Comparing the Ratchet Effects of Cold Atoms in Periodically Symmetric and Asymmetric Optical Potentials

We consider a particle in a spatial symmetric/asymmetric potential driven by time periodic bichromatic AC fields of ratchet type. The associated time-dependent Schrödinger equation is conveniently tackled with the Floquet theory. We next proceed to investigate the ratchet effect induced by the driver, comparing the symmetric with the asymmetric cases. It turns out that the current in the asymmetric case is stronger than that of the symmetric one. Besides, we also investigate the case where the driver is a delta kicked acting on our spatial potential with more emphasis on its chaotic behaviour. Here we check that the current emerges as the phase space is mixed and that the system with asymmetric spatial potential becomes more chaotic than the symmetric one at low kicking strength