Back to the future: The original time crystal makes a comeback

Like vinyl records, the strange concept of a time crystal is spinning back into fashion. In 2012, a Nobel Prize–winning physicist proposed that the properties of a system of quantum particles might cycle in time much as a crystal’s pattern of atoms repeats in space, even without the addition of energy, making it a bit like perpetual motion machine. But others soon proved a “no-go theorem” that said such a thing was impossible—and replaced it with a less fantastical definition of a time crystal that researchers soon demonstrated in the lab. But now, two physicists have shown that the original notion of a time crystal is possible after all—at least in theory.

“I think it’s right,” says Frank Wilczek, a theoretical physicist at the Massachusetts Institute of Technology in Cambridge, who dreamed up time crystals but who was not involved with the new work. The new scheme is “one way of getting around the ‘no-go.’” But realizing the system experimentally may be exceedingly difficult, other physicists say.

In physics, patterns can arise seemingly out of nowhere. For example, in a crystalline solid, the forces between atoms do not explicitly specify the position of the atoms or the distances between them. Cool the atoms into their ground state, however, and they nestle into a repeating pattern like the squares on a checkerboard.

Wilczek wondered whether, through similar physics, a system could have a ground state that repeated in some measurable way in time instead of in space. In 2012, his two papers on the subject triggered a flurry of research. However, in 2015 theoretical physicists Haruki Watanabe and Masaki Oshikawa, now both at the University of Tokyo, proved that, strictly speaking, time crystals were impossible. The lowest energy state of an isolated system in so-called thermodynamic equilibrium had to be static, they showed.

Other researchers expanded on Wilczek’s idea, however, and revealed that a system that is repeatedly prodded with energy—like child being pushed on a swing—could exhibit a novel behavior that they dubbed a discrete time crystal. Such a periodically agitated system often oscillates at frequencies that are multiples of those of the external stimulus. But, instead, interactions within the system could make it respond at half that external frequency, researchers predicted, like a child strangely swinging at half the frequency at which the parent pushes.

The effect has been seen in the real world. For example, in 2017, Christopher Monroe, an experimental physicist at the University of Maryland in College Park, and colleagues produced a discrete time crystal with 10 spinning rubidium ions arranged in a chain. Through magnetic interactions, the ions tend to try to point in opposite directions, and noise jostles them randomly. But by prodding the ions with pulses of microwaves, the researchers could lock in the pattern of spins so they flipped at exactly half the rate of the pulses.

Now, theoretical physicists Valerii Kozin of the University of Iceland in Reykjavík and Oleksandr Kyriienko of the University of Exeter in the United Kingdom have proved that, at least in theory, it’s possible to construct a system closer to Wilczek’s original idea. To do that, they toss out one of the premises of Watanabe and Oshikawa’s no-go theorem, which rests on the assumption that the strength of the interactions among the particles dies off with distance, as is the case for electric and magnetic forces. In contrast, Kozin and Kyriienko theoretically analyze the case of spinning particles, like Monroe’s ions, that interact in a way that does not die off with distance, something that is possible in theory.

With such long-range interactions the system can have a time crystal ground state that needs no added energy, the researchers report in Physical Review Letters . “What we show is a loophole, not a counterexample” to the theorem, Kyriienko says.

The hypothesized time crystal state is incredibly complex. Thanks to quantum mechanics, each ion can spin both up and down at the same time, and the time crystal is similar to the state in which all the particles spin up and down at the same time—except a lot more complicated. The signature of the time crystal is subtle and would be tough to measure: Certain correlations in the number of spins pointing up or down will oscillate in time, even though the system remains unperturbed in its least energetic state.

The result isn’t shocking, Watanabe says, because other bedrock results in theoretical physics go out the window when a system has long-range interactions. “I wouldn’t be too surprised by this kind of behavior in a long-range system,” he says. “But still, it’s nice to have a concrete, simple example.”

Can the system be realized experimentally? Kyriienko says he’s hopeful. “It should be possible, but it’s a challenging measurement.” Monroe is less optimistic. The long-range interactions that Kozin and Kyriienko posit in their model are far more complex than those at work among ions in a trap, Monroe says. “I don’t think we have in practice any physical system that allows such interactions,” Monroe says. “But we could be surprised. That’s the great thing about science.”