Time crystals: I’d hoped I’d never write about them again. A long time ago, there was a theory paper that proposed a new idea—time crystals. I was intrigued, but I was also confused. This either seemed like a trivial idea, or one so deep I didn’t fully grasp it. Now, it seems I might not have had a clue, as two research groups have reported producing actual time crystals.
Time crystals are not made of time
A time crystal is almost analogous to the crystals that you may be more familiar with, like salt and sugar. Salt consists of two atoms (sodium and chlorine) that are arranged in a fixed order in space. In any given direction, there is a characteristic length over which the crystal repeats itself. If I were located somewhere in the middle of a crystal and moved in any direction by the characteristic length (or a multiple of it), I would not actually be able to tell that I had moved.
This is more important than it sounds. The properties of matter are often dominated by the spatial order of the crystal. When you break that order, cool things happen (melting is an example of breaking spatial order).
Rather than order in space, a time crystal has to have order in time. And we all know things that have order in time: the hands on a clock or a playground swing. These all repeat themselves in time. Do they count? No. And the reason is a bit technical.
Pendulums slice time, but don’t crystallize
The difference is a bit semantic, but important. Things like the oscillation of a swing are described by solutions to equations that are time-independent. In other words, although things happen in time, the repetition that we see is due to the fact that the underlying forces are constant. Time crystals are things that repeat in time when this condition is not fulfilled.
Warning: what follows is a rather convoluted and mostly inaccurate analogy.
Imagine that you and a few friends are going to go zorbing on a perfectly flat surface (that’s rolling inside a plastic sphere). To keep track of the zorbs’ orientation, we can paint a pink dot on each one. In the first run, you all just travel along in straight lines at the same speed. If we take photos at just the right times, the pink dots always appear in the same place on the zorb.
This is not a time crystal. It is like a bunch of pendulums: you could use the location of the pink marker as a clock.
After everyone recovers and the mess is cleaned up, its time to zorb again. Now, the zorbs will be pushed along a trajectory in which they all collide with one another at regular intervals. The collisions are nicely timed, but the effect is that each zorb desynchronizes. Even though the collisions between the zorbs are regular and ordered, you can’t predict the rotation of one zorb based on the rotation of its neighbor. Nevertheless, each zorb, on average, still rotates at the same rate. These zorbs are neither a time crystal nor a clock.
And now we add noise. Each zorb has one person pushing it along its path, making sure that it collides with all the others at regular intervals, while someone else is running alongside, pushing it off its path irregularly. If the noise is handled just right, suddenly the zorbs all synchronize again. The additional bumps and bounces, combined with the regular collisions, bring them all into synchrony. This is a time crystal.
Bring forth the quantum
It might be fun to picture atoms and ions as little zorbs, where every now and again the nucleus gets motion sickness and throws up—maybe that could be my alternative-fact explanation for radioactivity. Sadly, they are not, and the time crystals aren’t built with atoms. The two publications used different quantum objects—one used nitrogen vacancy centers, the other used trapped ions—to demonstrate time crystals.
The two experiments are largely the same, so I’m only going to use ions for my explanation. To directly compare with the zorb analogy: the ions have a ground state and an excited state. If we shine a laser with the right color on the ion, it might or might not enter the excited state. At that point, the ion enters a quantum superposition state of being both in the ground state and the excited state.
If I make a measurement, however, I will get either the ground state or the excited state. If I make repeated measurements on identically prepared ions, I will learn the probabilities associated with the ground and the excited state.
Quantum mechanics, though, offers us more than that. If the light field contains enough photons in the right amount of time, the probability of finding the ion in the excited state is unity: it’s always there. If I double the number of photons, the probability is zero. That is, the ion cyclically oscillates between the ground state and the excited state in a periodic fashion. This is called a Rabi oscillation. And, if the light field is tuned exactly right, the ion will oscillate between the excited state and ground state at a kind of natural frequency that is controlled by the intensity of the light. This is the equivalent of what our zorb was doing when it was being pushed in a straight line.
But, what happens if I shift the color of the light just slightly? The ion still oscillates, but now it is like the zorb has a slight wobble to its motion so that the dot never quite makes it back. Instead of one Rabi frequency, you get two: one slightly lower than the natural frequency and one slightly higher. It’s as if you had two zorbs of slightly different diameters moving at the same speed.
(For those interested, you get two Rabi frequencies because the presence of the light causes the energy level of the energetic state to split into two. The ion is no longer cycling between the ground state and one excited state, but between the ground state and two excited states, hence two oscillation frequencies.)
And this is how the researchers drove their ions to oscillate. By introducing this shift, they get a clear signal for when this off-center drive frequency is dominating, and it’s different from the natural frequency. But that’s not an indication of a time crystal.
The next step is to introduce the equivalent of the zorb collisions. The ions are all sitting in an energy trap you can view like a bowl, and they oscillate back and forth in that bowl. Their oscillations all slightly distort the bowl and influence the motion and state of the others. Hence, the Rabi oscillations that I just described would naturally go out of sync simply because each ion is moving around in the trap and modifying the environment experienced by the other ions. By using a laser to give them all a bit of a kick, this cross coupling can be amplified considerably, and, critically, in a controllable way.
When the researchers do this, the nice clean oscillations observed earlier die away, leaving only noise. Each ion is still oscillating between the two states, but they do so at their own rate. Even though we cannot see the clean oscillations, they are still there, hidden in the noise.
The last step is to turn on the noise. The noise takes the same form as the kick given to the ions. However, unlike the earlier kick, which was deterministic—every ion gets a kick that is related to the one the other ions receive—this one is random. Each ion just gets a flash of light, the intensity and timing of which is set by a random number generator. This drives each ion to oscillate in a way that is completely independent of the others.
Now, if all of this comes together in the right way, the ions start to oscillate between the ground state and their excited state at their natural frequency again. They cannot do this if only the original kick laser is used, nor if any two of the driving components are used. No, this only occurs if all three processes—a drive, coupling between the ions, and noise—are present.
But is it really a crystal?
If it is a crystal, then, it should, at some point, melt. This is the equivalent of changing the color of the original drive laser. The crystal maintains its order as the color shifts until it reaches a threshold and rapidly loses order. So, yes, the researchers also observe the crystal melting.
Despite this, I’m still a bit skeptical. I accept the evidence, but I’m not sure that I think time crystals are all that relevant a concept just yet. My issue is that in classical systems, coupling and noise have huge effects on the periodicity of an oscillator. While this is a quantum system, all the evolution before the final measurement is governed by continuous evolution, just like a set of classical mechanical oscillators. So, do we really gain anything by calling this a crystal and describing it with phase transitions? I simply don’t know.
I can still be convinced of the importance of time crystals. I could have completely misinterpreted what they’ve achieved here. Or, I could be right, but the different perspective may lead to new insights and understanding, which is just as important as “finding new things.” Frankly, I’d be happy with either (even if my ego is shattered by the former).
As for my zorb analogy: let’s hope I don’t make a sequel.
Nature, 2017, DOI: 10.1038/nature21413
Nature, 2017, DOI: 10.1038/nature21426