Universal free-fermion multiply-excited eigenstates and their experimental signatures in 1D arrays of two-level atoms

One-dimensional subwavelength atom arrays display multiply-excited subradiant eigenstates which are reminiscent of free fermions. In this Letter, we show that such free-fermion eigenstates appear in case of a quadratic dispersion relation of the band of singly-excited states, by demonstrating that near the band-edge, Hamiltonians of the long-range resonant dipole-dipole interactions can be approximated by a nearest-neighbour-tunneling model diagonalized by Jordan-Wigner fermions. The universal mechanism for this phenomenon implies that the free-fermion ansatz extends to states with finite decay rates and we propose schemes for their observation, exploiting a physical transfer process between sub- and super-radiant free-fermion eigenstates, and by angular coincidences in the emission from a laser driven atomic array.