Quantum electrodynamics spontaneous emission

Another example of zero-point energy arises in the detailed quantum theory of the electromagnetic field, known as quantum electrodynamics. The empty vacuum with no photons present is actually the zero-point level with n = 0. The non-zero energy of this state cannot be measured directly, but does have some observable consequences. The vacuum is really a state of fluctuating electric and magnetic fields that are significant at the atomic level. Without them, there would be no mechanism for the spontaneous emission of photons from excited states. There also have very small effects on the energy levels of atoms (see Section 4.4). 

The Purcell s original idea [10] on modification of photon spontaneous emission rate is extended to modification of photon spontaneous scattering rate. Simultaneous account for local incident field and local density of photon states enhancements in close proximity to a silver nanoparticle is found to provide up to lO -fold Raman scattering cross-section rise up. Thus, single molecule Raman detection is found to be explained by consistent quantum electrodynamic description without chemical mechanisms involved. 

Abstract Rapid advances in quantum technology have made possible the control of quantum states of elementary material quantum systems, such as atoms or molecules, and of the electromagnetic radiation field resulting from spontaneous photon emission of their unstable excited states to such a level of precision that subtle quantum electrodynamical phenomena have become observable experimentally. Recent developments in the area of quantum information processing demonstrate that characteristic quantum electrodynamical effects can even be exploited for practical purposes provided the relevant electromagnetic field modes are controlled by appropriate cavities. A central problem in this context is the realization of an ideal transfer of quantum information between a state of a material quantum system and a quantum... 

It turns out that the spontaneous lifetime of the Rydberg levels is shortened if the cavity is tuned into resonance with the frequency a>o of the atomic transition n) n — 1). liis prolonged if no cavity mode matches coq [1297]. This effect, which had been predicted by quantum electrodynamics, can intuitively be understood as follows in the resonant case, that part of the thermal radiation field that is in the resonant cavity mode can contribute to stimulated emission in the transition n) n — 1), resulting in a shortening of the lifetime (Sect. 6.3). For the... 

So far we have neglected the fact that the levels a) and b) are not only coupled by transitions induced by the external field but may also decay by spontaneous emission or by other relaxation processes such as collision-induced transitions. We can include these decay phenomena in our formulas by adding phenomenological decay terms to (2.68), which can be expressed by the decay constant ya and yt (Fig. 2.17). A rigorous treatment requires quantum electrodynamics [2.23]. 

So far we have treated absorption and stimulated emission of radiation. However, it is well known that an atom can emit radiation even when it is not externally perturbed, i.e. spontaneous emission. It is not possible to treat this process fully here, since consideration of the quantization of the electromagnetic field as described by Quantum ElectroDynamics (QED) is necessary. According to QED a coupling between the atom and the "vacuum state" of the field is responsible for the emission. 

As for the quantum versus classical electrodynamics, QED description is of course the correct and complete theory to describe all the molecular plasmonics phenomena. Nevertheless, it requires the definition and the manipulation of quantities that are often not as intuitive as their classical counterparts. Moreover, classical electrodynamics is able to explain most of the molecular plasmonics phenomena, and, with a few expedients, even intrinsically quantum-mechanical phenomena such as spontaneous emission. Therefore, in the following we shall stick to a classical electrodynamics description of the system, and we refer the reader to other works for a QED treatment [60]. 

This discussion has been included to show that our understanding of such an apparently simple phenomenon as spontaneous emission is not perhaps as complete as we would wish. Other difficulties which are connected with divergent expressions which occur in quantum electrodynamics are discussed by Leighton (1959, Ch. 20.12). 

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