Optical lattice

Optical lattices are created to hold atoms in a periodic 2d structure via dispersive force. The simplest realization of an optical lattice is a standing wave produced by two counter-propagating beams. The potential has the form: $V(x)=V_0 cos^2(kx)$

Special optical lattices

Time-varying lattices

In some experiments it is required to modify lattice in time domain (see p 206 ). In order to create a time-varying potential two beams with slightly different frequencies are used (ω and δω). The frequency mismatch will lead to a potential:$V(x)=V_0 cos^2(kx -\frac{\delta \omega}{2}t)$ One more realization are phase and amplitude modulated lattices.

Superlattice

Bloch group has a lattice with two periods and it is created by two lasers 767 and 2*767=1534 nm. $V_1\sin^2(kx+\phi/2)+V_2\sin^2(kx+\pi/2)$