Discrete time crystal

A periodically driven system is subjected to a repeating sequence of changes with period T. In an ordinary synchronized response, observables repeat after T. In a discrete time crystal (DTC), suitable local observables instead repeat after nT, where n is an integer greater than one. The response therefore has a subharmonic frequency relative to the drive. For the simplest case, n = 2: a spin pattern flips after each drive cycle and returns to its original configuration after two cycles. This is spontaneous breaking of the drive's discrete time-translation symmetry, not a crystal moving perpetually without an energy source.

A lone spin can show period doubling if a drive pulse is tuned precisely, but small errors generally shift its response and make it fragile. In a many-body time-crystalline phase, interactions synchronize the degrees of freedom, making the subharmonic response rigid across a range of drive imperfections. Theory identifies distinct routes to this behavior, including many-body-localization-protected and prethermal discrete time crystals. They have different conditions and lifetimes; in particular, a prethermal response persists for a long but finite time before drive-induced heating undermines it.

Experiments have reported time-crystalline behavior in several controlled quantum platforms. A 2017 trapped-ion experiment observed a robust subharmonic response in a driven spin chain. In 2021, researchers reported a discrete time crystal on Google's Sycamore superconducting-qubit processor; the peer-reviewed study described signatures of many-body-localized time-crystalline eigenstate order and used protocols to assess finite-size and decoherence effects. Such laboratory observations are made over finite durations and system sizes, so they do not mean that a physical device has been shown to oscillate forever.

An ordinary spatial crystal breaks continuous translation symmetry in space by forming a repeating pattern of atoms. A discrete time crystal is an analogous kind of ordered response in time, but it is a driven, nonequilibrium phase: its defining comparison is between the period of an external drive and the period of the system's collective response. The distinction matters because simple periodic motion, a finely tuned oscillator, or any signal at half a driving frequency is not by itself sufficient to establish a DTC. Robustness, many-body behavior and the relevant symmetry-breaking properties must also be considered.