Ultracold atoms in Raman-dressed optical lattices allow for effective momentum-dependent interactions among single-species fermions originating from short-range s-wave interactions. These dressed-state interactions combined with the very flat bands encountered in the recently introduced optical flux lattices push the Stoner instability towards weaker repulsive interactions, making it accessible with current experiments. As a consequence of the coupling between spin and orbital degrees of freedom, the magnetic phase features Ising nematic order.
Ultracold atoms in Raman-dressed optical lattices allow for effective momentum-dependent interactions among single-species fermions originating from short-range s-wave interactions. These dressed-state interactions combined with the very flat bands encountered in the recently introduced optical flux lattices push the Stoner instability towards weaker repulsive interactions, making it accessible with current experiments. As a consequence of the coupling between spin and orbital degrees of freedom, the magnetic phase features Ising nematic order.
We study a model of a two-dimensional ultracold atomic gas subjected to an ``optical flux lattice'': a laser configuration where Raman-dressed atoms experience a strong artificial magnetic field. This leads to a band structure of narrow energy bands with nonzero Chern numbers. We consider the case of two-level (spin-1/2) fermionic atoms in this lattice, interacting via a repulsive s-wave contact interaction. Atoms restricted to the lowest band are described by an effective model of spinless fermions with interactions that couple states in a momentum-dependent manner across the Brillouin zone; a consequence of the Raman dressing of the two spin states. We present the results of detailed exact diagonalization studies of the many-body states for a range of filling factors, $\ensuremath{\nu}$. First, we present evidence for the existence of a phase with coupled ferromagnetic-nematic ordering, which was previously suggested by a mean-field analysis. Second, we present evidence indicating the presence of a Laughlin-like fractional quantum Hall state occurring at filling factor $\ensuremath{\nu}=1/3$. Finally, we observe a charge-density wave state at $\ensuremath{\nu}=1/2$, which we are able to cleanly distinguish from the Laughlin-like state by its translational symmetry breaking and relatively low participation ratio.
We describe a simple scheme by which "optical flux lattices" can be implemented in ultracold atomic gases using two-photon dressed states. This scheme can be applied, for example, to the ground-state hyperfine levels of commonly used atomic species. The resulting flux lattices simulate a magnetic field with high mean flux density, and have low-energy bands analogous to the lowest Landau level. We show that in practical cases the atomic motion significantly deviates from the adiabatic following of one dressed state, and that this can lead to significant interactions even for fermions occupying a single band. Our scheme allows experiments on cold atomic gases to explore strong correlation phenomena related to the fractional quantum Hall effect, both for fermions and bosons.
We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-metal-like atoms in optical lattices that can be effectively described by the two-band spin-1/2 Hubbard model including Hund's exchange coupling term. Our main goal is to investigate the effect of exchange interactions on finite-temperature magnetic phases for a wide range of lattice fillings. We use the dynamical mean-field theory approach and its real-space generalization to obtain finite-temperature phase diagrams including transitions to magnetically ordered phases. It allows to determine optimal experimental regimes for approaching long-range ferromagnetic ordering in ultracold gases. We also calculate the entropy in the vicinity of magnetically ordered phases, which provides quantitative predictions for ongoing and future experiments aiming at approaching and studying long-range ordered states in optical lattices.
In this thesis, we discuss ultracold quantum gases both in continuum and optical lattices. For the continuum Fermi gases in BCS-BEC crossover, we present an effective field theory study on the recently discovered puzzling damping phenomena on the BCS side of the crossover. We find that in contrast to the previous proposed pair-breaking mechanism of damping, the damping process is due to the interaction between superfluid phonons and thermally excited fermionic quasi particles. Results from our effective field theory are compared quantitatively with experiments, showing a good agreement. For the ultracold fermionic atoms in optical lattices, we propose two novel quantum phases. Firstly, we show that a novel superconducting pairing occurs for spin-imbalanced Fermi gases with the spin up and down Fermi levels lying within the px- and s- orbital bands of a quasi-one-dimensional optical lattice. The pairs condense at a finite momentum equal to the sum of the two Fermi momenta of spin up and down fermions, and form a p-orbital condensate. The phase diagram shows that the p-orbital pair condensate occurs in a wide range of fillings. Secondly, we study instabilities of single-species fermionic atoms in the p-orbital bands in two-dimensional square optical lattices. From the nearly-perfect nesting Fermi surfaces, charge density wave and orbital density wave orderings with stripe or checkerboard patterns are found for attractive and repulsive interactions, respectively. The superconducting phase, usually expected of attractively interacting fermions, is strongly suppressed. We also use field theory to analyze the possible liquid crystal phases in our system. For bosons, we study ultracold bosonic atoms loaded in a one-dimensional optical lattice of two-fold p-orbital degeneracy at each site, and find an anti-ferro-orbital, a homogeneous px Mott insulator phase and two kinds of superfluid phases distinguished by the orbital ordering.
We study Hubbard models for ultracold bosonic or fermionic atoms loaded into an optical lattice. The atoms carry a high spin F> 1/2, and interact on site via strong repulsive Van der Waals forces. Making convenient rearrangements of the interaction terms, and exploiting their symmetry properties, we derive low-energy effective models with nearest-neighbor interactions, and their properties. We apply our method to F =3/2, and 5/2 fermions on two-dimensional square lattice at quarter, and 1/6 fillings, respectively, and investigate mean-field equations for repulsive couplings. We find for F =3/2 fermions that the plaquette state appearing in the highly symmetric SU (4) case does not require fine tuning, and is stable in an extended region of the phase diagram. This phase competes with an SU (2) flux state, that is always suppressed for repulsive interactions in the absence of external magnetic field. The SU (2) flux state has, however, lower energy than the plaquette phase, and stabilizes in the presence of weak applied magnetic field. For F =5/2 fermions a similar SU (2) plaquette phase is found to be the ground state without external magnetic field.
Ferromagnetism is a pure quantum correlation phenomenon, and yet it is responsible for most magnetic phenomena that we encounter in everyday life. Metallic magnets, such as iron and nickel, owe their magnetic behavior to mobile conduction electrons, whose spins can align with one another giving rise to non-zero magnetization. In the 1930s, Edmund C. Stoner first devised a simple and minimal model, where a ferromagnetic instability of the homogeneous Fermi gas is afforded only through short-range repulsive interactions. While his model captures the fundamental physics behind itinerant ferromagnetism, various additional effects in solid materials, such as orbital couplings and peculiar band dispersions, make it difficult to isolate the Stoner mechanism. Here we present our experimental investigation performed on an ultracold Fermi mixture of 6Li atoms where only genuine short-range repulsive interactions are present. Studying the stability of an artificially created ferromagnetic state, we provide a signature of a Stoner-like instability in a metastable system.