Non-Hermitian Hamiltonian approach to the microwave transmission through one- dimensional qubit chain

We investigate the propagation of microwave photons in a one-dimensional waveguide interacting with a number of artificial atoms (qubits). Within the formalism of projection operators and non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme for the calculation of the transmission and reflection factors of the microwave signal in a waveguide which contains an arbitrary number \emph{N} of non-interacting qubits. It is shown that for identical qubits in the long-wave limit a coherent superradiance state is formed with the width being equal to the sum of the widths of spontaneous transitions of \emph{N} individual qubits.