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Physical Review A

Cloud of virtual photons surrounding a two-level atom driven by an external field

G. Compagno, S. Vivirito, Franco Persico

Published Dec 1, 1992• 6 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.46.7303

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Cambridge University Press eBooks•Aug 3, 1995•0 citations
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.
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.
We present an interaction scheme that exhibits a dynamical effect of virtual photons carried by a vacuum-field dressed two-level atom in the ultrastrong-coupling regime. We show that, with the aid of an external driving field, virtual photons provide a transition matrix element that enables the atom to evolve coherently and reversibly to an auxiliary level accompanied by the emission of a real photon. The process corresponds to a type of vacuum Rabi oscillation, and we show that the effective vacuum Rabi frequency is proportional to the amplitude of a single virtual photon in the ground state. Therefore, the interaction scheme could serve as a probe of ground-state structures in the ultrastrong-coupling regime.
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.
The normalised intensity correlation function of resonance fluorescence radiation from two-level atoms is studied in various respects. In the first part of the paper the author discusses only interference effects for several uncoupled, linearly arranged, atoms. It is shown that, depending on the distance between the atoms, the direction of observation and the strength of the driving field, an antibunching effect as well as a very big bunching effect may be observed. In the second part of the paper he studies for the case of two atoms and weak external fields the influence of the interaction between the atoms by means of a perturbation theory. It is shown that the coupling between the atoms strongly modifies the normalised intensity correlation function in comparison with the case of uncoupled atoms. He takes as the driving field a coherent external field as well as laser light and thermal light.
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.