of dipolar molecules

Tomasz Sowiński^1,2, Omjyoti Dutta², Philipp Hauke², Luca Tagliacozzo², Maciej Lewenstein²

1 Institute of Physics of the Polish Academy of Sciences, Poland

2 ICFO – The Institute of Photonic Sciences, Spain

Density-dependent processes

of dipolar molecules

in an optical lattice

Kraków, September 31, 2011

• Lattice potential

• Hamiltonian of the system

Bosons in optical lattice

• Natural units of the problem

- laser wave length - recoil energy

- lattice flattening

• Convenient basis

Wannier functions

wave function localized in i-th lattice site denotes appropriate Bloch band

• Single particle Hamiltonian

Field operator decomposition

the lowest band approximation

summation over nearest neighbours of i

• Interaction Hamiltonian

Field operator decomposition

sufficient approximation when we consider short range interactions

the lowest band approximation

density-density interaction between neighbouring sites

MI 1/2

MI 1

MI 3/2

MI 2

MI 5/2

MI 0

SF

MI 1

MI 4

MI 3

MI 2

MI 0

SF

Bose-Hubbard models

V > 0

V = 0

• Interaction Hamiltonian

Long range interactions

lowest band approximation

taking into account only one additional term is not consistent!

• Interaction Hamiltonian

Long range interactions

lowest band approximation

Studied Hamiltonian

• Considered interaction

- optical lattice laser wave length  = 790 nm - mass  mass of the RbCs molecule

Physical realization

• Two dimensionless parameters

s-wave scattering length electric dipole moment

• Model assumptions

- scattering length  100 Bohr Radius - dipole moment up to 3 debye

RED - whole Hamiltonian considered

Hopping fields

single particle SF

double particle SF METHOD:

Exact diagonalization of the 1D Hamiltonian with N = 8, 12, 16 sites

Half filled 1D system

RbCs LiK

BLUE - parameters T and P are neglected

• Susceptibility

Half filled system

Commonly neglected terms in the

extended Bose-Hubbard model

for dipolar molecules

can lead to NEW PHENOMENA