Frank Wilczek introduced in 2012 the idea (and name, through his wife) of a time crystal.[1][2]
The basic idea is that it could exist, but in time, the counterpart of a (spatial) crystal as a regular object in space whose ground state has less symmetry than its Hamiltonian. Such a phenomenon follows from the phenomenon of symmetry breaking. In space, a crystal breaks the continuous translation symmetry. In time, a crystal would break time invariance.
This was quickly criticized, first by Bruno[3] and then on more general grounds by Watanabe and Oshikawa.[4]
The topic got a second kick from the realization that under coherent driving, in the sense of periodic driving (Floquet physics), a weaker symmetry could be violated with . This gives rise to so-called discrete time crystals and then, when dissipation is also involved, dissipative time crystals.
One example of widely accepted time crystal is a constantly rotating ring of charged ions in one of its lowest-energy states,[5] which exhibit a broken time symmetry out of equilibrium.
The problem is, in its original form, interesting and appears to be very fundamental. First, it seems an obvious idea, and it is strange that it was never (seriously) entertained before Wilczek had to prepare lectures on symmetries in physics. Second, it tackles the space/time correspondence and how time differs so drastically from space (Wilczek himself mentions special relativity as an inspiration for the idea). Third, it is related to one of the oldest and most famous fantasies of the crazy scientist: perpetual motion. Fourth, but not least on this website, we ourselves arrived—on top of that, independently—to similar notions through our liquefaction of light which we initially did not connect to time crystals although I checked the Wilczek papers again when writing the papers, since even our terminology (liquid light, liquid time, etc.) brought us irresistibly to this topic, but we ruled them out as not directly related.
Following the PEPS conference and a talk from Alex Fainstein's group, our interest in the topic revived, with the idea that maybe our liquid light is closer to a time crystal than. Our quantum circular cascade has time-periodicity, self-organization
There is already great academic reference works available, including the witty brief history of time crystals [6] and a nice-looking book [7].