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The Surprising Complexity in One Dimension

The Surprising Complexity in One Dimension

Two experiments test a 50-year-old theory on particles that move in a straight line.


Artist's rendering of methane molecules flowing through a carbon nanotube.

Image credits:

Lawrence Livermore National Laboratory

Monday, November 27, 2017 - 15:00

Yuen Yiu, Staff Writer

(Inside Science) -- Unlike one-dimensional personalities, one-dimensional materials are actually very complex -- so complex that scientists are still working to decipher their behaviors. In 1-D materials, particle movement is confined to a line. Two independent groups of researchers, one based in Australia and one in China, performed some of the first experiments to put a 50-year-old theory about such materials to the test.

Line 'em up!

During a now famous speech in 1959, Richard Feynman said that "there's plenty of room at the bottom," referring to the potential to further shrink technology. He was right. Since the '50s, the size of a transistor -- a basic building block for a computer -- has gone from the size of a light bulb to smaller than a strand of DNA.

"But you can only miniaturize a system so much before the wires become very thin, maybe even one-dimensional," said Thierry Giamarchi, a physicist from the University of Geneva in Switzerland not involved in either project. In order to design these systems, one must understand how they may behave differently.

"Imagine that you're in a room with other people. Sure, you may bump into another person, but nevertheless you can move around by just avoiding other people," said Giamarchi. "Now imagine being in a queue for seeing a movie -- you simply cannot move unless the whole line is also moving."

Around the same time Feynman was giving his speech, physicists Shin'ichiro Tomonaga and Joaquin Mazdak Luttinger worked out a theory that can predict the behavior of a completely 1-D liquid. Many aspects of the theory, now known as the Tomonaga-Luttinger liquid model, still haven't been proven experimentally due to technological limitations. But this is quickly changing.

A chain of islands

With the rise of nanotechnology, scientists and engineers are racing to learn how miniaturization can transform a device's various properties. One such device is the Josephson junction, which is somewhat like the electrical energy storing component called a capacitor, but with a dose of spooky quantum magic.

Josephson junctions are already widely used for applications such as magnetic sensing, but they have recently garnered extra attention due to the emergence of another technology.

"The big news these days is using it to make superconducting qubits for quantum computers," said Timothy Duty, a physicist from the University of New South Wales in Australia.

A single Josephson junction is composed of two layers of superconductor -- where electron pairs can move around with zero resistance -- separated by an insulating barrier. Depending on a number of conditions, electrons can sometimes "teleport" across the insulating barrier due to an effect known as quantum tunneling.

Each junction is smaller than a speck of dust. By chaining thousands of them together, Duty and his team created a system that acts more or less one dimensionally and could be described with the Tomonaga-Luttinger liquid model. They studied the effect of disorder in the system -- disorder rooted in the physical imperfections and irregularities in the chain of junctions.

They found that depending on the interaction strength between the electron pairs, the chain sometimes acts like a superconductor and at other times like an insulator. They also found that the sweet spot where superconductivity exists depends on the relative amount of the electron pair interactions and the disorder present in the system -- if either one is too large or too little relative to each other, the chain becomes an insulator.

The results, published in a paper in the journal Physical Review Letters, agree with what the 50-year-old theory predicts.

"There were other beautiful experiments done in the mid ‘90s with similar ideas," said Giamarchi. "But this is the first paper that is able to quantitatively answer these questions."

While the Australian group focused on the behavior of electrons inside a chain of quantum islands, a group of researchers from the Hefei National Laboratory for Physical Sciences at the Microscale in China took a slightly different approach to make their line of atoms: They used lasers.

A sliced-up pancake

Using optical techniques, the researchers from China created a pancake-shaped "trap" that can suspend in mid-air about 200,000 rubidium atoms -- less than one-trillionth the number of atoms in a grain of salt. They then deployed a second laser to slice up this pancake of atoms into thin, individual lines, while keeping the levitating atoms colder than a chilling 0.1 microkelvin -- more than a million times colder than the background temperature of the universe. These feats are why scientists didn't do these experiments decades before.

Finally, the researchers used yet another laser to "pluck out" the atoms near the middle of one of the lines, and observed how fast the disturbance can ripple through the rest of the line. Imagine a grocery store checkout line where a few customers in the middle got frustrated and left. What the researchers were trying to do is learn how the rest of the queue adjusts to the newly opened space.

Again, the 50-year-old theory by Tomonaga and Luttinger has a prediction for this, and for the first time the prediction has been experimentally verified.

"The fact that we both studied the same theory but looked at different aspects of it with two completely different physical systems shows why this particular theory is so important," said Duty.

According to Zhen-Sheng Yuan, one of the authors of the optical trapping paper, their revelation goes beyond what the experiment directly shows. With more aspects of the theory now backed up by experiments, scientists can use the general theory with newfound confidence, whether they are studying electrons in a carbon nanotube or qubits along a quantum highway.

"This is the beauty of nature," wrote Yuan in an email, "that the collective behavior of 1-D systems is universal regardless of what kind of particle is in the system."

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Yuen Yiu covers the Physics beat for Inside Science. He's a Ph.D. physicist and fluent in Cantonese and Mandarin. Follow Yuen on Twitter: @fromyiutoyou.