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It is common knowledge that atoms can form molecules if they attract eachother. Here, we show that it is possible to create molecules where bound statesof the atoms are not the result of attractive interactions but have thetopological origin. That is, the bound states of the atoms correspond to thetopologically protected edge states of a topological model. Such topologicalmolecules can be realized if the interaction strength between ultra-cold atomsis properly modulated in time. A similar mechanism allows one to realizetopologically protected localization of an electron on a classical orbit if aRydberg atom is perturbed by a properly modulated microwave field.

Topological Molecules and Topological Localization of a Rydberg Electron on a Classical Orbit