Chronolith: Discrete Time Crystal
Quantum Foundations arc, page 12 of 193. Back to The Pixelated Physics Universe
Who they are
Tap Chronolith every beat, and she answers every other beat.
Chronolith is a character of the Quantum Foundations arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
A discrete time crystal is a driven many-body quantum system that responds at twice the drive period: kicked every T, it repeats every 2T, and the rhythm stays stable even when the kicks are imperfect. It breaks the time-translation symmetry of the drive. Frank Wilczek proposed time crystals in 2012; discrete time crystals were seen in 2017 with trapped ions and NV centres, and in 2021 on Google's Sycamore processor.
$$ \begin{gathered} H(t+T) = H(t) \\ \langle \sigma^{z}(t+2T)\rangle = \langle \sigma^{z}(t)\rangle \neq \langle \sigma^{z}(t+T)\rangle \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $H$ | Hamiltonian of the driven system | J |
| $T$ | drive period | s |
| $t$ | time | s |
| $\langle\sigma^{z}\rangle$ | mean spin (Pauli-z) expectation value | 1 |
Honest caveat: Equilibrium time crystals are ruled out (Watanabe and Oshikawa, 2015), and this is not perpetual motion: it needs a drive.
Sources
- Wilczek (2012) Quantum Time Crystals, Phys. Rev. Lett. 109, 160401
- Watanabe & Oshikawa (2015) Absence of Quantum Time Crystals, Phys. Rev. Lett. 114, 251603
- Zhang et al. (2017) Observation of a discrete time crystal, Nature 543, 217
- Mi et al. (2022) Time-crystalline eigenstate order on a quantum processor, Nature 601, 531
Crossovers
Chronolith meets Nutariel (Rabi Oscillation). Nutariel flops at the drive's own rhythm. Chronolith, driven at period T, answers at 2T, and keeps that rhythm stable against small errors because many interacting spins lock it in. One is a single two-level system; the other is a phase of matter.
Chronolith meets Aliasyne (Nyquist Sampling Aliasing). Chronolith is driven at period T and answers at 2T. Aliasyne points out that sampling her exactly once per drive period would show her flipping every sample, which is just the signature an experiment looks for. Sample more slowly and the rhythm can alias into something false.
Wear the lore
Concept keywords: Discrete Time Crystal, Chronolith, Quantum Foundations, physics lore, Pixelated Physics