A universal quantum computer—capable of crunching the numbers of any complex problem posed to it—is still a work in progress. But for specific problems in quantum physics, there’s a more direct approach to quantum simulation: Design a system that captures the physics you want to study, and then watch what it does. One of the systems most widely studied that way is the Fermi–Hubbard model (FHM), in which spin-up and spin-down fermions can hop among discrete sites in a lattice. Originally conceived as a stripped-down description of electrons in a solid, the FHM has attracted attention for its possible connection to the mysterious physics of high-temperature superconductivity.
Stripped down though it may be, the FHM defies solution, either analytical or numerical, except in the simplest cases, so researchers have taken to studying it experimentally. In 2017 Harvard University’s Markus Greiner and colleagues made a splash when they observed antiferromagnetic order—a checkerboard pattern of up and down spins—in their FHM experiment consisting of fermionic atoms in a 2D lattice of 80 optical traps. (See Physics Today, August 2017, page 17.) The high-temperature-superconductor phase diagram has an antiferromagnetic phase near the superconducting one, so the achievement promised more exciting results to come. But the small size of the experiment limited the observations the researchers could make.
Now researchers in Jian-Wei Pan’s group, including Xing-Can Yao and Yu-Ao Chen, at the University of Science and Technology of China have observed antiferromagnetism in a vastly expanded FHM system. Instead of two dimensions, their lattice has three, and instead of 80 sites, it has 800 000. As a result, they could quantitatively study the antiferromagnetic phase transition (which doesn’t even exist in two dimensions) and measure its critical exponents, key indicators of a system’s underlying physics.
Engineering such a large lattice was an experimental challenge. The standard way to make an array of optical traps is with pairs of counterpropagating laser beams. But laser beams typically have Gaussian intensity profiles, so the atoms at the center of the lattice experience brighter light—and may as a result be in a completely different phase—than those at the edges. Pan and colleagues designed custom optical elements to give their beams a uniform intensity profile over a region 50 µm (almost 100 lattice sites) in diameter.
By varying several different experimental parameters, the researchers tuned their system into and out of the antiferromagnetic phase. In every case, the quantified spin order followed a power law with an exponent of 1.396. That’s the value they expected—the same exponent is observed in the 3D Heisenberg model—but it had never been measured before in the FHM. With their experimental platform thus validated, they plan to explore other parts of the phase diagram in search of the elusive superconducting phase. (H.-J. Shao et al., Nature, 2024, doi:10.1038/s41586-024-07689-2.)
