  Time crystals are quantum many-body systems which, due to interactions
between particles, are able to spontaneously self-organize their motion in a
periodic way in time by analogy with the formation of crystalline structures in
space in condensed matter physics. In solid state physics properties of space
crystals are often investigated with the help of external potentials that are
spatially periodic and reflect various crystalline structures. A similar
approach can be applied for time crystals, as periodically driven systems
constitute counterparts of spatially periodic systems, but in the time domain.
Here we show that condensed matter problems ranging from single particles in
potentials of quasi-crystal structure to many-body systems with exotic
long-range interactions can be realized in the time domain with an appropriate
periodic driving. Moreover, it is possible to create molecules where atoms are
bound together due to destructive interference if the atomic scattering length
is modulated in time.
