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Nature has many rhythms: the seasons result from Earth's movement around the sun, the ticking of a pendulum clock results from the oscillation of its pendulum. These phenomena can be understood with very simple equations. However, regular rhythms can also arise in a completely different way—by themselves, without an external clock, through the complex interaction of many particles. Instead of uniform disorder, a fixed rhythm emerges—this is referred to as a "time crystal."

Calculations by TU Wien (Vienna) now show that such time crystals can also be generated in a completely different way than previously thought. The quantum physical correlations between the particles, which were previously thought to be harmful for the emergence of such phenomena, can actually stabilize time crystals. This is a surprising new insight into the quantum physics of many-particle systems.

The findings are in the journal Â鶹ÒùÔºical Review Letters.

Space crystals and time crystals

When a liquid freezes, the particles change their spatial order: In the liquid, they move wildly and randomly, with no structure. When the liquid freezes, a crystal forms in which the individual particles are located in very specific places in a very regular pattern. A liquid looks the same everywhere, it has the same properties everywhere and in every direction, it is completely symmetrical. In a crystal, however, this symmetry is broken: suddenly there is a regular structure, there is a direction that differs from other directions.

Can this kind of symmetry breaking also occur in time? Is it possible that a quantum system is initially disordered in time, that every point in time is the same as every other, but that a temporal order nevertheless emerges?

Quantum fluctuations: Harmful or useful?

"This question has been the subject of intensive research in quantum physics for over ten years," says Felix Russo from the Institute of Theoretical Â鶹ÒùÔºics at TU Wien, who is conducting research for his doctoral thesis in Prof. Thomas Pohl's team. In fact, it has been shown that so-called time crystals are possible—systems in which a temporal rhythm is established without the beat being imposed from outside.

"However, it was thought that this was only possible in very specific systems, such as quantum gases, whose physics can be well described by mean values without having to take into account the random fluctuations that are inevitable in quantum physics," says Russo. "We have now shown that it is precisely the quantum physical correlations between the particles, which were previously thought to prevent the formation of time crystals, that can lead to the emergence of time-crystalline phases."

The complex quantum interactions between the particles induce collective behavior that cannot be explained at the level of individual particles—similar to how the smoke from an extinguished candle can sometimes form a regular series of smoke rings; a phenomenon whose rhythm is not dictated from outside and which cannot be understood from single smoke particles.

Particles in the laser lattice

"We are investigating a two-dimensional lattice of particles held in place by laser beams," says Russo. "And here we can show that the state of the lattice begins to oscillate—due to the quantum interaction between the particles."

The research offers the opportunity to better understand the theory of quantum many-body systems—paving the way for new quantum technologies or high-precision quantum measurement techniques.