Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases

Abstract

Alkaline-earth and ytterbium cold atomic gases make it possible to simulate SU(N )-symmetric fermionic systems in a very controlled fashion. Such a high symmetry is expected to give rise to a variety of novel phenomena ranging from molecular Luttinger liquids to (symmetry-protected) topological phases. We review some of the phases that can be stabilized in a one dimensional lattice. The physics of this multi-component Fermi gas turns out to be much richer and more exotic than in the standard SU(2) case. For N > 2, the phase diagram is quite rich already in the case of the single-band model, including a molecular Luttinger liquid (with dominant superfluid instability in the N -particle channel) for incommensurate fillings, as well as various Mott-insulating phases occurring at commensurate fillings. Particular attention will be paid to the cases with additional orbital degree of freedom (which is accessible experimentally either by taking into account two atomic states or by putting atoms in the p-band levels). We introduce two microscopic models which are relevant for these cases and discuss their symmetries and strong coupling limits. More intriguing phase diagrams are then presented including, for instance, symmetry protected topological phases characterized by non-trivial edge states.

Direct Probing of the Mott Crossover in theSU(N)Fermi-Hubbard Model

“…with filling nd 3 = 1 is expected to faithfully realize the SU(N )-symmetric Heisenberg model, paving the way towards studying unexplored systems with reduced dimensions such as chains [27][28][29] and new magnetic phases in square lattices [7].…”

Chiral Haldane phases of SU(N) quantum spin chains

“…For a general discussion of onedimensional SU(N) spin systems and their realization in the strong coupling limit of Fermi-Hubbard models we refer to a recent review. 34 .…”

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

“…[5][6][7] It paves the way of the quantum simulation of SU(N ) manybody physics with the realization of exotic phases such as SU(N ) chiral spin liquid states or SU(N ) symmetry-protected topological phases. [8][9][10][11][12][13][14][15][16][17][18] A second important property of alkaline-earth-like atoms is the existence of a long-lived metastable excited state ( 3 P 0 ) coupled to the ground state ( 1 S 0 ) via an ultranarrow doublyforbidden transition. This makes them ideal systems for the realization of the most precise atomic clocks.…”

“…In this respect, several two-orbital SU(N ) fermionic lattice models with contact interactions can be considered in the context of alkalineearth-like atoms. 2,14,16,32,33 A first lattice model, the g − e model, which is directly relevant to recent experiments, [26][27][28] is defined from the existence of four different scattering lengths that stem from the two-body collisions with g and e atomic states: 2…”