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Time Crystals
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Time Crystals, a new form of matter that plays with time

Time crystals take the idea of crystals and apply it to time – in a pretty interesting way

Fancy theories are commonplace in physics, but when a Nobel Laureate comes up with one, they are taken seriously. In 2012, Nobel Laureate Frank Wilczek hypothesised the existence of a type of material called ‘time crystals’. Initially, they seemed to defy the laws of physics. Recently, these mysterious time crystals have been constructed in a laboratory – giving creedence to Wilczek’s bizarre proposition. In this article, we break down time crystals – why are they weird, how were they created and what can they mean for the future of physics?

When it comes to the laws of physics, symmetry is sacrosanct. Laws of physics are ‘spatially’ symmetric, as in no position in space is more favoured than the other. What if these symmetries are broken? Indeed, spatial symmetry breaking does happen often in nature. The gravitational force that binds the earth in orbit around the sun is spherically symmetric – not having any directional dependency, depending only on the distance between the two bodies. The motion resulting from this force, however, breaks symmetry by executing elliptical orbits which aren’t symmetric about its axes, unlike a sphere. This is an example of symmetry breaking in an ‘excited’ state of energy. More interesting is the case of symmetry breaking in the ground (lowest energy) state of the system, and this happens in the case of crystals. Crystals, like diamond, have lattice structures which repeat in space. They show discrete symmetry and periodicity which violates the above equivalence of space principle accorded by spatial symmetry. Now, the laws of physics are also symmetric in time, which disallow stable objects to change form over time. Thanks to Einstein and co-workers, we are used to unifying space and time into a single four-dimensional space. So, if spatial symmetry can be broken, can there be cases where temporal symmetry breaks?

Diamond
Visualization of diamonds lattice. Repeating structures are clearly visible

Time crystals do exactly that. The molecular structure of a crystal forms a pattern in space by repeating itself over regular intervals. The same way, time crystals ‘repeat’ structures over time intervals. What does time symmetry breaking mean? How does it manifest itself? Think of a body attached to a perfect spring dangling in frictionless air. If we perturb this system by slightly pulling the string, the body will execute a periodic motion in time, returning to its original position regularly. If drag was there, this periodic motion would die down and the body would come to rest. This periodicity in time is nothing special and plenty of systems execute such motion. Periodic motion is not symmetric in time, but such a motion does not count as time symmetry breaking. This is because most periodic motions are associated with some inherent energy. When we perturbed the spring by tugging at, we gave it some potential energy, which keeps getting converted into energy of motion and vice versa, keeping the system in a state of constant energy. Would the block do the same motion without the initial tug? Can a system have time periodicity in a state of zero or lowest energy? The answer is yes. When there is a time repeating pattern in the system at ground state – it indicates the breakdown of time symmetry. Time crystals keep oscillating in time and here’s the clincher. The oscillation occurs without any energy.

Imagine a collection of ions arranged in the form of a ring. If we cool them down to a temperature close to absolute zero, the ion system reaches its ground state – a state of equilibrium. Intuitively, one would imagine that this system doesn’t show any motion, similar to how the block and spring system wouldn’t in the absence of disturbance. Although, if we throw in time symmetry breakdown into the mix something weird can happen. The ions can start rotating in the ring in a perpetual circling motion. The breakdown of spatial symmetry manifested into a repeated pattern in space for crystals. Similarly, a time symmetry breakdown would create periodicity of motion in time. While this might sound like a perpetual motion machine, it really isn’t. In this case, the ions do move around in a loop, perpetually, but this movement doesn’t extract any energy from the system even in the ground state. The formidable law of conservation of energy also states that since there is no usage of energy there is also no energy available to extract for work. This ring-shaped crystal arrangement was one of the first feasible experiments postulated to create time crystals and was published along with Wilczek’s original paper in 2012. The method works in theory, but there are some practical difficulties.

Nobel Laureate Frank Wilczek
Nobel Laureate Frank Wilczek who first came up with the idea of time crystals

For one, quantum systems in equilibrium show no dependency on time and thus it is impossible for them to show any periodicity as well. To get around this, it was suggested that time crystals be created in a ‘non-equilibrium’ state, where a system is constantly driven by some periodic source. To keep the system from absorbing energy from this source, the constituent ions in the system had to be controlled such that they remain localised and not smeared out as the laws of probability for quantum particles dictate. A recipe based on the above considerations was suggested last year and two teams independently followed it to create a time crystal in the lab.

One of the teams from the University of Maryland used an array of ten ions and electrons with spins. Then they bombarded the system with two laser pulses timed with precision. One pulse created a magnetic field and the other flipped the electron spins. Because the system of electrons is interacting and spins are in a quantum entanglement (to put it simply: a change in one spin affects the other), this system settles into a state where the spins change periodically in space. This results in the spontaneous breaking of the spatial symmetry. As a simple picture, imagine a row with ten seats. The person on the first seat faces the movie screen, and the adjacent one faces away. This arrangement has the sort of repeating quality common to a crystal in ground state. Now after a time period, this arrangement switches and each individual changes the direction he is facing. After another interval, the system reaches back to its first state again. This signifies breakdown of time symmetry. Not only does the ion system behave like a crystal in space, but also oscillates back and forth in arrangements, in time. What is even more surprising is that if the period of the laser pulse driving is T, the arrangement of spins in the ions oscillates in time with a period of 2T – a behaviour that is impossible to occur in a normal system. Furthermore, on changing parameters of the driving pulse, the system remains in time oscillations with period 2T. Since there is no driving force with period 2T, the only way the ions could oscillate with that period is by breaking time symmetry. Voila, a time crystal!

Time Crystal meme

Technicality is too damn high

This might sound like technical gibberish but it’s a huge experimental achievement. What scientists have demonstrated is the existence of a new phase of matter, one that is never in equilibrium. A ground state of energy, carrying out a perpetual oscillation was believed to be impossible. How can a system move back and forth without using up energy? Until now, no one had broken the old guard of time symmetry. Now that it has been done, it opens the doors to some new, radical research. For instance, devices operating at the quantum level have a lifetime limit due to a phenomenon known as ‘decoherence’. This phenomenon is responsible for bringing a quantum system back to a classical state – where it is ruled by the laws of classical mechanics. For quantum computing devices, this is an undesirable effect.

D-Wave
A chip used in D-Wave’s Quantum Computer

Time crystals can potentially lead to devices that are stable against such effects, enabling better memory and computing devices for quantum computing applications. At a more fundamental level, since time crystals are an example of never seen before time symmetry breakdown, an experimental realisation is likely to provide scientists with access to states of matter that could only be theoretically possible in such systems. The fact that time crystals present a time based analogue to ordinary crystals that exhibit spatial symmetry breaking, indicates that maybe time as a concept must be unified with the fabric of space, something that current quantum mechanics doesn’t feature. In conclusion, we are at the cusp of some great discoveries which in the long run can alter our understanding of not only the standard states of matter but the fundamental concept of time itself.

This article was first published in March 2017 issue of Digit magazine. To read Digit’s articles first, subscribe here or download the Digit e-magazine app for Android and iOS. You could also buy Digit’s previous issues here.

Ronak Gupta