Influence of impurity on the rate of single photon superradiance and photon transport in disordered N qubit chain

Abstract

We investigate the rate of superradiant emission for a number of artificial atoms (qubits) embedded in a one-dimensional open waveguide. More specifically, we study the 1D (N+1)- qubit chain where N qubits are identical with respect to their excitation frequency Ω but have different rates of spontaneous emission Γn, and a single impurity qubit which is different from N qubits by its excitation frequency ΩP and the rate of spontaneous emission ΓP. We performed exact diagonalization of Hamiltonian and showed that the system has two hybridized collective states one of which accumulates the widths of all qubits. The energy spectrum of these states and corresponding probabilities are investigated as a function of the frequency detuning between the impurity and other qubits in a chain. It is shown that the inclusion of the impurity qubit alters the resonance widths of the system if the total width overlaps the frequency detuning between qubits and the impurity. In this case the resonance widths experience a significant repulsion. The photon transmission through disordered N- qubit chain with the impurity qubit is also considered. It is shown that a single photon transport through this system is described by a simple expression which predicts for specific photon frequency the existence of a complete transmission peak and transparency window between frequencies Ω and ΩP.