Subradiance of multilevel fermionic atoms in arrays with filling n ⩾ 2

We investigate the subradiance properties of $n⩾2$ multilevel fermionic atoms loaded into the lowest motional level of a single trap (e.g., a single optical lattice site or an optical tweezer). As pointed out in our previous work [A. Piñeiro Orioli and A. M. Rey, Phys. Rev. Lett. 123, 223601 (2019)], perfectly dark subradiant states emerge from the interplay between fermionic statistics and dipolar interactions. While previously we focused on the $n=2$ case, here we provide an in-depth analysis of the single-site dark states for generic filling $n$ , and show a tight connection between generic dark states and total angular momentum eigenstates. We show how the latter can also be used to understand the full eigenstate structure of the single-site problem, which we analyze numerically. Apart from this, we discuss two possible schemes to coherently prepare dark states using either a Raman transition or an external magnetic field to lift the Zeeman degeneracy. Although the analysis focuses on the single-site problem, we show that multisite dark states can be trivially constructed in any geometry out of product states of single-site dark states. Finally, we discuss some possible implementations with alkaline-earth(-like) atoms such as ¹⁷¹Yb or ⁸⁷Sr loaded into optical lattices, where they could be used for potential applications in quantum metrology and quantum information.