Time Crystals, a Romance Until the End of the World

Author: Sun Xiaobiao

On March 2, Science Advances published an article: "Realization of a discrete time crystal on 57 qubits of a quantum computer". Philipp Frey and Stephan Rachel, physicists at the University of Melbourne, designed a 57-qubit time crystal on IBM's quantum computer.

In fact, in July 2021, Google and a group of scientists used their own Sycamore quantum processor to realize a 20-qubit time crystal and published the results in Nature. Philip Frey and Stephen Rachel made a major breakthrough based on Google's research results and designed the largest time crystal to date. The significance of this achievement is that it demonstrates the ability of quantum computers to simulate complex systems, allowing theoretical models that can only exist in the minds of physicists to be transformed into objective entities.

Figure | Google published its research results on time crystals in Nature (Source: nature.com)

What is a time crystal?

There is a beautiful poem in The Three-Body Problem: I held out a gift for her, a small piece of solidified time, with beautiful patterns on it, and it felt as soft as mud in a shallow sea. In science fiction works, time is a tangible entity, a gift given to lovers, which preserves the romance of two people, and this romance will not disappear until the end of the universe.

Time crystals are also called space-time crystals, which are four-dimensional crystals with periodic structures in space and time. In our daily life, we are exposed to three basic forms of matter: solid, liquid, and gas. However, with the development of science, the concept of material form has also been expanded, such as plasma, Bose-Einstein condensate, supercritical fluid, etc. Time crystals are a new form of matter and a non-equilibrium phase that breaks the time translation symmetry.

The concept of time crystals was first proposed by Frank Wilczek, a Nobel Prize winner in physics, in 2012. We are familiar with crystals in three-dimensional space, such as ice cubes and diamonds. Crystals are geometrically symmetrical structures in which microscopic particles are periodically arranged in space. When teaching students, Wilczek began to think about whether the concept of three-dimensional crystals could be extended to four-dimensional space-time, so that matter could be arranged periodically in the dimension of time. In other words, time crystals have different states at different times, and the change of this state is periodic. To give a common example, a time crystal may be white sugar in the first second, brown sugar in the second second, and white sugar again in the third second.

Image | Frank Wilczek (Source: frankawilczek.com)

Three-dimensional crystals have broken spatial translation symmetry. By analogy, time crystals should also have broken time translation symmetry. The so-called symmetry of space translation means that after a physical system is translated to any distance in a certain direction in space, the laws of physics will not change. In simple terms, the same experiment is performed in different places, and the results are the same. The symmetry of time translation is about the same experiment being performed at different times, and the results are the same.

Symmetry can be high or low, and a circle has higher symmetry than a rectangle. Liquid water is isotropic, while solid ice is anisotropic, so water has higher symmetry than ice. This process of going from high symmetry to low symmetry is called symmetry breaking. Three-dimensional crystals must move an integer number of lattice constants to have the same spatial structure, and space-time crystals must also take a specific amount of time to return to their initial state. In other words, what you see in odd seconds, such as the 1st, 3rd, and 5th, is white sugar, and what you see in even seconds, such as the 2nd, 4th, and 6th, is brown sugar. The difference between brown sugar and white sugar is the breaking of the time translation symmetry of the time crystal.

A new perpetual motion machine?

In 1918, German mathematician Emmy Noether proposed the Noether theorem, which is of great significance in physics, that is, every symmetry has a related conservation law, and vice versa. Spatial translation symmetry corresponds to momentum conservation, spatial rotation symmetry corresponds to angular momentum conservation, and time translation symmetry corresponds to energy conservation. Time crystals break time translation symmetry, but they do not violate the law of conservation of energy, because time crystals have neither energy input nor energy output.

(Source: Pixabay)

Time crystals are like clocks. After 60 seconds, the second hand will return to its original position and continue to cycle. However, the rotation of clock hands requires external energy input such as mechanical energy or electrical energy, while time crystals do not require external energy input because they are in the minimum energy ground state. This seems to be contradictory. Time crystals can achieve time translation symmetry breaking, which means that they keep changing their state over time, that is, they are in a state of constant motion. The continuous movement of an object means that it has additional energy dissipation until the energy is exhausted and it stops moving.

For general systems, the energy when moving is higher than when at rest; but for some special systems, the energy when moving is lower than when at rest. After energy dissipation, this system will eventually reach a ground state of continuous movement, which is called spontaneous symmetry breaking in time.

There is a classic example of spontaneous symmetry breaking: suppose there is a Mexican hat, and a small ball is stationary on the top of the hat. When the ball slides from the top of the hat to the brim, the probability of it falling in any direction is equal. At this time, the system has rotational symmetry. Once the ball falls, it will only fall in one direction, which destroys the original symmetry of the system. This kind of symmetry destruction is not determined by physical laws, but caused by the instability of the ball itself. This is spontaneous symmetry breaking.

Figure | Mexican hat (Source: Pixabay)

These properties of time crystals sound a bit like perpetual motion machines, but the movement of time crystals does not require external energy input, and its kinetic energy cannot be output for use, so time crystals are not perpetual motion machines. Since time crystals continue to move when they are in the ground state, they can be used to transmit information. When matter is at absolute zero, the surrounding matter is in a stationary ground state, while time crystals continue to move in a ground state with lower energy. Scientists have a very wonderful idea about this. When the universe continues to increase in entropy and eventually reaches a state of heat death, time crystals can still maintain movement because they are in a ground state with lower energy.

Realization of time crystals

Proposing a theoretical model of time crystals is one thing, and realizing it is another. The concept of time crystals has been questioned by many scientists, who believe that it is impossible. In 2016, Norman Yao of the University of California, Berkeley designed a detailed blueprint for making time crystals. Yao likened his blueprint to a bridge between theoretical models and experimental methods.

Figure | Norman Yao's paper on the method of manufacturing time crystals (Source: journals.aps.org)

Based on Yao's blueprint, two teams from the University of Maryland and Harvard University independently produced time crystals. The two teams used different methods but obtained similar results, which confirmed that time crystals are indeed a new state of matter.

It should be pointed out that time crystals are divided into continuous time crystals and discrete time crystals. The time crystals currently realized are all discrete time crystals. Continuous time crystals are difficult to realize and are still controversial.

Rachel's time crystal is not perfect. It can only last for 50 cycles. In the future, time crystals can be used in quantum computers as a storage method. Perhaps, although time crystals are not as sci-fi as the time gems in Marvel movies, they can be as romantic as the poem in "The Three-Body Problem": She painted time all over her body, then pulled me up and flew to the edge of existence.

For physicists, the discovery of time crystals is like the discovery of a new continent, but it is still unknown whether this new continent is fertile land or a desert.

It will take time to uncover the mystery of time crystals.

References:

[1]https://www.science.org/content/article/physicists-produce-biggest-time-crystal-yet

[2]https://www.scientificamerican.com/article/time-crystals-could-be-legitimate-form-perpetual-motion/

[3]https://www.sciencealert.com/scientists-have-just-announced-a-brand-new-form-of-matter-time-crystals

Source: Academic Headlines