Ultracold Bosons in Optical Lattices

Optical potentials for ultracold atoms provide a highly controllable environment to mimick condensed matter physics and to engineer almost arbitrary quantum many-body systems. Similar to the ion-lattice forming a periodic potential for the electrons, an optical lattice provides a prectically perfect sinusoidal potential for neutral atoms ......

In our experiments, we use retro-reflected laser beams to create the optical lattice along three mutually orthogonal axes. Originally, we used light with a wavelength of ~840nm red detuned from the Rb transitions, resulting in a lattice spacing of ~420nm. This setup has been altered some time ago by changing the wavelength along one horizontal axis to 765nm ("short lattice", blue detuned) and adding a colinear second lattice at 1530nm ("long lattice", far red detuned). This configuration results in a so-called bichromatic superlattice which we can adjust independently in the relative phase between the long and short lattice and the respective lattice depths.

Extending the concept of the simple cubic optical lattice, we add a second standing wave along one horizontal direction. We chose the wavelengths of the two lattices to be $\lambda_s = 765\,{\rm nm}$ and $\lambda_l = 1530\,{\rm nm}$, respectively while the two transverse lattices are kept at about 840nm. This choice results into a superlattice of double wells or -- in other terms -- a lattice with basis 2.

A common retro mirror for both laser beams creating the superlattice leads to a fix relative phase $\phi$ of the standing waves at the surface of the mirror. Chosing a ratio $\lambda_l/\lambda_s = 2+\epsilon$ with $\epsilon \neq 0$ results in a slip in relative phase between the mirror surface and the atoms' position