Free-Fermion Multiply Excited Eigenstates and Their Experimental Signatures in 1D Arrays of Two-Level Atoms

One-dimensional (1D) subwavelength atom arrays display multiply excited subradiant eigenstates which are reminiscent of free fermions. So far, these states have been associated with subradiant states with decay rates proportional to N-3, with N the number of atoms, which fundamentally prevents detection of their fermionic features by optical means. In this Letter, we show that free-fermion states generally appear whenever the band of singly excited states has a quadratic dispersion relation at the band edge and, hence, may also be obtained with radiant and even superradiant states. 1D arrays have free-fermion multiply excited eigenstates that are typically either subradiant or (super)radiant, and we show that a simple transformation acts between the two families. Based on this correspondence, we propose different means for their preparation and analyze their experimental signature in optical detection.