Metallic and Insulating Phases of Interacting Fermions in a 3D Optical Lattice

Ulrich Schneider, Lucia Hackermüller, Sebastian Will +6 more

The fermionic Hubbard model plays a fundamental role in the description of strongly correlated materials. We have realized this Hamiltonian in a repulsively interacting spin mixture of ultracold (40)K atoms in a three-dimensional (3D) optical lattice. Using in situ imaging and independent control of external confinement and lattice depth, we were able to directly measure the compressibility of the quantum gas in the trap. Together with a comparison to ab initio dynamical mean field theory calculations, we show how the system evolves for increasing confinement from a compressible dilute metal over a strongly interacting Fermi liquid into a band-insulating state. For strong interactions, we find evidence for an emergent incompressible Mott insulating phase. This demonstrates the potential to model interacting condensed-matter systems using ultracold fermionic atoms.

Tilman Esslinger

Sebastian Will

Thereza Paiva

The ability to cool fermions in optical lattices to ultra cold temperatures has led to an interdisciplinary area of research, that has attracted a lot of attention in recent years. An interesting development in this area is the possibility to realize models for strongly correlated fermions in the laboratory, such as the fermionic Hubbard Model. Determinantal Quantum Monte Carlo simulations have proven to be an important tool in the study of fermionic atoms. Nonetheless, it is important to compare the results and efficiency of different methods. Here comparisons with Numerical Linked Cluster Expansion and Dynamical Mean Field Theory data for double occupation and short range correlations, both relevant to current optical lattice experiments, will be presented and discussed. Another topic relevant in the context of optical lattice experiments is the study of metal insulator transitions. Indeed, the Mott insulating phase has been realized and observed in two-flavor mixtures of fermionic atoms loaded on optical lattices, being characterized both by the double occupation and the compressibility. An interesting point that has been addressed in the literature over the years is whether the same fermion-fermion interaction, responsible for the Mott insulating state, could drive an insulating system metallic. Here we show that, when fermions are loaded in optical lattices with spatially varying interactions a correlation induced Mott insulator to metal transition can take place. The spatial modulation of the interactions was recently demonstrated and opens the possibility for the experimental realization of such exotic phases.

Ariel Sommer, Lawrence W. Cheuk, Mark Ku +3 more

Rei Hatsuda, Emiko Arahata

Motivated by recent developments in the experimental study of Bose-Fermi mixtures, we investigate ground-state phase diagrams and excitation spectra for Bose-Fermi mixtures in a three-dimensional (3D) optical lattice. The Gutzwiller approximation is used to identify a new phase in which both superfluid bosons and metal fermions coexist. As a useful probe to identify the quantum phases, we also calculate the excitation spectra. In Mott insulator phase, two excitation features appear in the spectra that correspond to particle and hole excitations. In superfluid phase, there are Bogoliubov modes and amplitude modes. In coexisting phase, two gapless dispersive modes are identified, which shift due to interaction between bosons and fermions.