SU(N) matter is about 3 billion times colder than deep space

Japanese and American physicists have used atoms about 3 billion times cooler than interstellar space to open a portal to an uncharted realm of quantum magnetism.

“Unless an extraterrestrial civilization is doing experiments like these right now, every time this experiment happens at Kyoto University, they’re making the coldest fermions in the universe,” Kaden said. Hazzard of Rice University, corresponding theoretical author of a study published today in Natural Physics. “Fermions are not rare particles. They include things like electrons and are one of two types of particles that all matter is made of.”

A Kyoto team led by study author Yoshiro Takahashi used lasers to cool its fermions, ytterbium atoms, to about a billionth of a degree absolute zero, the inaccessible temperature where all movement stops. It’s about 3 billion times colder than interstellar spacewhich is still warmed by the afterglow of the Big Bang.

“The payoff of having that cold is that the physics really change,” Hazzard said. “Physics is starting to get more quantum mechanical, and it’s letting you see new phenomena.”

Atoms are subject to the laws of quantum dynamics, just like electrons and photons, but their quantum behaviors only become evident when cooled to a fraction of a degree near absolute zero. Physicists have used laser cooling to study the quantum properties of ultracold atoms for more than a quarter of a century. Lasers are used to both cool atoms and limit their motion to optical gratings, 1D, 2D or 3D light channels that can serve as quantum simulators capable of solving complex problems beyond the reach of conventional computers.

Takahashi’s lab used optical gratings to simulate a Hubbard Model, an oft-used quantum model created in 1963 by theoretical physicist John Hubbard. Physicists use Hubbard’s models to study the magnetic and superconducting behavior of materials, especially those where interactions between electrons produce collective behavior, much like the collective interactions of enthusiastic sports fans who run “the wave” in crowded stadiums.

“The thermometer they’re using in Kyoto is one of the important things that our theory provides,” said Hazzard, an associate professor of physics and astronomy and a member of the Rice Quantum Initiative. “By comparing their measurements to our calculations, we can determine the temperature. The record temperature is reached thanks to some fun new physics related to the very high symmetry of the system.”

The Hubbard model simulated in Kyoto has a special symmetry known as SU(N), where SU stands for special unitary group – a mathematical way of describing symmetry – and N denotes the possible spin states of the particles in the model. The larger the value of N, the greater the symmetry of the model and the complexity of the magnetic behaviors it describes. Ytterbium atoms have six possible spin states, and the Kyoto simulator is the first to reveal magnetic correlations in a Hubbard SU(6) model that are impossible to calculate on a computer.

“That’s the real reason to do this experiment,” Hazzard said. “Because we are dying to know the physics of this SU(N) Hubbard model.”

Study co-author Eduardo Ibarra-García-Padilla, a graduate student in Hazzard’s research group, said the Hubbard model aims to capture the minimum ingredients for understanding why solid materials become metals, insulators, magnets or superconductors.

“One of the fascinating questions that experiments can explore is the role of symmetry,” said Ibarra-García-Padilla. “Having the ability to design it in a lab is amazing. If we can understand that, it can guide us towards making real materials with new desired properties.”

Takahashi’s team has shown that he can trap up to 300,000 atoms in his 3D network. Hazzard said that the precise calculation of the behavior of a dozen particles in a Hubbard SU(6) model is beyond the reach of the most powerful supercomputers. The Kyoto experiments offer physicists a chance to learn how these complex quantum systems work by observing them in action.

The results are a major step in that direction and include the first observations of particle coordination in a Hubbard SU(6) model, Hazzard said.

“At the moment, this coordination is short-range, but as the particles are cooled even more, more subtle and exotic phases of matter may appear,” he said. “One of the interesting things about some of these exotic phases is that they’re not ordered in any obvious pattern, nor are they random. There are correlations, but if you look at two atoms and ask, “Are they correlated? you won’t see them. They are much more subtle. You can’t look at two or three or even 100 atoms. You kind of have to look at the whole system.

Physicists do not yet have tools capable of measuring such behavior in the Kyoto experiment. But Hazzard said work is already underway to create the tools, and the success of the Kyoto team will boost those efforts.

“These systems are quite exotic and special, but the hope is that by studying and understanding them, we can identify the key ingredients that must be present in real materials,” he said.