Ultracold fermions in an optical lattice realize the celebrated Fermi-Hubbard model, a simple Hamiltonian that is widely believed to describe the physics of high-temperature superconductivity. As this model is theoretically intractable, quantum simulation with ultracold atoms is one of the few pathways open to understanding its novel phases, which include a d-wave superconducting state that develops upon doping an antiferromagnetic Mott insulator, a pseudogap regime which shows spectral remnants of the superconducting gap in the normal state, and a strange metal regime with anomalous transport coefficients. Our research goal is to develop new tools which are suitable for studying these various regimes. Previous experiments include exploring antiferromagnetic correlations with a strong magnetic field, studying charge-density wave correlations at finite doping, measuring the conductivity and charge diffusion constant in a strange metal regime, and developing an analog of angle-resolved photoemission spectroscopy (ARPES) which is compatible with our quantum gas microscope to probe pseudogap physics.

### Angle-resolved photoemission spectroscopy of a Fermi–Hubbard system

Brown, P., Guardado-Sanchez, E., Spar, B., Huang, E., Devereaux, T. & Bakr, W.

Nature Physics 16, 26-31 (2020)

Angle-resolved photoemission spectroscopy (ARPES) measures the single-particle excitations of a many-body quantum system with energy and momentum resolution, providing detailed information about strongly interacting materials. ARPES directly probes fermion pairing, and hence is a natural technique to study the development of superconductivity in systems ranging from high-temperature superconductors to unitary Fermi gases. In these systems, a remnant gap-like feature persists in the normal state. Developing a quantitative understanding of these so-called pseudogap regimes may elucidate details about the pairing mechanisms that lead to superconductivity, but this is difficult in real materials partly because the microscopic Hamiltonian is not known. Here, we report on the development of ARPES to study strongly interacting fermions in an optical lattice using a quantum gas microscope. We benchmark the technique by measuring the occupied single-particle spectral function of an attractive Fermi–Hubbard system across the BCS–BEC crossover and comparing the results to those of quantum Monte Carlo calculations. We find evidence for a pseudogap that opens well above the expected critical temperature for superfluidity. This technique may also be applied to the doped repulsive Hubbard model, which is expected to exhibit a pseudogap at temperatures close to those achieved in recent experiments.

### Bad metallic transport in a cold atom Fermi-Hubbard system

Brown, P., Mitra, D., Guardado-Sanchez, E., Nourafkan, R., Reymbaut, A., Hebert, C.-D., Bergeron, S., Tremblay, A. -M., Kokalj, J., Huse, D., Schauss, P. & Bakr, W.

Science 363, 379 (2019) [Selected for a “Science Perspective”]

Strong interactions in many-body quantum systems complicate the interpretation of charge transport in such materials. To shed light on this problem, we study transport in a clean quantum system: ultracold lithium-6 in a two-dimensional optical lattice, a testing ground for strong interaction physics in the Fermi-Hubbard model. We determine the diffusion constant by measuring the relaxation of an imposed density modulation and modeling its decay hydrodynamically. The diffusion constant is converted to a resistivity by using the Nernst-Einstein relation. That resistivity exhibits a linear temperature dependence and shows no evidence of saturation, two characteristic signatures of a bad metal. The techniques we developed in this study may be applied to measurements of other transport quantities, including the optical conductivity and thermopower.

### Quantum gas microscopy of an attractive Fermi-Hubbard system

Mitra, D., Brown, P., Guardado-Sanchez, E., Kondov, S., Devakul, T., Huse, D. Schauss, P. & Bakr, W.

Nature Physics 14, (2017)

The attractive Fermi–Hubbard model is the simplest theoretical model for studying pairing and superconductivity of fermions on a lattice. It exhibits many interesting features including a short-coherence length at intermediate coupling and a pseudogap regime with anomalous properties. Here we study an experimental realization of this model using a two-dimensional (2D) atomic Fermi gas in an optical lattice. Using a new technique for selective imaging of doublons with a quantum gas microscope, we observe chequerboard doublon density correlations in the normal state close to half-filling. With the aid of quantum Monte Carlo simulations, we show that the measured doublon density correlations allow us to put a lower bound on the strength of *s*-wave pairing correlations in our system. We compare the temperature sensitivity of the doublon density correlations and the paired atom fraction and find the correlations to be a much better thermometer. Accurate thermometry of attractive lattice systems will be essential in the quest for optimizing cooling schemes to reach superfluid phases in future experiments.

### Spin-imbalance in a 2D Fermi-Hubbard system

Brown, P., Mitra, D., Guardado-Sanchez, E., Schauss, P., Kondov, S., Khatami, E., Paiva, T., Trivedi, N., Huse, D. & Bakr, W.

Science 357, 1385 (2017)

The interplay of strong interactions and magnetic fields gives rise to unusual forms of superconductivity and magnetism in quantum many-body systems. Here, we present an experimental study of the two-dimensional Fermi-Hubbard model—a paradigm for strongly correlated fermions on a lattice—in the presence of a Zeeman field and varying doping. Using site-resolved measurements, we revealed anisotropic antiferromagnetic correlations, a precursor to long-range canted order. We observed nonmonotonic behavior of the local polarization with doping for strong interactions, which we attribute to the evolution from an antiferromagnetic insulator to a metallic phase. Our results pave the way to experimentally mapping the low-temperature phase diagram of the Fermi-Hubbard model as a function of both doping and spin polarization, for which many open questions remain.