Abstract
The interaction between superconducting qubits and one-dimensional microwave transmission lines has been studied experimentally and theoretically in the past two decades. In this work, we investigate the spontaneous emission of an initially excited artificial atom which is capacitively coupled to a semi-infinite transmission line, shorted at one end. This configuration can be viewed as an atom in front of a mirror. The distance between the atom and the mirror introduces a time delay in the system, which we take into account fully. When the delay time equals an integer number of atom oscillation periods, the atom converges into a dark state after an initial decay period. The dark state is an effect of destructive interference between the reflected part of the field and the part directly emitted by the atom. Based on circuit quantization, we derive linearized equations of motion for the system and use these for a semiclassical analysis of the transient dynamics. We also make a rigorous connection to the quantum optics system-reservoir approach and compare these two methods to describe the dynamics. We find that both approaches are equivalent for transmission lines with a low characteristic impedance, while they differ when this impedance is higher than the typical impedance of the superconducting artificial atom.
Highlights
Waveguide quantum electrodynamics (QED) has become a field of growing importance for quantum communication, quantum simulations, and quantum computation [1,2,3,4,5]
We have investigated the spontaneous emission dynamics of an initially excited superconducting artificial atom of transmon type, capacitively coupled to a semi-infinite transmission, shorted at a distance L from the transmon
We especially focused on the case where the atom is located at a node of the electromagnetic field, leading the atom to converge into a dark state with finite energy in the steady state
Summary
Waveguide quantum electrodynamics (QED) has become a field of growing importance for quantum communication, quantum simulations, and quantum computation [1,2,3,4,5]. The quantum emitters can be natural atoms, Rydberg atoms, trapped ions or artificial atoms such as quantum dots, nitrogen vacancy centers, and superconducting qubits [1] The latter are studied in a field called circuit QED [2,12,13,14,15]. To resolve the dynamics on this timescale, one needs to go beyond the Markov approximation, including effects of the time delay beyond phase shifts This has been done in several studies investigating lightmatter interaction regarding time delay, such as quantum optical approaches solving the equations of motion with Fourier transformation [8,30,31,32], recent methods involving matrix product states to solve time-delay equations [33,34,35,36], or Green’s function approaches [37,38]. IV we summarize the results and discussions presented in this article
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