
Physics 2015
Geometry of Bloch states probed by Stückelberg interferometryAbstract: Inspired by recent experiments with cold atoms in optical lattices, we consider a St\"uckelberg interferometer for a particle performing Bloch oscillations in a tightbinding model on the honeycomb lattice. The interferometer is made of two avoided crossings at the saddle points of the band structure (i.e. at M points of the reciprocal space). This problem is reminiscent of the double Dirac cone St\"uckelberg interferometer that was recently studied in the continuum limit [Phys. Rev. Lett. 112, 155302 (2014)]. Although the two problems share similarities  such as the appearance of a geometric phase shift  lattice effects, not captured by the continuum limit, make them truly different. The particle dynamics in the presence of a force is described by the Bloch Hamiltonian $H(\boldsymbol{k})$ defined from the tightbinding Hamiltonian and the position operator. This leads to many interesting effects for the lattice St\"uckelberg interferometer: a twisting of the two LandauZener tunnelings, saturation of the interband transition probability in the sudden (infinite force) limit and extended periodicity or even nonperiodicity beyond the first Brillouin zone. In particular, St\"uckelberg interferometry gives access to the overlap matrix of cellperiodic Bloch states thereby allowing to fully characterize the geometry of Bloch states, as e.g. to obtain the quantum metric tensor.
