Qubit-photon bound states in superconducting metamaterials

Abstract

We study quantum features of electromagnetic radiation propagating in the one-dimensional superconducting quantum metamaterial comprised of an infinite chain of charge qubits placed within two-stripe massive superconducting resonators. The Quantum-mechanical model is derived assuming weak fields and that, at low temperatures, each qubit is either unoccupied (N = 0) or occupied by a single Cooper pair (N = 1). We demonstrate the emergence of two bands of single-photon-qubitbound states with the energies lying outside the photon continuum: highly above and slightly below it. The higher energy band slowly varies with the qubit-photon center of mass quasi-momentum. It becomes practically flat provided that electromagnetic energy is far below the Josephson one, while the latter is small compared to the charging one. The dispersion of the lower band is practically identical to that of free photons. The emergence of bound states may cause radiation trapping indicating its application for the control of photon transport in superconducting qubit-based artificial media.