A brief introduction to time crystals

An object that has excited many physicists, and now that it’s been created in a quantum computer, its name sounds a bit sci-fi: the time crystal.

We all know ordinary crystals like salt crystals, in which the atoms are arranged in an orderly manner. It’s as if every atom sits on a square lattice, which scientists call a lattice. If you’re a quantum Ant-Man standing on one of the atoms, and you’re moving in a certain direction in space, you’ll encounter other identical atoms on a regular, periodic basis. The atomic structure of an ordinary crystal repeats over and over again in space, so if you look at any part of it, you’ll see the same pattern of repetition.

A brief introduction to time crystals

The reason atoms or molecules form crystals is that this places the structure in the lowest energy state of all its systems. In 2012, Nobel laureate in physics Frank M. Wilczek asked if it was possible to make crystals that were symmetrical in time rather than space. This means that the particles it contains are constantly rearranged into different configurations, but at certain intervals, they return to the exact same configuration.

Such behavior, Wilczek says, is like a clock that spontaneously appears in a particle system, ticking at a speed it sets for itself. Making time crystals isn’t just an intellectual exercise for physicists, it can also be useful: they will become natural timekeepers, beating their pulses according to their choice. Some researchers believe that time crystals may help us make better atomic clocks; Others argue that time crystals made from quantum particles could serve as components for building quantum computers.

The regular, cyclical behavior described by Wilczek looks a lot like a pendulum, where at the end of each back-and-forth swing, the pendulum or all the atoms it contains returns to the same position. But no matter how well it is made, an ordinary pendulum cannot swing forever. The friction at the pivot point will cause it to slowly lose energy until it stops swinging. Wilczek wondered if there was a way to make a time crystal that could remain in motion without injecting energy into the system.

Wilczek acknowledges that time crystals sound dangerous, like perpetual motion machines forbidden by the laws of thermodynamics. But he is optimistic that as long as he does not consume energy and does not produce energy, he should be able to oscillate forever. Three years later, other physicists proved that the quantum time crystal could not avoid the same problem as the pendulum, it would gradually dissipate the energy it started with, so the oscillations would slowly disappear.

But that didn’t make physicists lose interest in the time crystal, because we can push it slightly every once in a while, just like keeping a pendulum swinging, and the time crystal can keep oscillating by injecting energy into it by some kind of driving force. This should be no big deal, as we often see this happen, for example by pushing the swing to keep it swinging, and you will find that the swing oscillates at the same frequency as the one pushed.

But physicists realized that for the kind of quantum systems Wilczek had studied, something strange happened when you oscillated through this periodic driving force: the period of oscillation was different from the period of the drive, and it could be twice as long, or three times longer, or even any integer multiple. It’s as if the particles are saying thanks for pushing, but we’ll vibrate at the frequency we choose. So it turns out that this behavior is true time crystal behavior, because periodicity is generated by the interaction of particles within the crystal, not from the push. All the push does is prevent time crystals from running out of energy, and because the oscillation period is some integer or discrete multiple of the drive period, they are called discrete time crystals.

Manufacture time crystals

One way to make quantum-time crystals is to take a row of atoms that have a spin that can point up or down. In the time crystal state, spinning up or down flips back and forth along the row like a wave. They’ll do it somehow, making the structure a time crystal. We need to keep adding energy to sustain this wave, and then find a way to dissipate that energy so that the system doesn’t get too hot and fall apart.

In 2017, two teams reported that they had experimentally fabricated discrete quantum-time crystals in spin chains. Still, they can’t completely stop these systems from absorbing too much energy. It wasn’t until 2021 that two teams of scientists made a discrete quantum-time crystal that could theoretically remain oscillating forever. They actually made them in quantum computers.

A brief introduction to time crystals

Quantum computers use qubits for computation, which are like particles with spins that can point up or down, and these up or down states encode 1s and 0s of binary information. These bits are operated using the rules of quantum mechanics, which allows quantum computers to do things that ordinary classical computers would not have been able to do. In these experiments, oscillations disappear after only about 100 cycles, because qubits in any quantum computer today become chaotic when they interact with surrounding matter, a process called quantum decoherence. This has nothing to do with the failure of the time crystal itself.

Now it is possible to ask the question, is this a simulation of a time crystal taken on a quantum computer, or did they create a time crystal from the qubits of the computer? Interestingly, no one knows, but there may not be any difference between them.

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