A Decade of Time Crystals: Quo Vadis?

Abstract

Ten years ago, the new era of time crystals began. Time crystals are systems that behave in the time dimension like ordinary space crystals do in space dimensions. We present a brief history of a decade of research on time crystals, describe current research directions, indicate challenges, and discuss some future perspectives for condensed matter physics in the time domain.

Emergent time crystals from phase-space noncommutative quantum mechanics

“…the Supplementary Material). This suggests that a putative connection of the above results with the spontaneous formation of time quasi-crystals from atoms bouncing between a pair of orthogonal atom mirrors [40,42] also deserves further investigations.…”

“…Interestingly, 2-dim (or 3-dim) Bose-Einstein condensates with time crystal behavior have, in fact, been detected through a resonance between two (or three) oscillating atom mirrors through a configuration where the localized wave-packets are products of 1-dim wave-packets [40,41]. The results discussed above suggest a natural explanation for such effect, in this case, with quasi-periodic eigenstates driven by ξ 1 , ξ 2 , and γ replacing the 1-dim wave-packets.…”