A discrete time crystal (DTC), also called a Floquet time crystal, is a periodically driven system that oscillates at an integer fraction (a subharmonic) of the drive frequency. It is the regime in which time crystals have been most widely reported experimentally.
Definition
According to the source dossier, the initial discrete time-translation symmetry t → t + nT with n = 1 is spontaneously broken to a lower discrete time-translation symmetry with n > 1, where t is time, T the driving period, and n an integer. The dossier quotes Philip Ball's formulation that DTCs are so named because "their periodicity is a discrete, integer multiple of the driving period."
The dossier states that DTCs never reach thermal equilibrium, as they are a type (or phase) of non-equilibrium matter, and that breaking of time symmetry can occur only in non-equilibrium systems.
Strict criteria
The dossier distinguishes DTCs from other systems showing spontaneous time-translation symmetry breaking by three criteria:
- Broken symmetry — the system shows oscillations with a period longer than the driving force.
- Crypto-Equilibrium — the oscillations generate no entropy, and a time-dependent frame can be found in which the system is indistinguishable from equilibrium when measured stroboscopically. The dossier notes this is not the case for convection cells, oscillating chemical reactions and aerodynamic flutter.
- Long-range order — the oscillations are in phase (synchronized) over arbitrarily long distances and time.
Additionally, the broken symmetry is said to result from many-body interactions — a collective process, as in spatial crystals — which the dossier says is not the case for NMR spin echoes.
Reported realizations
The dossier reports DTCs in:
- Trapped ¹⁷¹Yb⁺ ions (Christopher Monroe, University of Maryland, 2016–2017), where a subharmonic oscillation of the drive was observed and the crystal showed "rigidity" — the oscillation frequency remained unchanged under perturbation until the crystal "melted."
- Nitrogen-vacancy centers in diamond (Mikhail Lukin, Harvard, 2016–2017), where spin polarization evolved at half the microwave drive frequency, persisting for over 100 cycles.
- Google's Sycamore processor (November 2021), using a 20-qubit chip in a many-body-localization configuration, driven into a Floquet system where all up spins flip to down and vice versa in periodic cycles that are multiples of the laser frequency. The dossier states that while the laser is necessary to maintain environmental conditions, no energy is absorbed from it, so the system remains in a protected eigenstate order.
- Quantum simulators (University of Maryland, June 2021; QuTech / TU Delft / TNO, November 2021), described as "virtual" Floquet time crystals.
- IBM Manhattan and Brooklyn processors (University of Melbourne, March 2022), observing a total of 57 qubits.
- Liquid-crystal devices — see wo2026174186, which claims classical DSTCs in a chiral nematic liquid crystal driven by a Floquet electrical signal, with period doubling relative to the drive.
Related work
- Time Crystal — the parent concept.
- Continuous Time Crystal (CTC) — the continuously driven counterpart.
- Floquet Theory — the mathematical framework.
- subharmonic-response — the signature of DTC order.
Source notes & attribution
- https://rexresearch.com/WilczekTimeCrystals/WILCZEKTimeCrystals.html