Geometric phase interferometry in two-dimensional optical lattices
Uri London , Omri Gat
Racah Inst. Physics, Hebrew University, Israel
A system of non-interacting cold atoms placed in a two-dimensional optical lattice and subjected to a constant force will undergo Bloch oscillations. With an introduction of a beam-splitter one can create a simple Mach-Zehnder interferometer with which the dynamical phase of a wavepacket can be measured. Using such measurements one can partially probe the band dispersion.
If the lattice doesn't have spatial reflection symmetry then the wavepacket acquires along its trajectory an additional phase which in subleading order in $\hbar$ is a Berry phase.
We present an analytic analysis of the dynamics of a Gaussian wave-packet in the considered system based on a semiclassical formulation and show how to interpret the resultant interference pattern, and how to extract the Berry curvature.