Topological phases with periodically kicked molecules

In the last decade technological advances have made possible unprecedented coherent manipulation of molecules. Improved control of the duration and temporal shape of laser pulses opens up new possibilities to create platforms for quantum simulation and information processing. In our work we propose to use molecules kicked by lasers as a non-hermitian topological system to probe topological modes. We utilize the polarization of the laser and the asymmetry of the molecule as additional degrees of freedom to realize topological phases and transitions between them. In particular, we show that using an elliptically polarized laser creates an effective two-dimensional lattice with non-trivial states at the boundary (analogous to chiral states for a hermitian chiral system). The explored theoretical models are experimentally feasible with the current techniques. This makes it possible to utilize these systems as building blocks for quantum computation with a higher level of control than in traditional solid state based systems.