High-temperature superconductors have a shadow state that has haunted condensed matter physics for decades. Cool a cuprate material and, before it becomes superconducting, it passes through a strange phase where the material behaves like a metal but with something missing: a gap in its low-energy excitations that should not be there. This pseudogap phase has been inferred, debated, and modeled for thirty years, but always indirectly, because the real materials are too complex to control.
A Harvard team has now reproduced that state atom by atom. In Nature, researchers led by Markus Greiner report the first experimental characterization of the pseudogap metal in the Fermi-Hubbard model, the minimalist theoretical description of interacting electrons on a lattice that underlies the physics of cuprates. They built it with ultracold atoms in an optical lattice, a quantum gas microscope that lets them place, image, and manipulate individual atoms, and cooled the system enough to watch the pseudogap appear.
The experiment
The Fermi-Hubbard model describes electrons hopping between lattice sites with an interaction energy when two occupy the same site. Doped Mott insulators, the regime relevant to cuprates, have resisted experimental access because the temperatures required are extraordinarily low. A 2025 advance in cryogenic neutral-atom simulators gave the Harvard group the several-fold temperature reduction needed.
The team used thermodynamic and spectroscopic measurements on the cold-atom simulator. On cooling, the compressibility (how readily the system absorbs particles) developed a maximum at intermediate doping, an inflection point in the equation of state. Tracking that maximum across interaction strengths revealed a line of thermodynamic anomalies separating an underdoped from an overdoped metal at large interactions. Lattice modulation spectra in the underdoped regime showed a loss of low-energy response, especially in the antinodal regions of the Brillouin zone, the signature of a pseudogap. From this they constructed a pseudogap phase diagram across interactions and doping.
What the pseudogap is
In a normal metal, electrons at the Fermi surface can be excited with arbitrarily small energies. In the pseudogap phase, those low-energy excitations are partially suppressed, a gap that is not quite a full gap, hence the name. In cuprates, the pseudogap sits in the doping regime adjacent to high-temperature superconductivity, and understanding it has been considered central to explaining why these materials superconduct at temperatures no conventional theory predicts.
The Hubbard model is the minimal theory that captures this physics, and the cold-atom simulator now provides a direct experimental window into it. The measurements confirm the existence of the pseudogap metal in the model, characterize its location in the phase diagram, and suggest connections to charge order that can be studied in future work.
The significance
This is a case of quantum simulation delivering on its promise: using a controllable quantum system to answer questions about a less controllable one. The cold-atom platform cannot replicate the full complexity of a cuprate, it is a model system, not a material, but that is precisely the point. By isolating the Hubbard model’s behavior, the experiment tests whether the pseudogap is a feature of the model itself, and thus a genuine piece of the cuprate puzzle, or an artifact of real-material complications.
The team’s numerical comparisons (dynamical quantum Monte Carlo and exact diagonalization on small clusters) support the experimental results. The pseudogap appears in the model, in the right place, with the right spectroscopic signatures. The next questions are already visible: whether the pseudogap connects to charge order, and whether the same simulator can be pushed into the regime where superconductivity itself emerges. The pseudogap, long a shadow, now has a face.
Sources
- Kendrick, L.H., Kale, A., Gang, Y., Deters, A.D., Lebrat, M., Young, A.W., Greiner, M. “Pseudogap in a Fermi-Hubbard quantum simulator.” Nature (2026). DOI: 10.1038/s41586-026-10875-z
- Xu et al., Nature 642:909-915 (2025)