object

time crystals

Non-equilibrium phases of matter exhibiting periodic motion without energy input.
16 related articles · 2 formulas

Description

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.

History

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.

How it works

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.

In practice

Time crystals are being explored for use in precision timekeeping, quantum memory, and as a platform for studying non-equilibrium quantum phases.

Fun fact

In 2021, researchers created a 'time crystal' with five ions that exhibited a hierarchy of multiple periodicities, like a matryoshka doll of rhythms.

Concept graph →

Formulas

$$F(\psi) = a \psi^2 + b \psi^4 + c \psi^6 - f_{\text{ext}} \psi$$
Describes phase transitions with order parameter.
What is in the formula
FvariableLandau free energy density — free energy density joule per cubic metre
ψvariableorder parameter — order parameter
avariablecoefficient of quadratic term, temperature-dependent — landau coefficient a joule per cubic metre
bvariablecoefficient of quartic term — landau coefficient b joule per cubic metre
cvariablecoefficient of sixth-order term — landau coefficient c joule per cubic metre
f_extvariableexternal field coupled to the order parameter — external field joule per cubic metre
f(ψ)=\frac{a}{2}ψ^2+\frac{b}{4}ψ^4+\frac{c}{6}ψ^6-f_{{ext}}ψ · 2606.29055
v(u)=\frac{a}{2}u^2+\frac{b}{4}u^4+\frac{c}{6}u^6 · 2606.29765
$$a_0 = \frac{e E_0}{m_e c \omega}$$
Dimensionless parameter comparing electron oscillation energy to rest mass.
What is in the formula
a_0variablerelativistic intensity parameter (normalized vector potential) — relativistic parameter
E_0variablepeak electric field amplitude of the laser — electric field volt per metre
ωvariableangular frequency of the laser — angular frequency radian per second
econstantcharge of a single proton — elementary charge = 1.602176634e-19 coulomb
m_econstantmass of an electron at rest — electron mass = 9.1093837015e-31 kilogram
cconstantuniversal speed limit of light in vacuum — speed of light = 299792458 metre per second
a_0=\frac{ee_0}{m_ecω}=\frac{\sqrt{i[\rmw/cm^2]λ^2[μm^2]}}{1.38*10^{18}}\ge1 · 2607.00505
a_0=\frac{ee_0}{m_ecω} · 2607.00505v1

Related articles · 16

Quantum Gases2026-07-301 minarXiv:2607.27999express
How Two Rhythms Give Birth to a Slow Quantum Wave
Moiré patterns are familiar to everyone. Two combs with different spacing, placed on top of each other, show dark fringes. Something similar has emerged in time. Physicists took a cloud of Rydberg atoms, particles with unusually large electron orbits, and illuminated it with two lasers.
A Day in the Quantum Beat: How Cesium Atoms Became an Eternal Metronome
An orchestra of billions of cesium atoms struck a single note, and it sounded for 17 hours without fading. That’s no exaggeration: Chinese physicists created a continuous time crystal with a record-breaking lifespan. A time crystal is a system that breaks time symmetry, spontaneously pulsating in an unchanging rhythm.
Optics2026-06-192 minarXiv:2606.21630express
A Time Crystal Trapped in a Cage of Sound
A pendulum that swings on its own, without any winding — in the quantum world, such 'pendulums' are called time crystals. In them, rhythmic motion arises spontaneously and does not decay. But until now, controlling this rhythm was nearly impossible: any intervention threatened to destroy the fragile order.
Statistical Mech2026-06-061 minarXiv:2606.08004express
How to Stabilize the Unstable: The Formula of Hidden Phases
Imagine a slide with three dips: the deepest one is a stable position for a ball, the middle one is precarious. A slight push and the ball rolls down. Yet, constant vibration of the right strength can hold it in the middle hollow for a long time. In the 1950s, physicists Lee and Yang discovered that all states of matter are separated by invisible points in the world of imaginary numbers.
Quantum Physics2026-05-262 minarXiv:2605.27211express
Time Crystals: Spontaneous Breaking of Time Translation Symmetry in Quantum Systems
Time crystals are quantum phases of matter that spontaneously oscillate, like a tuning fork with an infinitely decaying echo. If an ordinary spatial crystal repeats an atomic pattern in space, breaking translational symmetry, a time crystal exhibits periodicity in time, breaking time translation symmetry.
Quantum Physics2026-05-191 minarXiv:2605.19917express
Self-Running Quantum Clocks
Two quantum particles are linked by an invisible thread: one loses energy, the other gains it, but the total remains unchanged. If you watch only the first, its oscillations don't fade — the rhythm is steady, like that of a cosmic pulsar, even though it seems that entropy and chaos are increasing.
Quantum Gases2026-05-142 minarXiv:2605.14250express
Time Crystallizes Without a Kick
The pendulum of an old clock swings because a spring mechanism gives it a regular nudge. Now imagine a pendulum that decides on its own when to swing, and does so with a steady rhythm, just because the room is warm and there's a slight draft. That's exactly how time crystals behave, born in clumps of light and matter inside a semiconductor chip.
Quantum Gases2026-05-132 minarXiv:2605.13206express
One Tile to Rule Them All
Tile a floor with identical triangles, and you get a boring repeating pattern. But what if you want the pattern to never repeat, yet use just one tile? For a long time, mathematicians were sure it couldn't be done: you'd need at least two different shapes. The famous Penrose mosaic is a case in point: rhombi with acute and obtuse angles arrange into an infinitely varied but strictly ordered pattern.
Optics2026-05-042 minarXiv:2605.02406express
A Laser Pendulum in a Suitcase
A pendulum swings with such precision that, had it been counting seconds since the Big Bang, it would have drifted by only half a second by today. That is the stability of the new portable ultraviolet laser — the heart of aluminum atomic clocks.
Atomic Physics2026-03-121 minarXiv:2603.12170express
Atomic String and Harmony of Frequencies
A cloud of cesium atoms was made to behave like a single quantum string. By shining a laser and letting the particles interact, scientists launched self-sustaining oscillations — a rhythm emerged without an external conductor. Radio waves acted like frets on a fingerboard: it was possible to smoothly vary the sounding frequency.
Superconductivity2026-02-262 minarXiv:2602.22793express
Superconductor with Twisted Symmetry
An ordinary superconductor works like a perfect conductor: electrons pair up and flow without resistance. In the new material TaPtSi, the pairs are arranged differently: their internal symmetry is skewed, and when cooled below the critical temperature, tiny magnetic fields spontaneously emerge inside the crystal.
Optics2026-02-212 minarXiv:2602.18838express
Light Springs: Twisting a Beam to Outrun Light
A laser beam usually travels straight, like a jet of water from a hose. But what if you twist that jet like the thread of a corkscrew? You get a light spring — a beam that, as it moves, also spins around its own axis. At every point in space, its brightness traces a spiral, and if you place a flat screen in its path, you'll see a rotating spot of light.
Optics2026-02-201 minarXiv:2602.18418express
Light That Tunes Itself
When two light beams meet in a crystal, they can generate a third beam with a different frequency. For this process to be efficient, the waves need to stay in step, like two people walking side by side without breaking stride. Previously, two old tricks were used: either picking a crystal with the right properties, or slicing it into thin layers.
Quantum Physics2026-01-141 minarXiv:2601.09779express
Matryoshka Time Crystals: A Hierarchy of Rhythms in a System of Five Ions
Time crystals are an exotic phase of matter that exhibits periodic motion not in space but in time, even while in its ground, unexcited state. This idea, reminiscent of a perpetual clock that never needs winding, was first proposed by Frank Wilczek.
Strongly Correlated2026-01-042 minarXiv:2601.01531express
How Electronic Ice Melts
Electrons in a conductor usually behave like a gas: they dart around chaotically, collide, and don't hold formation. But if you spread them far apart and cool them down, their mutual repulsion can force them into place, like attendees in an overcrowded hall who settle into every other seat.
Quantum Physics2025-12-181 minarXiv:2512.16097express
Time crystals without chaos
Time crystals pulse in time, like a perpetual metronome that never needs winding. The idea was proposed by Frank Wilczek almost ten years ago. Previously, to keep such a metronome from losing its beat, disorder was deliberately introduced into the system — a paradox, but chaos helped the rhythm.