Regular space crystals are described by a spatially periodic distribution of particles observed at a fixed moment of time. To form time crystals [1, 2], the roles between time and space are interchanged. In this case the periodicity is observed in time by fixing a position in space and measuring the periodic detection of particles during the experimental time frame. Time crystal behavior can emerge spontaneously in many-body systems and can also be engineered by suitable external time-periodic driving. This allows to realize a variety of condensed-matter phenomena in the time domain [3, 4].
In this presentation, we demonstrate the notion of time-space crystalline structures (TSCS) which merge the ideas of time and space crystals to form systems that are both temporally and spatially periodic [5]. Starting with a particle in a one-dimensional periodic potential, an external periodic and resonant driving can be used to engineer a crystalline time structure at each potential well of the spatial lattice thus effectively forming a two-dimensional TSCS. This allows us to construct a system where each spatially orthogonal one-dimensional periodic potential comes equipped with a periodic structure in time. For a three-dimensional lattice with a proper choice of driving this leads to a six-dimensional TSCS. Realization of a six-dimensional crystalline structure paves the way towards investigation of higher-dimensional condensed-matter phases.