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

Kevin Lalumière, Barry C. Sanders, A. F. van Loo, A. Fedorov, A. Wallraff, and A. Blais
Phys. Rev. A 88, 043806 – Published 7 October 2013

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 exchange-type 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 [van Loo et al. (unpublished)].

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  • Received 12 June 2013

DOI:https://doi.org/10.1103/PhysRevA.88.043806

©2013 American Physical Society

Authors & Affiliations

Kevin Lalumière1, Barry C. Sanders2, A. F. van Loo3, A. Fedorov3, A. Wallraff3, and A. Blais1

  • 1Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1
  • 2Institute for Quantum Science and Technology, University of Calgary, Alberta, Canada T2N 1N4
  • 3Department of Physics, ETH Zurich, CH-8093 Zürich, Switzerland

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Vol. 88, Iss. 4 — October 2013

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