## Time Crystals: Breaking the Unbreakable

**By Ryan Cimmino**

No, they won’t power your time machine. And they won’t be featured in the latest line of wedding rings. Nonetheless, the fabrication of so-called “discrete time crystals” in 2017 quickly caused a stir in the realm of condensed matter physics, promising new insight into the study of non-equilibrium matter and quantum computing. While the somewhat mystifying name may cause more misconception than clarity, the creation of time crystals indeed marks an important development in our understanding of quantum phenomena.

First proposed in 2012 by Nobel laureate Frank Wilczek, time crystals encompass a phase of matter analogous to the “spatial” crystals we see every day, with one important distinction: the pattern of a time crystal repeats not in space, but in time.1 An ordinary spatial crystal of atoms—such as that found in diamonds—is characterized by a lattice structure in which the atoms form a geometric arrangement that repeats periodically in space. If we could analyze this object on a molecular level and observe it under rotations, we would soon notice that we would be able to tell the difference between two rotations at different angles. Concretely, one can envision this phenomenon as the rotation of a rigid shape such as an equilateral triangle: Unless we rotate the triangle at a multiple of 120 degrees, we will be able to tell that it has been rotated. By contrast, a circle can be rotated any which way, and there will be no way to distinguish it from the un-rotated circle.2 We say that a spatial crystal—in this case, the triangle—has broken spatial symmetry, whereas the circle maintains this symmetry. In a parallel way, if a space crystal can break “spatial symmetry”, a time crystal can break “time symmetry”: It exhibits a pattern of arrangements that repeat in time.

Symmetries offer physicists an elegant means of characterizing many physical phenomena, and they make systems theoretically and experimentally easier to study. The importance of symmetry also stems from an important mathematical principle—Noether’s Theorem—proved in the early 20th century by mathematician Emily Noether.3 The theorem states that a symmetrical system follows physical conservation laws. For instance, in a system that exhibits symmetry under any rotation, the total angular momentum is conserved. On the other hand, systems which break symmetries violate conservation laws. This idea is at the core of the theory behind time crystals: If there are systems that break spatial symmetries, can we create a system which breaks time symmetry, and hence violates conservation of energy?

As it turns out, we can answer this question in the affirmative. But there is one important caveat—even if the system does not conserve energy, no “useful” energy can be extracted from it. (Physically, this follows from the fact that a time crystal is, by definition, in its lowest energy state.) This property initially proved to be a theoretical stumbling block in the creation of time crystals. Shortly after Wilczek proposed the possibility of their existence, it was mathematically proven that no such crystal could be created such that the system is in equilibrium. Nevertheless, this left the door open for the fabrication of “non-equilibrium” matter, a phase of matter in which atoms cannot arrange themselves to form a motionless arrangement.4

Perhaps unsurprisingly, it can be quite difficult to experimentally create such a form of matter. In late 2016, however, two different groups managed to create a non-equilibrium time crystal using two distinct approaches. At the University of Maryland,a team led by Christopher Monroe arranged ten ytterbium ions with interacting electron spins as the basis for the time crystal.5 They repeatedly applied two laser pulses, one to induce a magnetic field and the other to partially adjust the atomic spins. The team soon found that the spins flipped in a stable and repeating pattern, and furthermore observed that the system was independent of the frequency of the laser pulses. At Harvard University, a team under Mikhail Lukin and Eugene Demler constructed a time crystal using a diamond embedded with millions of point defects known as nitrogen-vacancy (NV) centers. The team applied microwave pulses to draw the NV center spins out of equilibrium, and similarly observed that the spins flipped at a precise and repeating interval.6

These non-equilibrium time crystals do not exactly correspond to the initial idea proposed by Wilczek, but they feature a host of interesting physical properties and potential applications. The form of non-equilibrium matter seen in a time crystal defies our expectations for a system thrust out of equilibrium. We would typically expect such a system to heat up and approach an increasingly chaotic state. Time crystals demonstrate that this need not be the case. Instead, we can construct excited non-equilibrium systems which do not absorb energy.

In a more practical sense, time crystals constitute an important step towards quantum computing technology. Researchers working on quantum memory devices have long faced difficulties in combining a high density of quantum bits with a long quantum memory time, but time crystals attain both these important properties.7

Once expected to be a physical impossibility, time crystals continue to defy our intuition of the structure of matter on small scales. Much work remains in the exploration of this exciting phenomenon, which promises many rich insights in the realm of quantum theory and condensed matter physics.8

**Sources**

[1] http://news.berkeley.edu/2017/01/26/scientists-unveil-new-form-of-matter-time-crystals/

[2] https://www.space.com/38100-the-significance-of-time-crystals.html

[3] https://www.nature.com/news/the-quest-to-crystallize-time-1.21595

[4] https://phys.org/news/2017-04-physicists-crystals-key-quantum-machines.html#jCp

[5] https://phys.org/news/2017-01-physicists-unveil-mattertime-crystals.html

[6] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.010602

[7] http://www.nature.com.ezp-prod1.hul.harvard.edu/articles/nature21413.pdf

[8] http://www.lassp.cornell.edu/sethna/OrderParameters/BrokenSymmetry.html