# This quantum machine seems to contradict the universe’s desire for disorder.

- Transfer

### One of the first quantum simulators demonstrated a mysterious phenomenon: a series of atoms that periodically returns to an ordered state. Racing physicists are trying to explain what is happening.

*Melting ice cream is not subject to spontaneous freezing. However, one of the quantum simulators constantly returns to an ordered state after the system reaches equilibrium.*

Enough time will pass, and even in the most tidy room there will be a mess. Clothing, books and papers will leave their orderly state and scatter across the floor. And, annoyingly, this tendency toward disorder reflects a law of nature: disorder tends to grow.

If, for example, you open the diver’s balloon under pressure, the air molecules inside it will fly out and scatter around the room. Place an ice cube in hot water, and the water molecules frozen in an ordered crystal lattice will break their bonds and disperse. When mixed and distributed, the system tends to equilibrium with the environment, which is called thermalization.

This is a common and intuitive effect that was expected by physicists to line up 51 rubidium atoms in a row and hold them in place with lasers. Atoms began with an ordered structure, and switched between the "ground" state with minimal energy and the excited state. Researchers have suggested that this system quickly becomes thermalized: the alternation of the ground and excited states will calm down almost immediately in the form of some random sequence.

At first, the sequences did get messy. But then, to the scientists ’surprise, they returned to their original alternating sequence. After additional mixing, the atoms returned to their original configuration. The states alternated back and forth with a frequency several times per microsecond - long after the system had to be thermalized.

It all looked like you dropped an ice cube into hot water, and it didn't just melt, said Mikhail Lukin , a physicist at Harvard University and the leader of a group of scientists. “We see the ice melt and then crystallize, then melt, and crystallize again,” he said. “This is something very unusual.”

Physicists have called this strange behavior "multi-particle quantum scarring." Atoms, apparently, bear the imprint of the past, as if some kind of scar, which makes them return to the original configuration again and again.

In the 16 months since the publication of the work in the journal Nature, several groups of physicists tried to understand the nature of these quantum scars. Some believe that this discovery may open up a new category of interaction and behavior of quantum particles, denying the assumptions of physicists that such a system is inexorably moving toward thermalization. In addition, the scarring effect can lead to the creation of new types of quantum bits of long-term storage, which are the key ingredients of future quantum computers.

## Overcoming zero probability

Physicists, in fact, when constructing a system of 51 atoms, they had in mind quantum calculations. This system was conceived as a quantum simulator, a machine designed to simulate quantum processes that cannot be investigated by other methods using a classical computer. At one time, this system was the largest quantum simulator of all.

Atoms of the Harvard machine serve as qubits, and their states, basic or excited, are called Rydberg states . Researchers can adjust the system by changing, for example, the strength of the interaction of atoms with each other.

Researchers have prepared several initial sequences of the ground and excited states of atoms. Since atoms actively interact with each other, they must come to thermalization. But instead of interactions resembling molecules in a gas, atoms in such a quantum system produce a kind of deep quantum bond, known as entanglement. “And then the confusion spreads,” Lukin said. “That's how thermalization happens.”

*Mikhail Lukin*

And usually the complexity in the simulator grew. However, when the researchers launched the experiment, arranging the atoms in a sequence of alternating excited and ground states, the particles first became entangled, and then lost it, oscillating back and forth from the original configuration.

Such behavior seemed unlikely, on the verge of impossible. After the atoms begin to interact, their alternating sequence should be forgotten very quickly, since atoms can go into a huge number of possible sequences of excited and ground states. This is similar to the example with a cylinder, air molecules from which leave the original configuration and propagate around the room. For their distribution, there are a huge number of places, so the likelihood that they all accidentally squeezed back into the container is practically zero.

“A quantum system can exist in so many possible states that it would be extremely difficult for it to return to the original,” said Zlatko Papich , a physicist at the University of Leeds in England.

However, Lukin says that this is what they have observed. The system is endowed with some kind of special physics, allowing it to go back along its own path, said Papich. “She leaves behind a trail of breadcrumbs, and returns to the beginning of the path.”

“This is the first real discovery made with a quantum machine,” Lukin said.

Lukin and colleagues began to describe the experiment, but before the publication of the work, Lukin described it at a conference in the Italian Trieste in July 2017. “We did not know how to understand this,” said Papich, who was in the audience that day. “I don’t think any of those present had ideas to explain the reasons for this.”

## Scars in the stadium

Soon, however, Papich and colleagues realized that such behavior resembles a phenomenon discovered about 30 years ago. In the 1980s, physicist Eric Geller of Harvard studied quantum chaos: what would happen if quantum mechanics were applied to chaotic systems? In particular, Geller examined the bounce of balls inside the " Bunimovich Stadium " - a rectangular table with rounded corners. The system is chaotic; for a sufficiently long time, the ball will pass along all possible trajectories inside the stadium . But if you launch the ball at a certain angle, it will forever follow the same path.

In a thought experiment, Geller replaced the ball with a quantum particle. "The naive expectation is that if our classical system is already chaotic," said Papich, then after adding the rules of quantum mechanics, "one should expect even more chaotic behavior." The wave function of a particle - an abstract mathematical package of its quantum properties - must be smeared around the stadium, as the waves propagate through the pond. The probability of finding a particle in a specific place in the stadium should be equal for all of its points.

*A particle placed on a Bunimovich stadium can show scars, trajectories where the probability of its detection is high*

However, Geller found that the wave function does not spread evenly, but accumulates on paths repeating the trajectory of the classical example, along which the ball moves endlessly. As if the waves generate a memory of this particular trajectory. “It's like a way home for the waves,” Geller said. “They want to return to their place of birth.” So simple. ”

Being on this trajectory, the particle wave function constructively interferes with itself, adding peaks to peaks, and dips to dips. As a result, the particle is most likely to be somewhere along the way. On the graph, the probability distribution resembles a blurry version of classical periodic trajectories. “They seem like scars to me,” Geller said. Therefore, in his work in 1984, he called them that.

Perhaps a similar phenomenon can be explained by the fact that a system of 51 atoms is returning to its original configuration, Papich thought. Perhaps she also misses the house.

## Scar leaving incision

To find out, Papich and colleagues analyzed the quantum states of the 51-atom system model. They found that her strange oscillatory behavior really resembled Geller’s quantum scarring. They identified conditions that resembled those special cases that corresponded to the trajectories of the scars. By periodically returning to these states, the system could avoid thermalization. The connection with quantum scarring was strong enough so that in their last year’s work published in the journal Nature Physics, they called this phenomenon “multiparticle quantum scarring”.

Despite the initial skepticism caused by the analysis of Papich, Lukin, as well as Wen Wei Ho, a Harvard physicist, and others established a stronger connection with quantum scarring in a paper published in January. They determined a classical way of describing the state of a 51-atomic system as a point in abstract space. With a change in the state of the system, a point moves in space. The researchers found that when the system experiences its own strange vibrations, the point dangles back and forth like a ball on a special periodic trajectory laid along the stadium billiard table.

*An experimental setup in which researchers created a quantum simulator*

Having found a classical analogy, the researchers reinforced the claim that the phenomenon of one Heller particle is applicable to a many-particle system. “These guys obviously found something,” Geller said. “Definitely.”

One thing is clear - this experiment aroused the interest of researchers from around the world. One group from the California Institute of Technology has identified mathematical expressions for some of the special states of the 51-atom system. Another, from Princeton, suggested that scars could be part of a more general phenomenon applicable in various fields of condensed matter physics. “We think we seem to understand what is happening in this system,” Ho said. “However, we still do not have a generalized method for searching for other trajectories-scars.”

Deeper questions remain. “Scars are a useful description of the problem,” said Vedika Kemani., a Harvard physicist unrelated to the experiment. “But I don’t think that we have a real understanding of what leads to their appearance.”

## Structure in randomness

Despite all these unknowns, many-particle scarring is of great interest to physicists, since it can represent a new class of quantum systems.

Over the past few years, physicists have studied another similar class, multi-particle localization, in which random flaws prevent thermalization of the system. As an analogy, imagine a herd of cows walking on a flat field. Cows eventually have to scatter in different places - let's call it cow thermalization. But if random hills meet on the field, the cows will end up in lowlands.

Similarly, the many-particle quantum scars system is not a chaotic system that seeks to thermalize. But there are no hills in it either. “This work speaks of the existence of a new class of systems located somewhere in between,” Papich said.

To explain the scarring effect, a new analysis by Kemani suggests that the 51-atom system can be an integrable system (or approach one). This is a special, isolated case of a system with many limitations and features that are tuned to prevent its thermalization. So, if the scar system is integrable, it may turn out to be a unique case in a wider class of phenomena.

Physicists have been studying integrable systems for decades, and if the system turns out to be integrable, said Papich, then the consequences of this fact will not be as interesting as if this quantum system would be unique. Papich, Ho, and Lukin wrote a paper arguing against this possibility.

But regardless of whether scarring turns out to be a new class of quantum behavior, this discovery points to the tempting possibility of improving quantum computers. One of the problems of creating a quantum computer is the need to protect its fragile qubits. Any disturbance or disturbance from the environment can cause qubits to thermalize and erase any information stored in them, which will make the computer useless. “If we can find a common way to introduce scarring into other systems, we may be able to protect quantum information for a long time,” Ho said.

Scarring can then give the computer a way to hold onto the stored data, protecting the past from the erasing chaos of thermalization.

“There is some beautiful structure, somehow preserved in a completely random environment,” said Papich. - What physics allows this process to work? "This is a deep and multifaceted issue, covering many areas of physics, and this effect is one of its manifestations."