The mechanism underlying the formation of crystals is the breaking of symmetry in the spatial domain. Also responsible for phase transitions between liquid and solid it has long been associated with a system in equilibrium – that is a system in its ground state.
However, two independent teams of scientists have recently confirmed the existence of crystals in a non-equilibrium state – known as time crystals. Predicted in 2012 by Nobel Laureate Frank Wilczek these systems break symmetry in the time domain – where they show periodicities at an emergent sub-harmonic frequency and are robust to external perturbations. Could this be a resonant frequency of the quantum vacuum?
The basic idea of a time crystal is relatively straight-forward. A crystalline medium has a periodic, or regularly repeating structure. However, because of entropic considerations (forcing the substance into its lowest energy state) the crystal will not have the same repeating structure in all directions: it will be asymmetric -- this is known as symmetry breaking of spatial translation symmetry. So whereas with normal crystals this repeating, periodic structure is asymmetric spatially (the spatial configuration of the crystalline lattice); with a time crystal the asymmetric periodicity is not in spatial organization but in time-varying media.
Ultracold matter normally serves as the medium, where ions are cooled to such a low temperature that there is no longer thermal noise and they are confined within a magneto-optical trap. This should be a completely stationary arrangement, however because of a time varying oscillation driven into the ions they will interact with quantum vacuum fluctuations and the medium will rotate. This is a similar and related phenomenon to the dynamical casimir effect, where photons and phonons are emitted from the vacuum due to time-varying boundary conditions. In the case of the time crystal, this would allow for a perpetually rotating device (download paper here)
The reason this had not been observed until recently is that quantum processes are not governed by time-dependent variables, mainly because quantum particles at equilibrium do not have definite positions. However, Ytterbium ions in a magneto-optical trap can be made to undergo definite localization, and driven into non-equilibrium when subject to a periodic drive -- in this case a laser that periodically flips the spin of the ions; all of which causes them to become time-correlated. Now, since there should be a time-symmetrical periodic oscillation of the ions (an emergent sub-harmonic frequency of the rate of flipping the spin with the laser); time-symmetry can be broken, and a discrete time crystal is formed. The ring of trapped ions begins to rotate.
It is extremely interesting that such a situation is driven by the quantum vacuum fluctuations -- like the dynamical Casimir effect, the observation of an actual time-crystal is a clear demonstration of the real energy of the quantum vacuum.