The possibility of creating different geometries with the help of an extra synthetic dimension in optical lattices is studied. The additional linear potential together with Raman-assisted tunnelings are used to engineer well-controlled tunnelings between available states. The great flexibility of the system allows us to obtain different geometries of synthetic lattices with the possibility for adding synthetic gauge fields.

• Received 22 May 2016

DOI:https://doi.org/10.1103/PhysRevA.94.033602