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Physical Review A

Comment on "Theory of resonance fluorescence"

Jay R. Ackerhalt

Published Jan 1, 1978• 9 citations
Publisher

Abstract

We comment on the work of Kimble and Mandel with respect to Markovian approximations and the Lamb shift. The importance of the quantum properties of the free electromagnetic field in spontaneous-emission calculations is discussed.
DOI
10.1103/physreva.17.471

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The properties of an electron in an atom or molecule are not fixed; rather they are a function of the optical environment of the emitter. Not only is the spontaneous emission a function of the optical environment, but also the underlying wave functions and energy levels, which are modified by the potential induced by quantum fluctuations of the electromagnetic field. In free space, this modification of atomic levels and wave functions is very weak and generally hard to observe due to the prevalence of other perturbations like fine structure. Here, we explore the possibility of highly tailorable electronic structure by exploiting large Lamb shifts in tunable electromagnetic environments such as graphene, whose optical properties are dynamically controlled via doping. The Fermi energy can be chosen so that the Lamb shift is very weak, but it can also be chosen so that the shifts become more prominent than the fine structure of the atom and even potentially the Coulomb interaction with the nucleus. Potential implications of this idea include being able to electronically shift an unfavorable emitter structure into a favorable one, a new approach to probe near-field physics in fluorescence, and a way to access regimes of physics where vacuum fluctuations are not a weak perturbation but rather the dominant physics.
Any quantum-confined electronic system coupled to the electromagnetic continuum is subject to radiative decay and renormalization of its energy levels. When coupled to a cavity, these quantities can be strongly modified with respect to their values in vacuum. Generally, this modification can be accurately captured by including only the closest resonant mode of the cavity. In the circuit quantum electrodynamics architecture, it is, however, found that the radiative decay rates are strongly influenced by far off-resonant modes. A multimode calculation accounting for the infinite set of cavity modes leads to divergences unless a cutoff is imposed. It has so far not been identified what the source of divergence is. We show here that unless gauge invariance is respected, any attempt at the calculation of circuit QED quantities is bound to diverge. We then present a theoretical approach to the calculation of a finite spontaneous emission rate and the Lamb shift that is free of cutoff.