Quantum many-body analysis of spin-2 bosons with two-body inelastic decay

Bose-Einstein condensates of $^{87}\mathrm{Rb}$ atoms with a hyperfine spin of 2 are open quantum systems, where the atoms are lost through two-body inelastic collisions. In this dissipation process, a collision channel with total spin of 4 is forbidden by angular momentum conservation, which results in magnetization of the atoms remaining in the condensate. Here, we investigate the quantum many-body properties of spin-2 bosons that undergo two-body atomic loss. We show that the system finally reaches a steady state, which is a mixture of the states with maximum total spins. In addition, we find that a nonclassical steady state can be obtained by applying and quenching the quadratic Zeeman field.