# Magnetic helium makes superfluid time crystal

Sometimes, a paper contains so many buzzwords it is hard to take it seriously. Time crystals were first mooted in 2012, and a realistic discrete time crystal was observed in 2017. The crystals we are familiar with have a quasicrystal form, so time quasicrystals were soon discovered. But now, I’ve hit the jackpot with a time quasicrystal that is also a time supersolid.

If that makes no sense to you, don’t worry, it doesn’t make sense to me either.

Let’s unpack the word salad and see if we can extract something sensible from it.

## Crystals and quasicrystals: neither heals disease

A crystal in space is a unit that repeats at regular intervals so that it fills a space without gaps. The repeating unit can only be translated, not rotated. Thus, you can get arrangements of atoms that make up a cube, for example, to fill a space.

A quasicrystal also uses a repeating unit that will fill space without gaps. In this case, the repeating units are translated and rotated. The material is ordered, but it is not the order that we are used to seeing. Instead the order appears repeated in space via two overlapping patterns that repeat at different spatial intervals. On top of that, the ratios of those intervals are not neat integers.

## Exchanging space for time

In a discrete time crystal, rather than repeating the location of atoms, our repeating unit is some behavior. But it’s not like a pendulum swinging back and forth—you have think of it a bit differently. Imagine I want to create a time crystal from a pendulum. The pendulum has a natural oscillation frequency. I can push the pendulum at the oscillation frequency and it will start swinging. I can also push it at half the oscillation frequency, and it will also swing nicely.

But I cannot push it at twice the oscillation frequency and expect it to keep swinging. This is because the first push sets the swing in motion, while the second push ends up timed to stop the swing’s motion. To get strong oscillations, the frequency at which we drive the swing has to match a multiple of the natural frequency of the swing.

In a discrete time crystal, the frequency at which we push the swing’s oscillation doesn’t match the natural frequency of the swing. Instead of killing the oscillation, though, the swing starts swinging at a new frequency that is not its natural frequency and not commensurate with the drive frequency, either. Once you achieve something like this, you may have a time crystal.

In analogy with a normal quasicrystal, a time quasicrystal involves the swing swinging with two frequencies simultaneously—it’s probably better to think of two waves vibrating on a string in this case. However, neither of those frequencies is a multiple of the frequency at which we drive the swings. And just like ordinary quasicrystals, the two ratios of these two frequencies are not neat integers.

## It’s all just a bit bizarre

To observe both time crystals and quasitime crystals, researchers used helium-3 (helium with a missing neutron) cooled to within a whisker of absolute zero. Because of the uneven number of particles in the nucleus, helium three has a strong magnetic moment. The helium is put into a state where all the magnets point in the same direction, creating what is called magnon.

The researchers observed a quasitime crystal, formed by the magnon slowly spinning around in space. The magnon is driven by the magnetic field of the container that holds the helium in place, as well as an applied radio frequency field. The resulting oscillation of the magneton has two frequencies that are not evenly divisible by either the driving field or each other.

This is in part because the driving radio frequency field simply inputs random energy. And that makes it even harder to understand. Think of it like this: a toddler is randomly mashing piano keys, but you hear repeating scales, not random noises.

When the researchers switch the radio frequency field off, the time quasicrystal quickly falls apart and the system forms a discrete time crystal. In this case, the drive frequency comes from the fact that the magnetic field of the helium modifies the shape of the container, sloshing the helium about a bit.

But this has an expiration date. As the helium sloshes, the collisions cause some of the helium atoms to flip orientation. When this happens, their magnetic field flips direction and they are thrown out of the trap. That means that the discrete time crystal slowly fades away.

## A supersolid time crystal

So far, so weird. But it’s possible to get weirder. Helium three, at these low temperatures, forms a special kind of superfluid, called a topological superfluid. The magnon—the helium with all its spins aligned—has a non-zero spin associated with it, and this has to be conserved. So the transport of spin through a helium three superfluid also behaves like a superfluid—a superfluid in a superfluid if you will.

The magnon is also the time crystal, though. If we think of a crystal as a time solid, then this particular time crystal must be a supersolid.

What is a supersolid you ask? Well, it is a solid that exhibits no friction. Two supersolids can slide over each other without losing energy. Now, last I checked, the existence of non-theoretical supersolids was rather controversial and the evidence equivocal. It seems a bit premature to declare this the time crystal equivalent.

The research is very cool, though, and I like a good quasitime crystal.

Physical Review Letters, 2018, DOI: 10.1103/PhysRevLett.120.215301