Institute of Theoretical Physics and Astronomy, Vilnius University, Lithuania
Usually optical lattices are produced by interfering a number of laser beams. The atoms are trapped at the intensity minima or maxima of an emerging interference pattern. The tunneling matrix elements for atoms in such lattices are real, so the atomic motion is not affected by a magnetic flux. The magnetic flux can be induced via the laser-assisted tunneling between lattice sites or by shaking the lattice.
In the initial part of the talk a novel way will be presented for creating a topological optical lattice which is affected by a non-staggered magnetic flux without any conventional optical lattice added . Two atomic internal states are involved and their energies have opposite gradients in one spatial direction. The states are coupled by a multi-frequency laser radiation propagating in a direction perpendicular to the energy gradient. Such a periodic perturbation together with the energy gradient creates effectively (in the Floquet picture) a square optical lattice affected by a non-staggered magnetic flux. By proper tuning the parameters of the system, the energy bands of the lattice can be characterized by unit Chern numbers .
Subsequently we shall consider another possibility of producing a topological optical lattices by using a set of long lived atomic internal states as sites in an extra (synthetic) dimension [2,3]. By taking a standard 1D optical lattice and inducing the laser-assisted transitions between sites of the "extra dimension", one can effectively engineer a 2D lattice involving both real and synthetic dimensions, and the lattice is affected by a non-staggered magnetic flux . Usually such a semi-synthetic lattice has a square geometry. Here we talk about a recent analysis of semi-synthetic optical lattices characterized by a non-square geometry. In particular we shall talk about a possibility to produce a semi-synthetic zigzag lattice affected by a magnetic flux, and consider single and many-body properties of such a lattice .
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