4,070 research outputs found
Microscopic derivation of Hubbard parameters for cold atomic gases
We study the exact solution for two atomic particles in an optical lattice
interacting via a Feshbach resonance. The analysis includes the influence of
all higher bands, as well as the proper renormalization of molecular energy in
the closed channel. Using an expansion in Bloch waves, we show that the problem
reduces to a simple matrix equation, which can be solved numerically very
efficient. This exact solution allows for the precise determination of the
parameters in the Hubbard model and the two-particle bound state energy. We
identify the regime, where a single band Hubbard model fails to describe the
scattering of the atoms as well as the bound states.Comment: 4 pages, 2 figure
Crystalline phase for one-dimensional ultra-cold atomic bosons
We study cold atomic gases with a contact interaction and confined into
one-dimension. Crossing the confinement induced resonance the correlation
between the bosons increases, and introduces an effective range for the
interaction potential. Using the mapping onto the sine-Gordon model and a
Hubbard model in the strongly interacting regime allows us to derive the phase
diagram in the presence of an optical lattice. We demonstrate the appearance of
a phase transition from a Luttinger liquid with algebraic correlations into a
crystalline phase with a particle on every second lattice site.Comment: 4 pages, 2 figure
- …