Two-orbital physics of high spin fermionic alkaline earth atoms confined in a one-dimensional chain

TL;DR

This paper investigates the two-orbital physics of high-spin fermionic alkaline-earth atoms in a one-dimensional chain, revealing complex phase behavior including potential finite momentum pairing states and various gapped and gapless phases.

Contribution

It provides a detailed analysis of the renormalization group flow and phase diagram for high-spin alkaline-earth atoms, highlighting the effects of SU(N) symmetry and two-orbital coupling.

Findings

Identification of a non-stabilizing gapless Luttinger liquid state in 87Sr

Discovery of stable superconducting states in specific parameter regions

Analysis of the phase diagram showing gapped and gapless states with multiple velocities

Abstract

We study the effect of the coupling between the electronic ground state of high spin alkaline-earth fermionic atoms and their metastable optically excited state, when the system is confined in a one-dimensional chain, and show that the system provides a possible realization of a finite momentum pairing (Fulde-Ferrell-Larkin-Ovchinnikov-like) state without spin- or bare mass imbalance. We determine the $\beta$-functions of the renormalization group trajectories for general spin and analyze the structure of the possible gapped and gapless states in the hydrodynamic limit. Due to the SU(N) symmetry in the spin space, complete mode separation can not be observed even in the fully gapless 2N-component Luttinger liquid state. Contrary, 4 velocities characterize the system. We solve the renormalization group equations for spin-9/2 strontium-87 isotope and analyze in detail its phase diagram. The fully gapless Luttinger liquid state does not stabilize in the two-orbital system of the $^{87}$Sr atoms, instead, different gapped non-Gaussian fixed points are identified either with dominant density or superconducting fluctuations. The superconducting states are stable in a nontrivial shaped region in the parameter space as a consequence of the coupling between the two electronic states.