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Europhysics Letters (EPL)

Dressed Atoms and the Quantum Theory of Measurement

G. Compagno, Roberto Passante, Franco Persico

Published Jun 15, 1990• 13 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/12/4/003

Related papers

Further considerations on the nature of dressed states

G. Compagno, Roberto Passante, Franco Persico

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.

Cambridge University Press eBooks•Aug 3, 1995•0 citations

Bare bound states and the quantum theory of measurement

Giuseppe Compagno, Roberto Passante, Franco Persico

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.

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Strong-field Theory of Dressed Atoms and Dressed Photons

L. Lo Cascio, Franco Persico

We consider a two-level atom in a strong laser field, described by the Jaynes-Cummings Hamiltonian in the rotating-wave approximation, yielding the well known dressed states. Diagonalization of the total Hamiltonian is attained by introducing dressed-atomic and photon operators. The quantum theory of measurement of finite duration is used to explore the nature of the physical observables corresponding to the dressed operators. A measuring apparatus is contrived in order to observe the bare-atomic population and the bare-photon number in a dressed state of the system. It is shown that, if the duration of the measurement is longer than the Rabi period of the system, the apparatus leads to observation of the dressed-atomic population and of the dressed-photon number rather than of the corresponding bare quantities for which it was designed. Conceptual and practical consequences of this result are discussed.

Journal of Modern Optics•Jan 1, 1992•3 citations

Atoms dressed and partially dressed by the zero-point fluctuations of the electromagnetic field

Giuseppe Compagno, G. Massimo Palma, Roberto Passante +1 more

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.

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Atoms dressed by a real e.m. field

G. Compagno, Roberto Passante, Franco Persico

Introduction . The second part of the book is dedicated to the dressed atom, and it begins with this chapter, which deals mainly with the quantum-dynamical description of an atom dressed by a real electro-magnetic field. Here the emphasis is on the adjective ‘real’, by which we mean that the field is in an excited state populated by real photons and not just by the zero-point photon background. Due to the coupling discussed in the first part of the book, atom-photon correlations are established which admix, shift and split the levels of the system atom plus radiation field. The admixed and correlated states are called dressed-atom states. In Section 5.2 we obtain the Hamiltonian for an atom in a cavity with perfectly reflecting walls. The cavity selects a discrete set of field modes, and this leads us naturally to consider the simplest possible nontrivial atom-field system: the Jaynes-Cummings model describing a two-level atom coupled to a single-mode system. In Section 5.3 we develop the theory, based on a unitary transformation, to dress a two-level atom by a mode of the cavity populated by real photons. A necessary preliminary for dealing with more complicated atom-field models is the theory of spontaneous emission in free space, which is discussed in Section 5.4 in a Wigner-Weisskopf framework.

Cambridge University Press eBooks•Aug 3, 1995•1 citation

Detection of Half-Dressed Sources in Nonrelativistic QED

G. Compagno, Roberto Passante, Franco Persico

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.

Physica Scripta•Jan 1, 1988•12 citations
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.
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.
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 a two-level atom in a strong laser field, described by the Jaynes-Cummings Hamiltonian in the rotating-wave approximation, yielding the well known dressed states. Diagonalization of the total Hamiltonian is attained by introducing dressed-atomic and photon operators. The quantum theory of measurement of finite duration is used to explore the nature of the physical observables corresponding to the dressed operators. A measuring apparatus is contrived in order to observe the bare-atomic population and the bare-photon number in a dressed state of the system. It is shown that, if the duration of the measurement is longer than the Rabi period of the system, the apparatus leads to observation of the dressed-atomic population and of the dressed-photon number rather than of the corresponding bare quantities for which it was designed. Conceptual and practical consequences of this result are discussed.
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 second part of the book is dedicated to the dressed atom, and it begins with this chapter, which deals mainly with the quantum-dynamical description of an atom dressed by a real electro-magnetic field. Here the emphasis is on the adjective ‘real’, by which we mean that the field is in an excited state populated by real photons and not just by the zero-point photon background. Due to the coupling discussed in the first part of the book, atom-photon correlations are established which admix, shift and split the levels of the system atom plus radiation field. The admixed and correlated states are called dressed-atom states. In Section 5.2 we obtain the Hamiltonian for an atom in a cavity with perfectly reflecting walls. The cavity selects a discrete set of field modes, and this leads us naturally to consider the simplest possible nontrivial atom-field system: the Jaynes-Cummings model describing a two-level atom coupled to a single-mode system. In Section 5.3 we develop the theory, based on a unitary transformation, to dress a two-level atom by a mode of the cavity populated by real photons. A necessary preliminary for dealing with more complicated atom-field models is the theory of spontaneous emission in free space, which is discussed in Section 5.4 in a Wigner-Weisskopf framework.
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.