Table of contents

The physics of the electromagnetic vacuum, its fluctuations and its role in spontaneous emission has been studied since the early days of the quantum theory of radiation. In recent years there has been a renewed interest in the nature of the vacuum state and its potency in giving rise to observable effects. For example the question of amplification of photon signals and the way vacuum fluctuations may provide inescapable noise is fundamental to the theory of measurement. Quantum electrodynamics in cavities has become a very active area of research both experimentally and theoretically and the way the radiation field, even in vacuo, is changed by confinement is of interest and importance. The effective Einstein A-coefficient can be much smaller than in free space because the available modes are sparser in a cavity. Radiative connections such as the Lamb shift energies are also changed as the virtual photon modes are varied by the confinement. The existence of electromagnetic field energy (from the vacuum fluctuations) in the neighbourhood of atoms/molecules in their ground state is demonstrated by its effect on test molecules brought into the vicinity of the original sources. All the forces analogous to that of Van der Waals, including of course their Casimir retardations at long range, are explicable in terms of these virtual cloud effects.

The Adriatico Conference on "Vacuum in Non-Relativistic Matter-Radiation Systems" held in July 1987 brought together scientists in quantum optics, quantum field theorists and others interested in the electromagnetic vacuum. It was most successful in that the participants found enough mutual agreement but with clearly defined tensions between them to provide excitement and argument throughout the four days' meeting. This volume consists of most of the papers presented at the conference. It is clear that the collection ranges from the pedagogical and the review type article to research papers with original material.

The participants would like to thank Professor S Lundqvist and the Adriatico Research Conference Committee for their support and hospitality at the International Centre for Theoretical Physics in Trieste.

A Sicilian wine party will certainly be remembered by the participants as a most enjoyable social gathering.

We discuss the squeezing of vacuum fluctuations by resonant interaction with a suitably prepared atom. We demonstrate the crucial role of atomic dipole fluctuations in modifying the vacuum noise. We show how the generation of field squeezing in spontaneous and fluorescent processes is dependent on the squeezing of the atomic dipole.

Parts of the energy of any system containing charged particles stem from its coupling with the electromagnetic field; they change near conducting surfaces (mirrors), because these alter the normal modes of the field relative to unbounded space. Spontaneous decays are also affected. Such effects near a single plane mirror are reasonably familiar; between parallel mirrors (separation L) they are now becoming measurable, mainly in Rydberg states. They are interesting also to theory, partly because they raise questions about the role of classical and other interpretations in quantum physics.

For L small compared to the important transition wavelengths, frequency shifts in neutral atoms are essentially electrostatic (unretarded), and of order 1/L³. For large L, they are conditioned by retardation, of order (1/L) log L, and subject to weak but peculiar resonance effects when L is tuned to a downward transition wavelength. Some interpretations emerge by hindsight, but seem to have little predictive power.

We review the basic principles and results of a formulation of quantum-electrodynamics based on the self-energy of the electron, rather than quantized fields. The applications include relativistic spontaneous emission rates, the effect of cavities on Lamb-shift, spontaneous emission and Casimir-Polder forces. We also review the relativistic two-body equations including radiative processes with applications to hydrogen, muonium and positronium spectra.

In this paper I review those properties of quantum electrodynamics which lead to nonlinear effects in the dynamics of the electromagnetic field.

The environmental effects on the rate of radiative transitions, the Lamb shift and mass renormalization, produced by external modifications of the electromagnetic vacuum, are studied from the point of view of stochastic electrodynamics (SED), using the harmonic oscillator as an atomic model. The vacuum can be modified by adding external radiation to alter the energy content of its modes, or by introducing metallic objects that alter the mode distribution. General formulas are derived for the effects of these modifications on the radiative corrections and some specific cases are calculated yielding the same results as the quantum formalism.

A fluctuation-dissipation theorem is obtained, which guarantees the independence of the quantum states from environmental changes; only the radiative corrections are affected by the surroundings. Some conceptual differences between this and the usual quantum approaches are discussed. SED is shown to offer a unified and physically clear explanation of the various external effects on the radiative corrections.

A nonrelativistic, quantum-mechanical neutral source is considered, which is coupled to the quantized e.m. field in vacuo. The dressed ground state of the coupled system is obtained in terms of the bare ground state and of other excited states in absence of coupling. This dressed ground state is characterized by a cloud of virtual photons in the space surrounding the source, which yields nonvanishing quantum averages of the magnetic and electric field energy densities. The source-field coupling is modeled by a Craig-Power Hamiltonian, and the ground state energy densities are shown to behave like r^-7 at distance r from the dressed source. Half-dressed sources are introduced as sources surrounded by incomplete virtual photon clouds. The time evolution of an initially bare source is discussed in terms of time-dependent field energy densities in the Heisenberg picture and it is shown to lead asymptotically to a fully dressed ground state source. The results obtained, as well as the limits of validity of the approach adopted, are discussed in the light of previous theories for charged half-dressed sources in quantum electro- and mesodynamics.

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.

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.

This paper answers the title question by giving an operational definition of quantum jumps based on measurement theory. This definition forms the basis of a theory of quantum jumps which leads to a number of testable predictions. Experiments are proposed to test the theory. The suggested experiments also test the quantum Zeno paradox, i.e., they test the proposition that frequent observation of a quantum system inhibits quantum jumps in that system.

The unequal time commutators of the field operators of the free electromagnetic field, and their physical interpretation in terms of the simultaneous measurability of the EM field components at different space time points, have long been known since the work of Jordan and Pauli, and Bohr and Rosenfeld. The behaviour of these commutators can be understood in terms of the field of uncertain strength unavoidably generated as a consequence of a measurement of field strength in some region in space time. This field propagates freely in space, and if present in some other region in space time at which another field measurement is made, will affect the outcome of this measurement in an uncontrollable way.

In the presence of matter, these unequal time commutators are modified, with readily understandable consequences for the measurability properties of the field. When calculating these commutators, the matter can be treated in two different ways. First of all is the case in which the matter occurs in bulk as in a macroscopic dielectric, with the quantized description of the EM field obtained by imposing classical boundary conditions on the EM field. The second case is that in which the matter is treated quantum mechanically. In both cases, the modified commutators contain terms whose physical significance can be understood as representing the effect of the field generated by a field measurement being scattered by the matter present. Thus one measurement can affect another either through the disturbing field propagating freely from one space time region to the other, or through the scattering of this field.

In this paper, an outline is given of the general kinds of results obtained, how they can be obtained in each case, and where the results have played a role in determining the behaviour of certain quantum systems including the Glauber model of a photodetector, and in the theory of frequency filtered photon detection.

Several experimental schemes of vacuum-confinement in electromagnetic-bounded structures are presented together with related results involving Spontaneously Emitting (SE) molecules. Striking anomalies in the SE spatial-distribution and decay-times are detected. In addition, an anomalous "zero-threshold-laser" behaviour of molecular Stimulated Emission (StE) in a single-mode Casimir-type microscopic cavity is reported. This novel effect is due to an unexpected collective molecular process taking place at an exceedingly low excitation level in the optical-pumping scheme. In the framework of "Phase-transition" theory this effect corresponds to an order-disorder transition taking place at a critical-temperature T_c which is virtually infinite.

We discuss general notions of the regularisation and renormalisation of ground-state observables in quantum field theory. We evoke a theorem by Ramanujan to introduce the concept of the cut-off independent parts of vacuum observables and discuss their measurement and methods for their calculation. The role of Atiyah-Patodi-Singer spectral invariants in determining the vacuum structure of relativistic matter fields is illustrated.

Theories of the interactions of charged particles and the electromagnetic vacuum are reviewed. A new technique is introduced in which a canonical transformation is used to transform the Hamiltonian to one without counter-rotating terms. In the new Hamiltonian, the dressed ground-state coincides with the ground-state of the free Hamiltonian. A feature of the Hamiltonian is that it can be regarded as having a symmetric combination of momentum (p.A) and position (d.E) couplings. The new theory is able to treat transitions occurring on time-scales of an optical period or less. The coupling varies as f^1/2 at low frequencies, and so the theory does not have the infra-red divergence or causality problems that occur in minimal coupling theories.

This problem has a long history of confusion and error. One crucial question is whether the leading correction δμ/μ is of order α/mL or α/(mL)², where L is the distance from or between the mirrors. For a particle of infinite mass but finite μ, δμ/μ is of order α/(μL)² in the weak field limit B → 0. The same is true in quantum mechanics and remains true for a (non-second-quantized) Dirac electron.

Several quantum optics problems in which spontaneous emission and/or vacuum fluctuations play an important role are discussed. These include the spontaneous decay of an atom and the damping of the field in a cavity (both in the presence of ordinary and `squeezed' vacuum), the correlated (spontaneous) emission laser or CEL, and quantum beats in V- and Λ-type three-level atoms.

A review of the status of the Lamb shift of the n = 2 state of hydrogen is given. An expression containing all known theoretical contributions, including recently calculated recoil effects, is provided. Remaining uncalculated terms are briefly discussed.

The interpretation of gauge transformations in the semiclassical theory of radiation has been the subject of much discussion and controversy over the past ten years or so. A consistent formulation of this problem that involves a gauge-independent Heisenberg picture of the motion and related gauge-dependent Schrödinger pictures is presented. The role of the canonical momenta and their representation as differential operators on wave functions is clarified. Some discussion of the physical interpretation is also given.

Suppose there is a zero-point field corresponding to the zero-point energy in vacuum. We can use time-dependent perturbation theory to calculate the influence of the field on the energy of atoms. When the field is applied to atoms which are in the ground state initially, the energy change of the atoms shows a linear dependence on time with a constant energy shift. This constant shift is the usual energy shift of atoms.

Some thoughts on the electromagnetic vacuum are presented in connection with the vacuum and source fields as alternative physical bases for understanding spontaneous emission, the Lamb shift, Casimir effects, van der Waals forces, and the "thermalization" of vacuum fluctuations for a uniformly accelerated observer.

`And sometimes it seemed that something never yet seen yet long desired was about to happen, that a veil would drop from it all; but then it passed, nothing happened, the riddle remained unsolved, the secret spell unbroken... and still one knew nothing perhaps, was still waiting and listening.' Hermann Hesse, Narcissus and Goldmund

One of the most surprising facets of the world-view presented by quantum field theory is the nature and the potency of the vacuum. To the layman it is quite unexpected that the state consisting of no particles is non-trivial and efficacious. In this lecture these circumstances are examined in the context of the electromagnetic field as an introduction to the salient concern of the conference. Starting with elementary quantum mechanics we build up the structures required to (i) obtain, and (ii) use the wave functional

for the electromagnetic vacuum. We demonstrate some physical consequences of vacuum fluctuations in such diverse topics as colloidal stability and the Lamb shift. Involved in these calculations are perturbations on the vacuum due to atoms/molecules. Changes in the vacuum due to confinement are discussed in a non-perturbative fashion. A re-look at Jaynes' neoclassical electrodynamics will be mentioned. The lecture will finish with an introduction to the Heisenberg form for the electromagnetic fields in the neighbourhood of molecules.

The phase diffusion coefficient for the laser is due to various mixtures of spontaneous emission and vacuum fluctuation noise depending upon the type of spectrometer used or measurement made.

Some of the possible reasons for the presently existing statistically significant discrepancy between the experimental and the theoretical values of the electron (g - 2) would lead to fundamental revisions of QED.

The electromagnetic field operators in the vicinity of a neutral molecule are obtained in the Heisenberg picture. The fields are found using the multipolar Hamiltonian and the interaction includes electric dipole, magnetic dipole, electric quadrupole, and diamagnetic couplings. These fields are used to calculate the dispersion energy between two neutral molecules. The dispersion energy may be obtained by treating one molecule as a test body and calculating its response to the field of the other. A note-worthy feature of this test-body approach is that the energy expressions so obtained are valid for all intermolecular separations outside overlap and retardation effects are fully taken into account. The method is applied to the calculation of dispersion energy between a pair of molecules with different polarizability characteristics. The contribution of the diamagnetic coupling to the energy shift is also presented. The theory is adapted to the calculation of N-molecule dispersion interactions and applied to 3- and 4-molecule systems.