Yet, order can also appear in a far more surprising way -- on its own, without any external timer. When countless particles interact in complex ways, they can spontaneously fall into a repeating rhythm instead of behaving chaotically. This phenomenon is known as a "time crystal." Researchers at TU Wien (Vienna) have now demonstrated that time crystals can form through an entirely different mechanism than scientists had believed possible. Their calculations reveal that quantum correlations between particles, once thought to disrupt these patterns, can in fact help stabilize them. The finding offers a striking new perspective on how collective behaviors emerge in quantum many-particle systems.

Space crystals and time crystals

When a liquid freezes, its particles shift from disorder to order. In the liquid state, the particles move freely and randomly, showing no particular pattern. As the liquid solidifies, the particles lock into precise positions, forming a regular and repeating spatial structure -- a crystal. A liquid is uniform in every direction, but in a crystal that symmetry breaks: it gains structure, with certain directions becoming distinct from others.

Can a similar kind of symmetry breaking happen over time rather than in space? Could a quantum system that initially behaves identically at every moment spontaneously develop a repeating temporal pattern -- a rhythm that marks the emergence of order in time itself?

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 Physics 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 Felix 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 behaviour 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 Felix 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.

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