Topological molecules and topological localization of a Rydberg electron on a classical orbit

It is common knowledge that atoms can form molecules if they attract eachother. Here, we show that it is possible to create molecules where boundstates of the atoms are not the result of attractive interactions but havethe topological origin. That is, the bound states of the atoms correspondto the topologically protected edge states of a topological model. Suchtopological molecules can be realized if the interaction strength betweenultracold atoms is properly modulated in time. A similar mechanism allowsone to realize topologically protected localization of an electron on aclassical orbit if a Rydberg atom is perturbed by a properly modulatedmicrowave field.