Here at the Greiner Lab, we study ultracold gases that are put into artificial crystals of light called optical lattices. The atoms in the optical lattice end up behaving like electrons in a solid. That means we can use these atoms to simulate models from condensed matter physics in a highly controlled environment.

We have developed a microscopy technique that lets us image atoms in optical lattices with submicron optical resolution, so we can see and manipulate individual atoms. This technique gives us unprecedented understanding of the quantum states we create, and lets us perform experiments with remarkable levels of control and accuracy.

# News

##### Microscopy of the interacting Harper-Hofstadter model in the two-body limit

The interplay between magnetic fields and interacting particles can lead to exotic phases of matter that exhibit topological order and high degrees of spatial entanglement. Although these phases were discovered in a solid-state setting, recent innovations in systems of ultracold neutral atoms - uncharged atoms that do not naturally experience a Lorentz force - allow the synthesis of artificial magnetic, or gauge, fields. This experimental platform holds promise for exploring exotic physics in fractional quantum Hall systems, owing to the microscopic control and precision that is achievable in cold-atom systems. However, so far these experiments have mostly explored the regime of weak interactions, which precludes access to correlated many-body states. Here, through microscopic atomic control and detection, we demonstrate the controlled incorporation of strong interactions into a two-body system with a chiral band structure.

##### A cold-atom Fermi-Hubbard antiferromagnet
A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanasz-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, M. Greiner

Many exotic phenomena in strongly correlated electron systems emerge from the interplay between spin ordering and motional degrees of freedom. For example, doping an antiferromagnet is expected to give rise to interesting phases including pseudogap states, stripe-ordering and incommensurate spin order. Ultracold fermions in optical lattices offer the potential to answer open questions on the low-temperature regime of the doped Hubbard model, which is thought to capture essential aspects of the cuprate superconductor phase diagram but is numerically intractable in that parameter regime.

##### Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model

Exotic phases of matter can emerge from strong correlations in quantum many-body systems. Quantum gas microscopy affords the opportunity to study these correlations with unprecedented detail. Here, we report site-resolved observations of antiferromagnetic correlations in a two-dimensional, Hubbard-regime optical lattice and demonstrate the ability to measure the spin-correlation function over any distance. We measure the in situ distributions of the particle density and magnetic correlations, extract thermodynamic quantities from comparisons to theory, and observe statistically significant correlations over three lattice sites. The temperatures that we reach approach the limits of available numerical simulations. The direct access to many-body physics at the single-particle level demonstrated by our results will further our understanding of how the interplay of motion and magnetism gives rise to new states of matter.

##### Quantum thermalization through entanglement in an isolated many-body system

Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrdinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis.

##### Ultra-precise holographic beam shaping for microscopic quantum control

High-resolution addressing of individual ultracold atoms, trapped ions or solid state emitters allows for exquisite control in quantum optics experiments. This becomes possible through large aperture magnifying optics that project microscopic light patterns with diffraction limited performance. We use programmable amplitude holograms generated on a digital micromirror device to create arbitrary microscopic beam shapes with full phase and amplitude control. The system self-corrects for aberrations of up to several $\lambda$ and reduces them to $\lambda/50$, leading to light patterns with a precision on the $10^{−4}$ level. We demonstrate aberration-compensated beam shaping in an optical lattice experiment and perform single-site addressing in a quantum gas microscope for $^{87}\mathrm{Rb}$.