Nature of the Lamb shift in weakly anharmonic atoms
From normal-mode splitting to quantum fluctuations
Mario Gely (TU Delft - QN/Steele Lab, Kavli institute of nanoscience Delft)
Gary A. Steele (Kavli institute of nanoscience Delft, TU Delft - QN/Steele Lab)
D. Bothner (TU Delft - QN/Steele Lab, Kavli institute of nanoscience Delft)
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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.