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

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