We consider the interplay between the structure and the dynamics of a quantum source and the virtual photon cloud surrounding it in two simple models: as first case we examine the structure of the virtual cloud surrounding a model of static source formed by the N = 1, N = 2 shells of the hydrogen atom when a static uniform electric field acts on the source. The distortion induced on the source is reflected on the structure of the virtual cloud. In fact in the presence of the external field new components of the virtual cloud appear. These new components extend to large distances and have the same spatial symmetry of the one induced by the static field on the source. We then consider a three level system interacting with a boson field. Its intermediate level is metastable and decays with emission of two quanta to the lowest level. Due to the interaction with the field the intermediate and the lower level are dressed by a virtual photon cloud. The effects of the dressing are taken into account by a unitary transformation. Then the two quanta decay amplitude is obtained using the resolvent technique. The dressed lineshape obtained is then compared with the one obtained in the decay between bare states In the dressed decay one of the emitted quanta has the same distribution as the virtual quanta surrounding the excited state.
We consider the interplay between the structure and the dynamics of a quantum source and the virtual photon cloud surrounding it in two simple models: as first case we examine the structure of the virtual cloud surrounding a model of static source formed by the N = 1, N = 2 shells of the hydrogen atom when a static uniform electric field acts on the source. The distortion induced on the source is reflected on the structure of the virtual cloud. In fact in the presence of the external field new components of the virtual cloud appear. These new components extend to large distances and have the same spatial symmetry of the one induced by the static field on the source. We then consider a three level system interacting with a boson field. Its intermediate level is metastable and decays with emission of two quanta to the lowest level. Due to the interaction with the field the intermediate and the lower level are dressed by a virtual photon cloud. The effects of the dressing are taken into account by a unitary transformation. Then the two quanta decay amplitude is obtained using the resolvent technique. The dressed lineshape obtained is then compared with the one obtained in the decay between bare states In the dressed decay one of the emitted quanta has the same distribution as the virtual quanta surrounding the excited state.
An atom or a molecule is constituted by a set of bound electric charges with dynamics governed by the laws of quantum mechanics. These charges are sources of the quantized electromagnetic field which also binds them together, and thus the effects of their interaction with the field cannot be disregarded in principle. Consequently even overall neutral atoms, on which we focus our attention, are driven by a dynamics which is inextricably related to the dynamics of the quantized electromagnetic field. One of the most prominent aspects of the atom-held interaction is the existence of a cloud of virtual photons which dresses the atom even in the lowest possible energy state of the system. In this paper we review the static as well as the dynamic aspects of the theory of the virtual cloud around the neutral atoms. We begin by reviewing various forms of the atom-field coupling as well as various models of simplified atoms which will be used in the rest of the paper. The question then arises as how to characterize quantitatively the shape of the virtual cloud, and we show that the energy density of the electromagnetic field is a physical quantity suitable for this purpose. First a perturbative approach to calculating this shape is developed and applied to several physical models of a ground-state dressed atom. The next step is to consider virtual clouds which are out of equilibrium and examine their time development. This leads to the concept of half-dressed sources, which are discussed in a different physical context both in the absence and in the presence of real photons. In particular the role of the virtual cloud in ensuring causality of the field propagating in dressing and undressing processes is emphasized. Finally, the nature of the virtual cloud is further discussed in the light of theories concerning the dynamics of an atomic pair, the quantum theory of measurement and the effects of a driving electromagnetic field.
Introduction . The main theme of this chapter is the explicit calculation of the shape of the virtual cloud surrounding different kinds of ground-state sources. In Section 7.1 two of the three examples considered in Section 6.1 are taken up again, and it is argued that a convenient description of the shape of the virtual cloud is given by the energy density of the field around the source. This energy density is evaluated in detail for the static source of mesons and for the Fröhlich polaron. Section 7.2 is dedicated to an analogous calculation of the electric energy density around a two-level atom within a perturbation scheme. The virtual cloud around a two-level atom is again the subject of Section 7.3, where we evaluate the magnetic energy density as well as the coarse-grained energy density. From the results of the first three sections we conclude that the qualitative picture of the virtual cloud proposed in Section 6.2 is well founded. Moreover, the discussion of the two-level atom leads us to an important conclusion: the space surrounding an atom can be divided into a near zone and a far zone, where the energy density of the virtual cloud behaves differently as a function of the distance from the atom. In Section 7.4 we evaluate the energy density of the virtual cloud surrounding a slow free electron, separating classical and quantum contributions.
The distortions of the cloud of virtual photons surrounding a ground-state two-level atom, induced by an external field driving the atom, are investigated. It is first shown that if the driving field is coupled to the atom via diagonal dipole matrix elements, then a region of quasistability for the virtual cloud exists. Then the number of photons in this virtual cloud is evaluated by perturbation theory, as a function of the intensity of the external driving field. Finally, the analytical expression obtained is discussed using approximations appropriate to different ranges of the intensity of the driving field.
Specific properties of quantum field theory are described by considering the combination of the system under investigation and the cloud of virtual or real particles associated with the field. Such a structure is called a “dressed system”, in contrast with the bare one in the absence of the interaction with the field. The description of the properties of such clouds in various physical situations is, today, an active research area. Here, we present the main features associated with virtual and real dressings, focusing on photon dressing. In analogy to virtual photon clouds dressing electrons in vacuum, virtual phonon clouds appear in solid-state physics. The interaction between real photons and the schematized two-level structure of an atom paves the way to flexible quantum control. Here, a unifying Floquet engineering approach is applied to describe single- and multiple-dressed atom configurations. Connections with the past and present atomic physics experiments are presented.
A two-level atom interacting simultaneously with an external static field is reinvestigated. Here, first the Hamiltonian of the atom and the external field is diagonalized and then the interaction of the radiation field is considered. This method yields, directly, the state populations for the atom, and the lineshape and linewidth of the spontaneously emitted radiation. The earlier result on the state populations by Bali and Higgins has been compared with the present work and found to be in good agreement. The line shape of the emitted radiation is Lorenzian and the halfwidth is found to be increasing with increasing external perturbation. For the case where the atom is initially in the excited state, the intensity of the emitted radiation decreases with increasing perturbation and finally reaches a saturation limit. However, when the atom is considered to be in the ground state, initially, the intensity increases with increasing perturbation and it again reaches a saturation limit at a large perturbation field.
In quantum field theory, bare particles are dressed by a cloud of virtual particles to form physical particles. The virtual particles affect properties such as the mass and charge of the physical particles, and it is only these modified properties that can be measured in experiments, not the properties of the bare particles. The influence of virtual particles is prominent in the ultrastrong-coupling regime of cavity quantum electrodynamics (QED), which has recently been realised in several condensed-matter systems. In some of these systems, the effective interaction between atom-like transitions and the cavity photons can be switched on or off by external control pulses. This offers unprecedented possibilities for exploring quantum vacuum fluctuations and the relation between physical and bare particles. We consider a single three-level quantum system coupled to an optical resonator. Here we show that, by applying external electromagnetic pulses of suitable amplitude and frequency, each virtual photon dressing a physical excitation in cavity-QED systems can be converted into a physical observable photon, and back again. In this way, the hidden relationship between the bare and the physical excitations can be unravelled and becomes experimentally testable. The conversion between virtual and physical photons can be clearly pictured using Feynman diagrams with cut loops.