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

Edina Szirmai
The effect of the coupling between the electronic ground state of high spin alkaline-earth fermionic atoms and their metastable optically excited state is studied, when the system is confined in a one-dimensional chain. We determine the $\beta$-functions of the RG 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 Luttinger liquid state. Contrary, 4 velocities characterize the system as a consequence of the coupling between the two electronic states. We solve the RG equations for spin-9/2 Strontium-87 isotope and analyze in detail its phase diagram. Luttinger liquid state does not stabilize in the two-orbital system of the Strontium-87 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 regime in the parameter space.
View original: http://arxiv.org/abs/1307.7558