Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms

Abstract

We study the collective effects that emerge in waveguide quantum electrodynamics where several (artificial) atoms are coupled to a one-dimensional superconducting transmission line. Since single microwave photons can travel without loss for a long distance along the line, real and virtual photons emitted by one atom can be reabsorbed or scattered by a second atom. Depending on the distance between the atoms, this collective effect can lead to super-and subradiance or to a coherent exchangetype interaction between the atoms. Changing the artificial atoms transition frequencies, something which can be easily done with superconducting qubits (two levels artificial atoms), is equivalent to changing the atom-atom separation and thereby opens the possibility to study the characteristics of these collective effects. To study this waveguide quantum electrodynamics system, we extend previous work and present an effective master equation valid for an ensemble of inhomogeneous atoms driven by a coherent state. Using input-output theory, we compute analytically and numerically the elastic and inelastic scattering and show how these quantities reveal information about collective effects. These theoretical results are compatible with recent experimental results using transmon qubits coupled to a superconducting one-dimensional transmission line [A. F. van Loo et al.].

Enhanced resonant force between two entangled identical atoms in a photonic crystal

“…In particular it has been discussed how photonic bandgap materials can be used to preserve the maximally symmetric entangled state [30,31] . Also, it has been shown that symmetrical state can be easily realized considering two superconducting qubits in 1-D trasmission line, where the photon-mediated interaction between the two artificial atoms leads to correlated states [32,33]. The interaction energy between the two atoms can be obtained using the resolvent formalism: the discrete level energies are given by the poles of the resolvent [34].…”

Quantum scattering theory of a single-photon Fock state in three-dimensional spaces

“…(1) without any approximation. The theoretical framework is built upon methods developed for electrons scattered by magnetic impurities in condensed matter physics [2,3] as well as recent progress in one-dimensional waveguide quantum electrodynamics [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Although we illustrate the theory based on single photons, the framework is fundamentally compatible with and can be extended to multi-photons.…”

Multistability and switching in a superconducting metamaterial

“…In the quantum limit, efforts to build many-qubit systems blur the border between circuit quantum electrodynamics and metamaterials [5][6][7][8] while even the classical case holds a multitude of interesting and yet unexplored possibilities. Implementations of these structures, for instance in the form of parametric amplifiers 9 , have already attracted a great deal of attention and continue to do so as the field of superconducting metamaterials evolves.…”