Kolovsky, Andrey

Date: Thursday October 16, 2014
Time: 11:00
Place: ETH Zurich, Hönggerberg, HPF G 6
Hosts: Daniel Greif, Tilman Esslinger

Bloch oscillations and Wannier-Stark states of a quantum particle in a generic two-dimensional lattice

Andrey Kolovsky
L. V. Kirensky Institute of Physics, Siberian Branch of Russian Academy of Sciences, Krasnoyarsk, Russia

By definition, Wannier-Stark states are the eigenstates of a quantum particle in a periodic potential in the presence of a static field F. For a simple 1D lattice of the period a the spectrum of WS-states is a set of energy levels with the level spacing aF, known as the Wannier-Stark ladder. The equidistant spectrum implies periodic dynamics of the particle which is nothing else as celebrated Bloch oscillations. If the lattice period is doubled, Bloch oscillations become a complicated process because of the Landau-Zener tunneling between two subbands that emerge from a single band due to the period doubling. In the past decade BOs and LZ-tunneling in 1D double periodic lattices has attracted much attention in cold atoms physics and photonics thanks to applications to interferometric measurements and as a method for manipulating localized wave-packets. In the talk I review theory of WS-states in 1D double-periodic lattices and show how the interband LZ-tunneling is encoded in these states. Then I extend the theory to 2D double-periodic lattices. The fundamental difference of 2D lattices as compared with 1D lattices is that the Wannier-Stark spectrum and WS-states depend not only on the strength of a static field but also on its orientation relative to the primary axes of the lattice. This opens a pandora of spectral and dynamical effects which I shall discuss in the talk.