Have you heard of time crystals?

A crystal is any object whose atoms are arranged in a fixed pattern in space, with the pattern repeating itself. So what we typically know to be crystals are really space crystals. We didn’t have to bother with the prefix because space crystals were the only kind of crystals we knew until time crystals came along.

Time crystals are crystalline objects whose atoms exhibit behaviour that repeats itself in time, as periodic events. The atoms of a time crystal spin in a fixed and coordinated pattern, changing direction at fixed intervals.

Physicists sometimes prefer to quantify these spin patterns as quasiparticles to simplify their calculations. Quasiparticles are not particles per se. To understand what they are, consider a popular one called phonons. Say you strike a metal spoon on the table, producing a mild ringing sound. This sound is the result of sound waves propagating through the metal’s grid of atoms, carrying vibrational energy. You could also understand each wave to be a particle instead, carrying the same amount of energy that each sound wave carries. These quasiparticles are called phonons.

In the same way, patterns of spinning charged particles also carry some energy. Each electron in an atom, for example, generates a tiny magnetic field around itself as it spins. The directions in which the electrons in a material spin collectively determine many properties of the material’s macroscopic magnetic field. Sometimes, shifts in some electrons’ magnetic fields could set off a disturbance in the macroscopic field – like waves of magnetic energy rippling out. You could quantify these ‘spin waves’ in the form of quasiparticles called magnons. Note that magnons quantify spin waves; the waves themselves can be from electrons, ions or other charged particles.

As quasiparticles, magnons behave like a class of particles called bosons – which are nature’s force-carriers. Photons are bosons that mediate the electromagnetic force; W and Z bosons mediate the weak nuclear force responsible for radioactivity; gluons mediate the strong nuclear force, which carries the energy you see released by nuclear weapons; scientists have hypothesised the existence of gravitons, for gravity, but haven’t found them yet. Like all bosons, magnons don’t obey Pauli’s exclusion principle and they can be made to form exotic states of matter like superfluids and Bose-Einstein condensates.

Other quasiparticles include excitons and polarons (useful in the study of electronic circuits), plasmons (of plasma) and polaritons (of light-matter interactions).

Physicist Frank Wilczek proposed the existence of time crystals in 2012. One reason time crystals are interesting to physicists is that they break time-translation symmetry in their ground state.

This statement has two important parts. The first concerns time-translation symmetry-breaking. Scientists assume the laws of physics are the same in all directions – yet we still have objects like crystals, whose atoms are arranged in specific patterns that repeat themselves. Say the atoms of a crystal are arranged in a hexagonal pattern. If you kept the position of one atom fixed and rotated the atomic lattice around it or if you moved to the left or right of that atom, in both cases by an arbitrary amount, your view of the lattice will also change. This happens because crystals break spatial symmetry. Similarly, time symmetry is broken if an event repeats itself in time – like, say, a magnetic field whose structure changes between two shapes over and over.

The second part of the statement concerns the (thermodynamic) ground state – the state of any quantum mechanical system when it has its lowest possible energy. (‘Quantum mechanical system’ is a generic term for any system – like a group of electrons – in which quantum mechanical effects have the dominant influence on the system’s state and behaviour. An example of a non-quantum-mechanical system is the Solar System, where gravity dominates.) Wilczek revived interest in time crystals as objects that break time-translation symmetry in their ground states. Put another way, they are quantum mechanical systems whose constituent particles perform a periodic activity without changing the overall energy of the system.

The advent of quantum mechanics and relativity theory in the early 20th century alerted physicists to the existence of various symmetries and, through the work of Emmy Noether, their connection to different conservation laws. For example, a system in which the laws of nature were the same throughout history and will be in future – i.e. preserves time-translation symmetry – will also conserve energy. Does this mean time crystals violate the law of conservation of energy? No. The atoms’ or electrons’ spin is not the result of the electrons’ or atoms’ kinetic energy but is an inherent quantum mechanical property. This energy can’t be used to perform work the same way, say, a motor can pump water. The system’s total energy is still conserved.

Now, physicists from Germany have reported that they have observed a time crystal ‘in action’ – a feat notable on three levels. First, it’s impressive that they have created a time crystal in the first place (even if they are not the first to do so). The researchers passed radio frequency waves through a strip of nickel-iron alloy a few micrometers wide. According to ScienceAlert, this ‘current’ “produced an oscillating magnetic field on the strip, with magnetic waves travelling onto it from both ends”. As a result, they “stimulated the magnons in the strip, and these moving magnons then condensed into a repeating pattern”.

Second, while quasiparticles are not actual particles per se, they exhibit some properties of particles. One of them is scattering, like two billiard balls might bounce off each other to go off in different directions at different speeds. Similarly, the researchers created more magnons and scattered them off the magnons involved in the repeating pattern. The post-scatter magnons had a shorter wavelength than they did originally, in line with expectations, and the researchers also found that they could control this wavelength by adjusting the frequency of the stimulating radio waves.

An ability to control such values often means the process could have an application. The ability to precisely manipulate systems involving the spin of electrons has evolved into a field called spintronics. Like electronics makes use of the electrical properties of subatomic particles, spintronics is expected to leverage spin-related properties and enable ultra-fast hard-drives and other technologies.

Third, the researchers were able to produce a video showing the magnons moving around. This is remarkable because the thing that makes a time crystal so unique is the result of quantum mechanical processes, which are microscopic in nature. It’s not often that you can observe their effects on the macroscopic scale. The principal reason the researchers were able achieve this is feat is the method they used to create the time crystal.

Previous efforts to create time crystals have used systems like quantum gases and Bose-Einstein condensates, both of which require sophisticated apparatuses to work with, in ultra-cold conditions, and whose behaviour researchers can track only by carefully measuring their physical and other properties. On the other hand, the current experiment works at room temperature and uses a more ‘straightforward’ setup that is also fairly large-scale – enough to be visible under an X-ray microscope.

Working this microscope is no small feat, however. Charged particles emit radiation when they’re accelerated along a circular path. An accelerator called BESSY II in Berlin uses this principle to produce X-rays. Then the microscope, called MAXYMUS, focuses the X-rays onto an extremely small spot – a few nanometers wide – and “scans across the sample”, according to its official webpage. A “variety of X-ray detectors”, including a camera, observe how the X-rays interact with the sample to produce the final images. Here’s the resulting video of the time crystal, captured at 40 billion frames per second:

I asked one of the paper’s coauthors, Joachim Gräfe, a research group leader in the department of modern magnetic systems at the Max Planck Institute for Intelligent Systems, Stuttgart, two follow-up questions. He was kind enough to reply in detail; his answers are reproduced in full below:

  1. A time crystal represents a system that breaks time translation symmetry in its ground state. When you use radio-frequency waves to stimulate the magnons in the nickel-iron alloy, the system is no longer in its ground state – right?

The ground state debate is the interesting part of the discussion for theoreticians. Our paper is more about the experimental observation and an interaction towards a use case. It is argued that a time crystal cannot be a thermodynamic ground state. However, it is in a ground state in a periodically alternating potential, i.e. a dynamic ground state. The intriguing thing about time crystals is that they are in ground states in these periodically alternating potentials, but they do not/will not necessarily have the same periodicity as the alternating potential.

The condensation of the magnonic time crystal is a ground state of the system in the presence of the RF field (the periodically alternating potential), but it will dissipate through damping when the RF field is switched off. However, even in a system without damping, it would not form without the RF field. It really needs the periodically alternating potential. It is really a requirement to have a dynamic system to have a time crystal. I hope I have not confused you more than before my answer. Time crystals are quite mind boggling. 😵🤯

  1. Previous experiments to observe time crystals in action have used sophisticated systems like quantum gases and Bose-Einstein condensates (BECs). Your experiment’s setup is a lot more straightforward, in a manner of speaking. Why do you think previous research teams didn’t just use your setup? Or does your setup have any particular difficulty that you overcame in the course of your study?

Interesting question. With the benefit of hindsight: our time crystal is quite obvious, why didn’t anybody else do it? Magnons only recently have emerged … as a sandbox for bosonic quantum effects (indeed, you can show BEC and superfluidity for magnons as well). So it is quite straightforward to turn towards magnons as bosons for these studies. However, our X-ray microscope (at the synchrotron light source) was probably the only instrument at the time to have the required spatial and temporal resolution with magnetic contrast to shoot a video of the space-time crystal. Most other magnon detection methods (in the lab) are indirect and don’t yield such a nice video.

On the other hand, I believe that the interesting thing about our paper is not that it was incredibly difficult to observe the space time crystal, but that it is rather simple to create one. Apparently, you can easily create a large (magnonic) space time crystal at room temperature and do something with it. Showing that it is easy to create a space time crystal opens this effect up for technological exploitation.