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Physica Scripta

Detection of Half-Dressed Sources in Nonrelativistic QED

G. Compagno, Roberto Passante, Franco Persico

Published Jan 1, 1988• 12 citations
Publisher

Abstract

A previously introduced model for half-dressed sources, namely sources of a quantized field surrounded by incomplete clouds of virtual quanta, is discussed in the framework of nonrelativistic QED. This model describes a ground-state nonrelativistic atom coupled to the e.m. field through the Craig-Power Hamiltonian. An incomplete cloud of virtual quanta is obtained by assuming the atom to be in its bare ground state at t = 0. The time evolution of the incomplete virtual field is discussed; its energy density is investigated in detail and it is shown to be highly singular. Also, the complementary case of the fate of the virtual field of a source being decoupled from the field at t = 0 is studied. The interaction of this field with a test oscillator is studied and it is shown that the virtual field can release energy to a model detector, consisting of an oscillator, which is assumed to be initially at rest.

DOI
10.1088/0031-8949/1988/t21/007

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We study the radiative emission due to the self-dressing of a two-level atom, initially in its bare ground state, interacting with the zero-point electromagnetic field. Evolution in time leads to the formation of a dressed ground state of lower energy. This energy difference between bare and dressed ground state is taken into account by the emission of real photons. In order to describe this aspect of the self-dressing process we study the transition probability amplitude from the initial bare state to an asymptotic state consisting of the atom in its dressed ground state plus some real photons. Adopting nonperturbative techniques based on the resolvent method we find that the bare-dressed transition occurs at the lowest order with the emission of two photons. The spectral distribution obtained shows that there is a probability for emission of photons at frequency of the order of the atom's transition frequency.

Physical Review A•Feb 5, 2002•5 citations
A previously introduced model for half-dressed sources, namely sources of a quantized field surrounded by incomplete clouds of virtual quanta, is discussed in the framework of nonrelativistic QED. This model describes a ground-state nonrelativistic atom coupled to the e.m. field through the Craig-Power Hamiltonian. An incomplete cloud of virtual quanta is obtained by assuming the atom to be in its bare ground state at t = 0. The time evolution of the incomplete virtual field is discussed; its energy density is investigated in detail and it is shown to be highly singular. Also, the complementary case of the fate of the virtual field of a source being decoupled from the field at t = 0 is studied. The interaction of this field with a test oscillator is studied and it is shown that the virtual field can release energy to a model detector, consisting of an oscillator, which is assumed to be initially at rest.
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.
A gedanken experiment is discussed to measure the population of a two-level atom interacting with a single-mode radiation field. The atom-field system is taken to be in the dressed ground state. The measuring apparatus consists of a classical pointer linearly coupled to the atom. It is shown that the result of the measurement depends strongly on the duration τ on the measuring process. For τ shorter than the time of the vacuum fluctuations creating the virtual photon cloud around the atom, the pointer perceives the atom as bare. In the opposite case the atom is perceived by the pointer as dressed or partially dressed. The insight gained in the nature of the virtual photon cloud, in the meaning of the quantum detection process and in the preparation of partially dressed states, is discussed in the light of this result.
A bare bound state is modeled as a ground-state two-level atom which at t=0 is deprived of most of the low-frequency components of its virtual radiation field. This state is expected to evolve into a fully dressed ground state through reconstruction of the full cloud of virtual quanta. The quantum theory of measurement is used to show that the dynamics of the two-level atom due to this reconstruction can be detected experimentally under appropriate conditions. The measuring apparatus is modeled by a pointer coupled to the atom. The theory predicts that for sufficiently short measurements the bound state can be used as a probe of the dressing process. This result is discussed in connection with the theory of the excitonic polaron in a semiconductor.
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.
Introduction . In this final chapter we review two topics of the literature concerning dressed atoms which are of conceptual relevance and capable of shedding some light on the physical meaning and significance of atomic dressing. The first section is devoted to some recent work in connection with the quantum theory of measurement. We include the measuring apparatus in the Hamiltonian along with an appropriate apparatus-atom coupling. We argue that the theory of measurement of finite duration provides us with a tool for detecting the spectral composition of the virtual cloud surrounding an atom. In fact, we show that in a measurement of duration T on a two-level atom fully dressed by the vacuum fluctuations, as discussed in Chapters 6 and 7, the apparatus perceives the atom as dressed only by photons of frequency larger than T -1 . In the case of a two-level atom dressed by a single-mode field populated by real photons, discussed in Chapter 5, we show that if T is smaller than the inverse Rabi frequency ħΔ -1 , the atom is perceived by the apparatus as bare; on the contrary, if T is larger than ħΔ -1 , the atom is perceived as dressed. The time scales for the two cases of dressing, by vacuum fluctuations or by a real single-mode field, are very different, but the similarity of the effects indicates a common physical aspect of the two kinds of dressing.
We study the radiative emission due to the self-dressing of a two-level atom, initially in its bare ground state, interacting with the zero-point electromagnetic field. Evolution in time leads to the formation of a dressed ground state of lower energy. This energy difference between bare and dressed ground state is taken into account by the emission of real photons. In order to describe this aspect of the self-dressing process we study the transition probability amplitude from the initial bare state to an asymptotic state consisting of the atom in its dressed ground state plus some real photons. Adopting nonperturbative techniques based on the resolvent method we find that the bare-dressed transition occurs at the lowest order with the emission of two photons. The spectral distribution obtained shows that there is a probability for emission of photons at frequency of the order of the atom's transition frequency.