Ab initio calculation of Hubbard parameters for Rydbergdressed atoms in a onedimensional optical lattice
Abstract
We obtain ab initio the Hubbard parameters for Rydbergdressed atoms in a onedimensional (1D) sinusoidal optical lattice on the basis of maximallylocalized Wannier states. Finite range, softcore interatomic interactions become the trait of Rydberg admixed atoms, which can be extended over many neighboring lattice sites. In contrast to dipolar gases, where the interactions follow an inverse cubic law, the key feature of Rydbergdressed interactions is the possibility of making neighboring couplings to the same magnitude as that of the onsite ones. The maximallylocalized Wannier functions (MLWFs) are typically calculated via a spreadminimization procedure (Marzari N and Vanderbilt D 1997 Phys. Rev. B 56 12847) and are always found to be real functions apart from a trivial global phase when an isolated set of Bloch bands are considered. For an isolated single Bloch band, the above procedure reduces to a simple quasimomentumdependent unitary phase transformation. Here, instead of minimizing the spread, we employ a diagonal phase transformation which eliminates the imaginary part of the Wannier functions. The resulting Wannier states are found to be maximally localized and in exact agreement with those obtained via a spreadminimization procedure. Using these findings, we calculate the Hubbard couplings from the Rydberg admixed interactions, including dominant densityassisted tunneling (DAT) coefficients. Finally, we provide realistic lattice parameters for the stateoftheart experimental Rydbergdressed rubidium setup.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 July 2016
 DOI:
 10.1088/09534075/49/14/144005
 arXiv:
 arXiv:1602.00500
 Bibcode:
 2016JPhB...49n4005C
 Keywords:

 Condensed Matter  Quantum Gases;
 Quantum Physics
 EPrint:
 Submitted to J. Phys. B for special issue on Rydberg atomic physics