Japanese and U.S. physicists have used atoms about 3 billion times colder than interstellar space to open a portal to an unexplored realm of quantum magnetism.

“Unless an alien civilization is doing experiments like these right now, anytime this experiment is running at Kyoto University it is making the coldest fermions in the universe,” said Kaden Hazzard, associate professor of physics and astronomy at Rice University and corresponding theory author of a study published Sept. 1 in Nature 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, atoms of ytterbium, within about one-billionth of a degree of absolute zero, the unattainable temperature where all motion stops. That’s about 3 billion times colder than interstellar space, which is still warmed by the afterglow from the Big Bang.

At such low temperatures, quantum behavior starts to emerge in larger and larger collections of matter, beyond individual electrons and photons.

“The payoff of getting this cold is that the physics really changes,” Hazzard said. “The physics starts to become more quantum mechanical, and it lets you see new phenomena.”

Physicists have used laser cooling to study the quantum properties of ultracold atoms for more than a quarter century. Lasers are used to both cool the atoms and restrict their movements to optical lattices, one, two or three dimensional channels of light that can serve as quantum simulators capable of solving complex problems beyond the reach of conventional computers.

Cooling matter to these unprecedented low temperatures allows experimental observations, initially benchmarked against calculations, to be extended to regimes that can't be modeled on a computer, said Richard Scalettar, distinguished professor in the Department of Physics and Astronomy at UC Davis and a coauthor on the paper.

A Hubbard model of collective behavior

Takahashi’s lab used optical lattices to simulate a quantum model called a Hubbard model. Physicists use Hubbard models to investigate the magnetic and superconducting behavior of materials, especially those where interactions between electrons produce collective behavior, somewhat like the collective interactions of cheering sports fans who perform “the wave” in crowded stadiums.

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

Electrons in solids can come in different ‘flavors,’ Scalettar said. They have two possible directions for their "spin" (the way they rotate about their axes) and they also can occupy different atomic orbitals (energy bands). But in almost all situations in solid state physics, these flavors each have different energy, that is, the flavors are not equivalent, he said.

“What is unique about this new work is that the (cold atom) experimentalists have found a way to build a system of quantum particles with N=6 flavors which are completely symmetric. This leads to beautiful and novel states of quantum matter when the atoms are cooled," Scalettar said.

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

“One of the fascinating questions that experiments can explore is the role of symmetry,” Ibarra-García-Padilla said. “To have the capability to engineer it in a laboratory is extraordinary. If we can understand this, it may guide us to making real materials with new, desired properties.”

Takahashi’s team showed it could trap up to 300,000 atoms in its three dimensional lattice. Hazzard said accurately calculating the behavior of even a dozen particles in an SU(6) Hubbard model is beyond the reach of the most powerful supercomputers. The Kyoto experiments offer physicists a chance to learn how these complex quantum systems operate by watching them in action.

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

“Right now this coordination is short-ranged, but as the particles are cooled even further, subtler and more exotic phases of matter can appear,” he said. “One of the interesting things about some of these exotic phases is that they are not ordered in an obvious pattern, and they are also not 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 don’t 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 Kyoto team’s success will spur those efforts.

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

An open source software package for determinant quantum Monte Carlo (DQMC) was one of the primary theory tools used in the study. The software resulted from work by Scalettar and Professor Zhaojun Bai, UC Davis Department of Computer Science. Ibarra-García-Padilla will join UC Davis this Fall as a postdoctoral researcher.

Other co-authors include Shintaro Taie, Naoki Nishizawa and Yosuke Takasu of Kyoto, Hao-Tian Wei of both Rice and Fudan University in Shanghai and Yoshihito Kuno of the University of Tsukuba in Ibaraki, Japan.

The research was supported in part by the Welch Foundation and the National Science Foundation.