  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.
