One-dimensional spin-1/2 fermionic gases with two-body losses: Weak dissipation and spin conservation

We present a theoretical analysis of the dynamics of a one-dimensional spin-1/2 fermionic gas subject to weak two-body losses. Our approach highlights the crucial role played by spin conservation in the determination of the full time evolution. We focus in particular on the dynamics of a gas that is initially prepared in a Dicke state with a fully symmetric spin wave function, in a band insulator, or in a Mott insulator. In the latter case, we investigate the emergence of a steady symmetry-resolved purification of the gas. Our results could help with the modelization and understanding of recent experiments with alkaline-earth(-like) gases like ytterbium and fermionic molecules.