Visualizing the emission of a single photon with frequency and time resolved spectroscopy

Aleksei Sharafiev1, Mathieu L. Juan2, Oscar Gargiulo1, Maximilian Zanner3, Stephanie Wögerer3, Juan José García-Ripoll4, and Gerhard Kirchmair1,3

1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstrasse 21a, 6020 Innsbruck, Austria
2Institut quantique and Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada
3Institute for Experimental Physics, University of Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
4Instituto de Fisica Fundamental IFF-CSIC, 28006 Madrid, Spain

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At the dawn of Quantum Physics, Wigner and Weisskopf obtained a full analytical description (a $\textit{photon portrait}$) of the emission of a single photon by a two-level system, using the basis of frequency modes (Weisskopf and Wigner, "Zeitschrift für Physik", 63, 1930). A direct experimental reconstruction of this portrait demands an accurate measurement of a time resolved fluorescence spectrum, with high sensitivity to the off-resonant frequencies and ultrafast dynamics describing the photon creation. In this work we demonstrate such an experimental technique in a superconducting waveguide Quantum Electrodynamics (wQED) platform, using single transmon qubit and two coupled transmon qubits as quantum emitters. In both scenarios, the photon portraits agree quantitatively with the predictions of the input-output theory and qualitatively with Wigner-Weisskopf theory. We believe that our technique allows not only for interesting visualization of fundamental principles, but may serve as a tool, e.g. to realize multi-dimensional spectroscopy in waveguide Quantum Electrodynamics.

We report on a direct measurement of a single photon "wave function" (electrical field amplitude distribution) in frequency and time domains. The "wavefunction" has been measured directly (without any post-processing) taking advantage of superconducting quantum circuits platform for the first time. We demonstrate the technique on a rather simple example of a two-level system emitting a single excitation into a waveguide – the situation with well known analytical description. This technique can be readily applied, for instance, to study near field radiation from an artificial atom or to realize a multi-dimensional spectroscopy of an artificial matter.

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