Exploring the Hubbard Model With Ultracold Fermionic Atoms in an Optical Lattice

These lecture notes review recent progress in studying the Fermi-Hubbard model using ultracold gases in optical lattices. We focus on results from quantum gas microscope experiments that have allowed site-resolved measurements of charge and spin correlations in half-filled and doped Hubbard systems, as well as direct imaging of various types of polaronic quasiparticles. We also review experiments exploring dynamical properties of the Hubbard model through transport and spectroscopy. Moving beyond the plain-vanilla square-lattice Hubbard model, we present more recent work exploring Hubbard systems with novel lattice geometries and long-range interactions that stabilize new phases. Finally, we discuss the realization of entropy distribution protocols to cool these systems to ultralow temperatures where comparison to unbiased numerics is no longer possible.These lecture notes review recent progress in studying the Fermi-Hubbard model using ultracold gases in optical lattices. We focus on results from quantum gas microscope experiments that have allowed site-resolved measurements of charge and spin correlations in half-filled and doped Hubbard systems, as well as direct imaging of various types of polaronic quasiparticles. We also review experiments exploring dynamical properties of the Hubbard model through transport and spectroscopy. Moving beyond the plain-vanilla square-lattice Hubbard model, we present more recent work exploring Hubbard systems with novel lattice geometries and long-range interactions that stabilize new phases. Finally, we discuss the realization of entropy distribution protocols to cool these systems to ultralow temperatures where comparison to unbiased numerics is no longer possible.

arXiv:2507.04042Jul 5, 20250 citations

Fermi-Hubbard physics with ultracold fermions in optical lattices

Thomas Uehlinger, Daniel Greif, Gregor Jotzu +2 more

Bulletin of the American Physical SocietyJun 14, 20110 citations

Site-resolved observables in the doped spin-imbalanced triangular Hubbard model

Davis Garwood, Jirayu Mongkolkiattichai, Liyu Liu +2 more

The suppression of antiferromagnetic ordering in geometrically frustrated Hubbard models leads to a variety of exotic quantum phases including quantum spin liquids and chiral states. Here, we focus on the Hubbard model on one of the simplest frustrated lattice geometries, a triangular lattice. Motivated by the recent realization of ultracold fermionic atoms in triangular optical lattices, we study the properties of the triangular-lattice Hubbard model through a numerical linked-cluster expansion algorithm. We investigate the Mott insulator transition finding a critical interaction ${U}_{c}/t=7.0(2)$ and use spatial two- and three-point correlation functions to explore doped and imbalanced systems. Our results demonstrate that many interesting features occur at temperatures previously obtained for ultracold fermions in optical lattices and are accessible by upcoming experiments. Our calculations will be helpful for thermometry in ultracold atom quantum simulators and can guide experimental searches for exotic quantum phases in atomic triangular Hubbard quantum simulators.The suppression of antiferromagnetic ordering in geometrically frustrated Hubbard models leads to a variety of exotic quantum phases including quantum spin liquids and chiral states. Here, we focus on the Hubbard model on one of the simplest frustrated lattice geometries, a triangular lattice. Motivated by the recent realization of ultracold fermionic atoms in triangular optical lattices, we study the properties of the triangular-lattice Hubbard model through a numerical linked-cluster expansion algorithm. We investigate the Mott insulator transition finding a critical interaction ${U}_{c}/t=7.0(2)$ and use spatial two- and three-point correlation functions to explore doped and imbalanced systems. Our results demonstrate that many interesting features occur at temperatures previously obtained for ultracold fermions in optical lattices and are accessible by upcoming experiments. Our calculations will be helpful for thermometry in ultracold atom quantum simulators and can guide experimental searches for exotic quantum phases in atomic triangular Hubbard quantum simulators.

arXiv:2205.12233Physical Review AJul 11, 202216 citations

Adiabatic Loading of One-Dimensional SU(N) Alkaline-Earth-Atom Fermions in Optical Lattices

Lars Bonnes, Kaden R. A. Hazzard, Salvatore R. Manmana +2 more

Ultracold fermionic alkaline earth atoms confined in optical lattices realize Hubbard models with internal SU(N) symmetries, where N can be as large as ten. Such systems are expected to harbor exotic magnetic physics at temperatures below the superexchange energy scale. Employing quantum Monte Carlo simulations to access the low-temperature regime of one-dimensional chains, we show that after adiabatically loading a weakly interacting gas into the strongly interacting regime of an optical lattice, the final temperature decreases with increasing N. Furthermore, we estimate the temperature scale required to probe correlations associated with low-temperature SU(N) magnetism. Our findings are encouraging for the exploration of exotic large-N magnetic states in ongoing experiments.Ultracold fermionic alkaline earth atoms confined in optical lattices realize Hubbard models with internal SU(N) symmetries, where N can be as large as ten. Such systems are expected to harbor exotic magnetic physics at temperatures below the superexchange energy scale. Employing quantum Monte Carlo simulations to access the low-temperature regime of one-dimensional chains, we show that after adiabatically loading a weakly interacting gas into the strongly interacting regime of an optical lattice, the final temperature decreases with increasing N. Furthermore, we estimate the temperature scale required to probe correlations associated with low-temperature SU(N) magnetism. Our findings are encouraging for the exploration of exotic large-N magnetic states in ongoing experiments.

arXiv:1207.3900Physical Review LettersNov 14, 201246 citations

General Hubbard Model for Fermions in an Optical Lattice

J. P. Kestner, Luming Duan

Bulletin of the American Physical SocietyMar 19, 20090 citations

{U}_{c}/t=7.0(2)

and use spatial two- and three-point correlation functions to explore doped and imbalanced systems. Our results demonstrate that many interesting features occur at temperatures previously obtained for ultracold fermions in optical lattices and are accessible by upcoming experiments. Our calculations will be helpful for thermometry in ultracold atom quantum simulators and can guide experimental searches for exotic quantum phases in atomic triangular Hubbard quantum simulators.