Another symmetry, another symmetry breaking.

—A Brief History of Time Crystals, arXiv:1910.10745, 2019.

Time Crystal

Frank Wilczek introduced the idea (and name, through his wife) of a time crystal in 2012.

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 and then on more general grounds by Watanabe and Oshikawa, providing so-called no-go theorems.

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 periods of oscillations that are multiple of the driving period. This gives rise to so-called discrete time crystals (DTC).

A third kick came with a (gradual but firm) return to the original idea of breaking the continuous time-translation symmetry thanks to dissipation, i.e., this time with no frequency imparted from outside. This gives rise to continuous time crytals (CTC) or dissipative time crystals.

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 and repeatedly—to similar notions through our Self-interfering wavepackets and liquefaction of light. We did not initially connect the latter 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. By the time of SIP, we were not even aware of the time crystal business and still talked about spacetime crystals in the way Rabi oscillations structure themselves in spacetime.

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 we initially thought. Our quantum circular cascade has indeed time-periodicity and self-organization. It is not, however, many-body.

There are already great academic reference works available, including the witty brief history of time crystals  and a nice-looking book . Wilczek wrote a nice overview.