A system of a two-level atom of an impurity (qubit) inserted into a periodic chain coupled to the continuum is studied with the use of the effective non-Hermitian Hamiltonian. Exact solutions are derived for the quasistationary eigenstates, their complex energies, and transport properties. Due to the presence of the qubit, two long-lived states corresponding to the ground and excited states of the qubit emerge outside the Bloch energy band. These states remain essentially localized at the qubit even in the limit of sufficiently strong coupling between the chain and the environment when the super-radiant states are formed. The transmission through the chain is studied as a function of the continuum coupling strength and the chain-qubit coupling; the perfect resonance transmission takes place through isolated resonances at weak and strong continuum coupling, while the transmission is lowered in the intermediate regime.
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