Extremely subradiant states in a periodic one-dimensional atomic array

We study the subradiant collective states of a periodic chain of two-level atoms with either transversal or longitudinal transition dipole moments with respect to the chain axis. We show that long-lived subradiant states can be obtained for the transversal polarization by properly choosing the chain period for a given number of atoms in the case of no open diffraction channels. These highly subradiant states have a linewidth that decreases with the number of atoms much faster than it was shown previously. In addition, our study shows that such states are present even if there are additional interaction channels between the atoms, i.e. they interact via waveguide mode of an optical nanofiber for instance. We develop a theoretical framework allowing to describe the spectral properties of the system in terms of contributions from each collective eigenstate and we show that subradiant states manifest themselves in the transmission and reflection spectra, allowing to observe interaction-induced transparency in a very narrow spectral range. Such long-lived collective states may find potential applications in nanophotonics and quantum optics.