Non-equilibrium phases of matter exhibiting periodic motion without energy input.Time crystals are a phase of matter where the system exhibits periodic motion in time without consuming energy, breaking time-translation symmetry. Unlike ordinary crystals, which have repeating patterns in space, time crystals have repeating patterns in time. They are non-equilibrium phases: they are driven periodically (e.g., by laser pulses) and respond with a subharmonic oscillation, meaning their period is a multiple of the drive period, and this motion persists indefinitely without heating up.
The concept was proposed by Frank Wilczek in 2012, but his original idea of a spontaneous time crystal was shown to be impossible in equilibrium. The discrete time crystal, driven by periodic pulses, was theoretically developed in 2015-2016 and first experimentally realized in 2017 in ion traps and diamond spin systems.
The key is that the system is periodically driven (Floquet engineering) and has strong interactions that cause it to synchronize into a state that oscillates at a fraction of the drive frequency. This is possible because the system enters a many-body localized phase, where interactions prevent thermalization and the drive does not heat the system to infinite temperature. The time crystal then exhibits a robust, persistent oscillation that is protected by the disorder-induced localization.
Time crystals are being explored for use in precision timekeeping, quantum memory, and as a platform for studying non-equilibrium quantum phases.
In 2021, researchers created a 'time crystal' with five ions that exhibited a hierarchy of multiple periodicities, like a matryoshka doll of rhythms.
| F | variable | Landau free energy density — free energy density joule per cubic metre |
| ψ | variable | order parameter — order parameter |
| a | variable | coefficient of quadratic term, temperature-dependent — landau coefficient a joule per cubic metre |
| b | variable | coefficient of quartic term — landau coefficient b joule per cubic metre |
| c | variable | coefficient of sixth-order term — landau coefficient c joule per cubic metre |
| f_ext | variable | external field coupled to the order parameter — external field joule per cubic metre |
| a_0 | variable | relativistic intensity parameter (normalized vector potential) — relativistic parameter |
| E_0 | variable | peak electric field amplitude of the laser — electric field volt per metre |
| ω | variable | angular frequency of the laser — angular frequency radian per second |
| e | constant | charge of a single proton — elementary charge = 1.602176634e-19 coulomb |
| m_e | constant | mass of an electron at rest — electron mass = 9.1093837015e-31 kilogram |
| c | constant | universal speed limit of light in vacuum — speed of light = 299792458 metre per second |









