DOE Pulse
  • Number 374  |
  • October 22, 2012

Berkeley Lab researchers propose a practical space-time crystal

Ultracold ions continue rotating at their lowest energy state. The structure periodically repeats to form a space-time crystal. (Courtesy of Xiang Zhang group)

Ultracold ions continue rotating at their
lowest energy state. The structure
periodically repeats to form a space-time
crystal. (Courtesy of Xiang Zhang group)

Early in 2012, Nobel Prize-winning theorist Frank Wilczek of the Massachusetts Institute of Technology came up with a novel idea: “Inspired by special relativity, or simply by analogy, it is natural to consider the possibility of spontaneous breaking of time translation symmetry” – in other words, the possibility of a space-time crystal, one in which a four-dimensional system adopts a discrete symmetry, an oriented repetitive structure in time analogous to that of a three-dimensional crystal in space.   

In a paper published in Physical Review Letters (PRL), an international team of scientists led by researchers with DOE’s Lawrence Berkeley National Laboratory (Berkeley Lab) has now proposed a method which could provide the basis for actually constructing such a space-time crystal. The scheme starts with an ion trap, an arrangement of electric and magnetic fields, which confines ultracold particles at their lowest energy state. The mutual Coulomb repulsion of the charged particles arranges them in a ring inside the trap, and if the ring were nudged into rotation, over time the constituent ions would periodically return to the same or equivalent positions. A space-time diagram would reveal that the ring-shaped crystal in space forms a spiral-cylinder crystal in time.

“Under the application of a weak static magnetic field, this ring-shaped ion crystal will begin a rotation that will never stop,” says Xiang Zhang of Berkeley Lab’s Materials Sciences Division, who led the research. “The persistent rotation of trapped ions produces temporal order, leading to the formation of a space-time crystal at the lowest quantum energy state.”

Tongcang Li, lead author of the PRL paper and a postdoc in Zhang’s research group, concedes that “a space-time crystal looks like a perpetual motion machine and may seem implausible at first glance.”

But, he says, “Keep in mind that a superconductor or even a normal metal ring can support persistent electron currents in its quantum ground state, under the right conditions.” Since the space-time crystal the Zhang team proposes exists at its lowest quantum energy state, there is no energy output and therefore it is not a perpetual motion machine.

As a many-body system, says Li, a space-time crystal would provide a new way to explore classic many-body physics questions. “How does time-translation symmetry-break? What are the quasiparticles in space-time crystals? What are the effects of defects on space-time crystals? Studying such questions will significantly advance our understanding of nature.”

A space-time crystal would be invaluable for these and numerous other scientific studies, and there are obvious practical applications as well. As Wilczek wrote when he came up with the idea, “We’ve been discussing the spontaneous emergence of clocks.” He didn’t stop there. “More complex systems of this kind ... could be quantum computers, capable of dodging the heat death of the universe for a very long time.”

Imagine clocks and computers that outlast the universe and keep on ticking and calculating – perhaps for eternity.

[Lynn Yarris, 510.486.5375,]