Nature of the Lamb shift in weakly anharmonic atoms

From normal-mode splitting to quantum fluctuations

Journal Article (2018)
Author(s)

Mario Gely (TU Delft - QN/Steele Lab, Kavli institute of nanoscience Delft)

G. A. Steele (Kavli institute of nanoscience Delft, TU Delft - QN/Steele Lab)

D. Bothner (TU Delft - QN/Steele Lab, Kavli institute of nanoscience Delft)

Research Group
QN/Steele Lab
Copyright
© 2018 M.F. Gely, G.A. Steele, D. Bothner
DOI related publication
https://doi.org/10.1103/PhysRevA.98.053808
More Info
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Publication Year
2018
Language
English
Copyright
© 2018 M.F. Gely, G.A. Steele, D. Bothner
Research Group
QN/Steele Lab
Issue number
5
Volume number
98
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Abstract

When a two-level system (TLS) is coupled to an electromagnetic resonator, its transition frequency changes in response to the quantum vacuum fluctuations of the electromagnetic field, a phenomenon known as the Lamb shift. Remarkably, by replacing the TLS by a harmonic oscillator, normal-mode splitting leads to a quantitatively similar shift, without taking quantum fluctuations into account. In a weakly anharmonic system, lying in between the harmonic oscillator and a TLS, the origins of such shifts can be unclear. An example of this is the dispersive shift of a transmon qubit in circuit quantum electrodynamics (QED). Although often referred to as a Lamb shift, the dispersive shift observed in spectroscopy in circuit QED could contain a significant contribution from normal-mode splitting that is not driven by quantum fluctuations, raising the question: how much of this shift is quantum in origin? Here we treat normal-mode splitting separately from shifts induced by quantum vacuum fluctuations in the Hamiltonian of a weakly anharmonic system, providing a framework for understanding the extent to which observed frequency shifts can be attributed to quantum fluctuations.

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