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OK, WTF Is a Time Crystal?

Physicists have made a new phase of matter called a time crystal—but what does that even mean?

Last month, a team of physicists from UC Berkeley said they'd created a blueprint for a new phase of matter called a time crystal. Their paper, in Physical Review Letters, turned what was once a pretty far out speculation into a practical recipe for cooking up a time crystal in a laboratory.

Indeed, since the preprint paper was published online last year, researchers at the University of Maryland and Harvard University have followed the UC Berkeley recipe and created time crystals of their own using two different mediums: lasers and trapped ions.

A time crystal isn't something you can hold in your hands, and it isn't something you can grow in your kitchen with some table salt and a glass of water. For a long time, the time crystal concept existed only on paper as a mathematical oddity. It's only now that time crystals have been realized in a lab in (quantum) physical form.

Time crystals are an insanely complicated subject and not particularly relevant to 99 percent of the population (at least for now), which is probably why you haven't heard much about them, despite the magnitude of this scientific breakthrough. Indeed, after spending a few hours discussing the matter with a handful of physicists who are on the front line of time-crystallography, I was still only able to grasp the subject at a relatively rudimentary level. Yet thanks to these physicists' near infinite patience and input, I was able to distill the essence of a time crystal into the simplest, most accurate explanation I could muster, and it's still pretty complicated.

Why spend all this time trying to understand time crystals? Well, despite being pretty esoteric, this breakthrough is a big deal—after all, it's not every day that you come up with a practical recipe for an entirely new phase of matter, albeit one that is quite different from solids, liquids, and gases. Time crystals might one day have technological implications, too. For example, time crystals may form the basis for a nearly perfect memory unit for powerful quantum computers. Still, one of the most exciting things about time crystals is that because they're so new and exotic, even physicists can't get a grasp of their full potential yet.

CRYSTALS: A SPACE (AND TIME) ODYSSEY

First let's ignore that extra dimension—time—and consider your run-of-the-mill 3D crystal. A crystal is basically just a number of atoms arranged in a periodic, or repeating, pattern in space.

Before a liquid crystallizes, the space it occupies is homogeneous. In other words, if water, say, is in a full cup, you could sample the bottom, the top, or anywhere in the middle, and it would be the same, which is another way of saying that space exhibits symmetry.

Yet when the water crystallizes, the atoms form rigid, set arrangements. The space occupied by the crystal has become periodic. The crystal has broken spatial symmetry because it exhibits repeating patterns in some directions—anyone who's grown salt water into sodium chloride crystals has seen them push up— rather than being the same in all directions.

In 2012, the Nobel laureate Frank Wilczek predicted that the periodicity of crystals could be extended into the fourth dimension: time. Wilczek imagined a system in its lowest possible energy state, which would effectively render it frozen in space like a normal crystal.

But if the atoms in that system were to move from their original position in some way, he argued, it would break time-translation symmetry, which is essentially the idea that each instant in time is the same as any other instant in time. For example, if you were flipping a coin, the chances of it landing on heads or tails is 50/50—flipping the coin in 10 seconds or 10 nanoseconds doesn't change the probability of it landing on heads or tails.

So just like how in the previous example the water was the same throughout the space it occupied (spatial symmetry), objects exist through time in a similar way, which means that just like the atoms in a spatial crystal occur at regular intervals in space, the movement of the Wilczek's 4D crystal occurs at regular intervals in time (aka periods).

To take up the coin example again, when the time crystal breaks time-translation symmetry that means that it is making a particular period in time special, which would be like having a 50/50 chance with the coin now, but knowing that if you waited a certain interval of time, say 10 seconds, those odds would change to 75/25.

Image: Stéphane Magnenat/Flickr

Just like physics allows for the spontaneous formation of crystals, whose periodicity breaks the symmetry of space, so too should it allow for the spontaneous formation of time crystals, whose periodicity break the symmetry of time. According to Wilczek, this would show itself in the periodic behavior of various thermodynamic processes, such as a rotating ring of ions in their lowest energy state. This would act like a sort of naturally occurring pendulum that could be used to measure time, or as Wilczek told the MIT Technology Review in 2012, "the spontaneous formation of a time crystal represents the spontaneous emergence of a clock."

Wilczek's idea was visionary in its originality and elegant in its simplicity, but ultimately he got the details wrong. One of the most glaring problems was that his time crystal approached something that looked suspiciously like perpetual motion—after all, where did the system in its lowest possible energy state (meaning energy cannot be extracted from it) get the energy to produce the periodic motion in the first place?

On an even more fundamental level, it wasn't entirely clear just how physicists could go about turning this mathematical oddity into an experiment that could be tested in a lab.

TAKING TIME CRYSTALS FROM PAPER TO THE LAB

It wasn't until 2016 that a group of physicists working at Station Q, a Microsoft research facility at UC Santa Barbara, figured out a way to correct the theoretical problems with Wilczek's time crystals and provided the stepping stone to actually make them. The group, led by physicist Chetan Nayak, built on prior research from Princeton University, which found that time crystals can spontaneously break a fundamental symmetry called time-translation symmetry to exhibit periodicity over time.

According to Nayak and co's research, the spontaneous break with time-translation symmetry that defines a time crystal should occur in a type of quantum system known as a Floquet many body localized driven system. This is basically just a fancy way of describing a system that is intrinsically out of thermal equilibrium. In other words, these systems never heat up, and cannot be characterized by any temperature, since the very idea of temperature supposes equilibrium.

A rough approximation of this idea might be to imagine a pot that has a burning match on one side and an ice cube on the other. If someone asked you what the temperature of the pot was, you'd be hard pressed to give an answer. The side with the match is hot and the side with the ice cube is cold—in other words, the system is out of equilibrium. Once the match went out and the ice cube melted, however, the system would be in equilibrium and you could determine a temperature for the pot.

As the Station Q physicists discovered, these non-equilibrium Floquet systems are able to host new states of matter that wouldn't be possible in equilibrium systems, like the glass of water that turns to ice crystals. Whereas, say, equilibrium systems like liquids and gasses can spontaneously break natural spatial symmetries, by considering a non-equilibrium system, the Microsoft and UCSB researchers were able to predict spontaneously broken time-translation symmetry, aka a time crystal.

Put simply, Wilczek's original idea would've required the continuous time-translation symmetry to break down in order to produce a time crystal. In Nayak and co's model, the system breaks the discrete time-translation symmetry of a periodically driven system.  

Although they didn't provide a fine-grained plan for creating an experimental time crystal, Nayak and co's theory revealed something incredibly interesting about their nature. When a time crystal is driven, or pushed, at a certain period or frequency, it doesn't respond at the same frequency that it was driven—in other words, if a laser is pulsed (the driving mechanism) at a chain of ions (the medium of the time crystal) every ten seconds, those ions will exhibit a period not of ten seconds, but twenty, thirty or some other multiple of the original period.

To help explain why this was so remarkable, consider this analogy.

Imagine three people playing jump rope: Bob and Rob hold the end of the rope and Alice jumps in the middle. Every three seconds, Bob and Rob's arms make one full rotation, the rope goes around once and their arms return to their original position, which establishes the time-translation symmetry where the period is three seconds.

Image: Ed Schipul/Flickr

Now, to make a time crystal in this analogy, you have to break this time-translation symmetry by having the system respond at a different frequency. What that would mean is that Bob and Rob's arms make multiple full rotations, but the rope only makes one full rotation. Put differently, Bob and Rob's arms might make four full rotations, but Alice only has to jump over the rope once—which is pretty damn weird.

The question, then, was how to realize this mathematical oddity in a physical experiment. Enter Norman Yao and his team at UC Berkeley.

Whereas Nayak's group was responsible for clearing up the theoretical problems with Wilczek's idea, Yao and his colleagues provided a nuts and bolts guide to actually creating a time crystal in a laboratory.

THERE'S MORE THAN ONE WAY TO MAKE A TIME CRYSTAL

Following the publication of the preprint of Yao's paper last year, two teams at the University of Maryland and Harvard managed to experimentally realize a time crystal for the first time. The teams used entirely different setups, but both followed Yao's recipe.

The Maryland team worked with Yao to create a chain of 10 ytterbium ions whose electron spins were entangled, much like the qubit systems being tested for some quantum computers. To keep the ions out of equilibrium, the researchers pulsed them with two lasers, one which was used to create a magnetic field and the other which was used to flip the spins of the electrons. Because the electrons were entangled, the spin flipping of one caused the spin flipping of another and so on, creating a repetitive pattern that broke the time translation symmetry needed for a time crystal (in this case, the period of the ion flipping was twice the period of the laser pulse).

By changing up the electric field and period of the laser pulse, it is possible to change the phase of the time crystal, the non-equilibrium equivalent of a phase change in equilibrium matter, like a solid melting into a liquid. Yao also worked with the Harvard team to create their time crystal, making use of small imperfections in diamonds as their medium instead of ytterbium ions.

The results from both the Maryland and Harvard are currently under review for publication and as such the physicists involved were unable to go into much detail about the experiments.

Now that physical time crystals have apparently been realized in a lab (the work is currently under peer review and will be published in Nature in the coming months if accepted), physicists are beginning to consider their potential applications. At Microsoft's Station Q on the UCSB campus, researchers are trying to figure out how to integrate the idea into a quantum computer. The focus there is on topological quantum computers, which differ from trapped ion quantum computers insofar as the qubits are based on quasiparticles that emerge from interactions inside matter instead of manipulating the energy levels of ions.

According to Nayak, this approach seems tailored to time crystals, since it is based on tightknit interactions between particles, such as was witnessed in Maryland ytterbium ion chain.

"There's actually a rather natural connection here to what we're doing [with quantum computing]," Nayak told me. "A quantum computer is going to be doing lots of operations on some kind of clock cycle and it is in fact being periodically driven, so it behooves us to look at how topological phases behave in periodically driven systems."

"As it turned out, many of the ideas and mathematical techniques we've been developing for quantum computing were immediately applicable to this project and allowed us to make that breakthrough on time crystals," Nayak added.

Yet as Nayak was quick to mention, Station Q's research is still exploratory. It will be a long time before time crystals find any practical application.

"In this group we do a fair amount of exploration of new ideas in physics with the hope that they'll be useful for the quantum computing stuff we're doing," said Nayak. "Now that we know what time crystals are, we have some ideas about how to exploit them for topological quantum computing ideas, but that's still very much a work in progress."

So even the physicists involved in creating time crystals are still trying to wrap their heads around possible use cases for this new phase of matter, which leaves little hope for us laypeople who just want to understand wtf time crystals actually are in the first place. This was about as simple as a simpleton like myself could break down this ridiculously complex topic, and perhaps you're no closer to understanding time crystals now than you were before. I'm not so sure myself, but hey—you can't say we didn't try.  

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Correction: A previous version of this article incorrectly stated that Microsoft's Station Q discovered time crystals in driven systems. This credit actually belongs to Shivaji Sondhi and his colleagues at Princeton University, who had discovered this phenomenon several months prior. Motherboard regrets the error.