an electric dipole moment when a direction is imposed by an electric field, 25 allowing study of long-range anisotropic interactions.…”

Causality and quantum criticality in long-range lattice models

“…The powerful tools of field theory used in this paper can be employed to study a range of interesting, and experimentally relevant, long-range interacting systems [16,[53][54][55][56], such as a huge variety of spin-1/2 [57][58][59][60], spin-1 [41,61,62], and higher-spin [63,64] models, generalized Hubbard [63,65,66] and t-J models [58,59], and spin-boson problems [67], among many others, in one or more spatial dimensions. In general, these models exhibit new universal behavior not captured by standard long-range interacting classical models, since the quantum-to-classical mapping generates classical models with long-range interactions in all spatial directions except the one corresponding to the imaginary time dimension of the quantum model [39].…”

Quantum-defect model of a reactive collision at finite temperature

“…Another possibility is to study reactions of cold atoms and ions [18][19][20]. Apart from studying the inelastic collisions, ultracold atoms, ions and molecules offer the opportunity to act as quantum simulators of many-body effects, or to implement quantum information processing protocols [21][22][23][24][25].…”