Four Dimensional Crystal Clock That Will Never Stop

An international team of scientists led by researchers with the U.S. Department of Energy's Lawrence Berkeley National Laboratory have proposed an innovative design of a space time crystal based on an electric field ion trap and the Coulomb repulsion of particles that carry the same electric charge.

This "space time crystal" has a four dimensional crystal that has periodic structure in time as well as space. 

"The electric field of the ion trap holds charged particles in place and Coulomb repulsion causes them to spontaneously form a spatial ring crystal," says Xiang Zhang, a faculty scientist with Berkeley Lab's Materials Sciences Division who led this research. "Under the application of a weak static magnetic field, this ring-shaped ion crystal will begin a rotation that will never stop. The persistent rotation of trapped ions produces temporal order, leading to the formation of a space-time crystal at the lowest quantum energy state."

The reason being the space time crystal is already at its lowest quantum energy state. Its time keeping will continue even after the rest of the universe gradually declines.

Zhang, who holds the Ernest S. Kuh Endowed Chair Professor of Mechanical Engineering at the University of California (UC) Berkeley, where he also directs the Nano-scale Science and Engineering Center, is the corresponding author of a paper.

The detail of the paper, "Space-time crystals of trapped ions" is being published in the Physics Review Letters (PRL).  

The concept of a crystal that has discrete order in time was proposed earlier this year by Frank Wilczek, the Nobel-prize winning physicist at the Massachusetts Institute of Technology. Now Zhang is focusing on the temporal order in a different system, and has produced a space-time crystal that is discrete both in space and time.

"Great progress has been made over the last few decades in exploring the exciting physics of low-dimensional crystalline materials such as two-dimensional graphene, one-dimensional nanotubes, and zero-dimensional buckyballs," says Tongcang Li, lead author of the PRL paper and a post-doc in Zhang's research group. "The idea of creating a crystal with dimensions higher than that of conventional 3D crystals is an important conceptual breakthrough in physics and it is very exciting for us to be the first to devise a way to realize a space-time crystal."

Under the scheme devised by Zhang and Li and their colleagues, a spatial ring of trapped ions  in persistent rotation will periodically reproduce itself in time, forming a temporal analog of an ordinary spatial crystal. With a periodic structure in both space and time, the result is a space-time crystal.

"While a space-time crystal looks like a perpetual motion machine and may seem implausible at first glance," Li 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. Of course, electrons in a metal lack spatial order and therefore can't be used to make a space-time crystal."

The space time crystal is not a perpetual motion machine. There is no energy output because it is at its lowest quantum energy state.

"The space-time crystal would be a many-body system in and of itself," Li says. "As such, it could provide us with a new way to explore classic many-body questions physics question. For example, how does a space-time crystal emerge? How does time translation symmetry break? What are the quasi-particles in space-time crystals? What are the effects of defects on space-time crystals? Studying such questions will significantly advance our understanding of nature."

According to the researchers space-time crystal might also be used to store and transfer quantum information across different rotational states in both space and time.

"These analogs could open doors to fundamentally new technologies and devices for variety of applications," he says.

"The main challenge will be to cool an ion ring to its ground state," Xiang Zhang says. "This can be overcome in the near future with the development of ion trap technologies. As there has never been a space-time crystal before, most of its properties will be unknown and we will have to study them. Such studies should deepen our understandings of phase transitions and symmetry breaking."