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arXiv:1602.00866 · Physical review. B./Physical review. B

One-dimensional two-orbital SU( N ) ultracold fermionic quantum gases at incommensurate filling: A low-energy approach

V. Bois, Pierre Fromholz, P. Lecheminant

Published Apr 13, 2016• 14 citations
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Abstract

We investigate the zero-temperature phase diagram of two-orbital $\mathrm{SU}(N$) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a low-energy approach that takes into account explicitly the $\mathrm{SU}(N$) symmetry, we find that a spectral gap for the nuclear-spin degrees of freedom is formed for generic interactions. Several phases with one or two gapless modes are then stabilized which describe the competition between different density instabilities. In stark contrast to the $N=2$ case, no dominant pairing instabilities emerge and the leading superfluid one is rather formed from bound states of $2N$ fermions.

DOI
10.1103/physrevb.93.134415

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We investigate the zero-temperature phase diagram of two-orbital SU(N\mathrm{SU}(NSU(N) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a low-energy approach that takes into account explicitly the SU(N\mathrm{SU}(NSU(N) symmetry, we find that a spectral gap for the nuclear-spin degrees of freedom is formed for generic interactions. Several phases with one or two gapless modes are then stabilized which describe the competition between different density instabilities. In stark contrast to the N=2N=2N=2 case, no dominant pairing instabilities emerge and the leading superfluid one is rather formed from bound states of 2N2N2N fermions.
We study ultracold quantum gases of alkaline-earth-like atoms loaded into three-dimensional statedependent optical lattice.In particular, we focus on the fermionic ytterbium-173 atoms due to their unique properties, in particular, low-lying metastable excited e electronic state, decoupling of the nuclear spin from the electronic degrees of freedom and different AC-polarizabilities of the ground g and e states.This allows to realize the two-band Hubbard model and study its unique critical properties.The theoretical analysis is performed in the region of applicability of the tight-binding approximation at different lattice depths and different fillings by atoms in the g-and e-orbital states.By means of dynamical mean-field theory, we analyze stability regions of the emerging ordered phases.
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 the quantum phase diagrams of Bose-Fermi mixtures of ultracold atoms confined to one dimension in an optical lattice. For systems with incommensurate densities, various quantum phases, e.g., spin- or charge-density waves, pairing, phase separation, and the Wigner crystal, are found to be dominant in different parameter regimes within a bosonization approach. The structure of the phase diagram leads us to propose that the system is best understood as a Luttinger liquid of polarons (i.e., atoms of one species surrounded by screening clouds of the other species). Special fillings, half filling for fermions, and unit filling for bosons, and the resulting gapped phases are also discussed, as well as the properties of the polarons and the experimental realization of these phases.
The phase diagram of one-dimensional alkaline-earth fermionic atoms and ytterbium 171 atoms is investigated by means of a low-energy approach and density-matrix renormalization group calculations. For incommensurate filling, four gapless phases with a spin gap are found and consist of two superconducting instabilities and two coexisting bond and charge density-waves instabilities. In the half-filled case, seven Mott-insulating phases arise with the emergence of four non-degenerate phases with exotic hidden orderings.
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It is argued that an ultracold quantum degenerate gas of ytterbium 173 Yb atoms having nuclear spin I =5/2 exhibits an enlarged SU(6) symmetry. Within the Landau Fermi liquid theory, stability criteria against Fermi liquid (Pomeranchuk) instabilities in the spin channel are considered. Focusing on the SU( n >2) generalizations of ferromagnetism, it is shown within mean-field theory that the transition from the paramagnet to the itinerant ferromagnet is generically first order. On symmetry grounds, general SU( n ) itinerant ferromagnetic ground states and their topological excitations are also discussed. These SU( n >2) ferromagnets can become stable by increasing the scattering length using optical methods or in an optical lattice. However, in an optical lattice at current experimental temperatures, Mott states with different filling are expected to coexist in the same trap, as obtained from a calculation based on the SU(6) Hubbard model.