TIME CRYSTALS!!! A name and concept that seem to come straight out of a science fiction or fantasy novel. But are they as fictional as we expect them to be?

A time crystal is a novel phase of matter. It is a system which oscillates repeatedly from one stable ground state to another without absorbing or “burning” any energy in the process. Despite being a constantly evolving system, a time crystal is perfectly stable. Analogous to regular crystals in space which break the spacial-translational symmetry, time crystals spontaneously break time-translational symmetry – the usual rule that a stable system will remain the same throughout time. No work is carried out by such systems and no usable energy can be extracted from them, so finding them would not violate the well-established principles of thermodynamics.

In 2012, the Nobel laureate in physics, Frank Wilczek proposed the existence of the titular time crystals. Wilczek envisioned a diamond-like multi-part object which breaks the time-translation symmetry in its equilibrium, moving in periodic, continuous motion and eventually returning to its initial state. However, this model turn out to be impossible as laws of thermodynamics dictate that in order to minimise their energy, quantum particles in the thermodynamic limit prefer to stop rather than to move. Scientists had to come up with other, slightly different models to make the creation of time crystals more plausible.

“If you think about crystals in space, it’s very natural also to think about the classification of crystalline behavior in time,”

– Frank Wilczek

Over the past few years, researchers have tried to developed various methods and approaches to create systems which very closely resemble the theorised time crystals. Such systems require some “ingredients” or specific techniques to be constructed. Consider a one-dimensional chain of spins. First, particles such as electrons are prepared in a polarised spin state. Naturally, these particles will try to settle into an arrangement which minimalised their energy. However, random destructive interference will trap them in higher-energy configurations. Our system is now experiencing a many-body localisation. These many-body localised systems exhibit a very special kind of order: if you flip the spin orientation of each particle, you will create another stable many-body localised state.

If you act on our system with a periodic driver such as a very specific laser, you will find that the spin orientations will flip back and forth, repeatedly and indefinitely moving between two many-body localised states. It is important to note that the particles do not heat up and absorb any net energy from the driving laser. By definition, our system has formed a time crystal.

In 2021, a new development in the fields of quantum computing and theoretical condense matter physics made the headlines. Researches at Google and physicists Stanford and Princeton and other universities were able to demonstrate the existence of such time crystals using Google’s revolutionary quantum computers.

Quantum computers operate on qubits – controllable quantum particles. The controllable aspects of the qubits prove to be especially useful in creating a time crystal. We can randomise the interaction strengths between the qubits, creating the necessary destructive interference between them, which in turn, allows us to achieve the many-body localisation. In this experiment, microwave lasers act as our periodic drivers, flipping the spins of the qubits. By running thousands of such demonstrations for various initial configurations, the researchers were able to observe that the spins were flipping back and forth between two many-body localised states. During these processes the particles never absorbed or dissipated any energy from the microwave laser, keeping the entropy of the system unchanged. They were able to create an extremely stable time crystal within a quantum computer.

“Something that’s as stable as this is unusual, and special things become useful,”

–  Roderich Moessner, director of the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany and co-author of the Google quantum computer time crystal paper.

Time crystals have the potential to finally allow us to take our condense matter research into the fourth dimension. They may help us create a whole new generation of novel devices and technologies. Their applications might include: being used as a new techniques of more precise timekeeping, simulating ground states in quantum computing schemes and even being implemented as a robust method of storing memory in quantum computers. However, due to the exotic nature of these systems and our poor knowledge of their physics, it might be a while until we will be able to grasp time itself in the palm of our hands.

References:

• Classical Time Crystals, A. Shapere and F. Wilczek, Phys. Rev. Lett. 109, 160402 (2012), https://link.aps.org/doi/10.1103/PhysRevLett.109.160402
• Eternal Change for No Energy: A Time Crystal Finally Made Real, Natalie Wolchover, https://www.quantamagazine.org/first-time-crystal-built-using-googles-quantum-computer-20210730/
• Time crystals enter the real world of condensed matter, P. Hannaford and K. Sacha, https://physicsworld.com/a/time-crystals-enter-the-real-world-of-condensed-matter/
• Viewpoint: Crystals of Time, Jakub Zakrzewski, https://archive.ph/20170202102150/http://physics.aps.org/articles/v5/116#selection-625.0-625.16
• How to Create a Time Crystal, Phil Richerme, https://physics.aps.org/articles/v10/5#c2
• Physicists Create World’s First Time Crystal, https://www.technologyreview.com/2016/10/04/157185/physicists-create-worlds-first-time-crystal/