In this contribution quantum-effects in the radiation-atom interaction will be reviewed. It is well known that most of the phenomena involving laser light can be described by semi-classical methods however phenomena such as laser noise the spectra and photon statistics of resonance fluorescence and the interaction of atoms in the single-atom maser require a quantization of the radiation field. In this paper we will describe results on the latter two effects. We will start with the discussion of resonance fluorescence. 1. RESONANCE FLUORESCENCE The resonant interaction of laser light with atomic systems has received considerable theoretical and experimental attention over the past decade. Until the advent of the laser light sources for spectroscopy consisted of ordinary spectral lamps excited by DC or RF discharges and produced light having a very broad spectral width and hence very short correlation time and a relatively low intensity. For such fields both the experimental and theoretical results are in general well understood. However the development of the laser made available light sources which are sufficiently intense that an atomic (or molecular) transition can be very easily saturated. In addition the lasers are highly monochromatic having a coherence time much greater than typical natural lifetimes of excited atomic states and finally tunable making it possible to selectively excite particular atomic transitions. The theoretical analysis of this physical situation requires the use of techniques more general than
In this contribution quantum-effects in the radiation-atom interaction will be reviewed. It is well known that most of the phenomena involving laser light can be described by semi-classical methods however phenomena such as laser noise the spectra and photon statistics of resonance fluorescence and the interaction of atoms in the single-atom maser require a quantization of the radiation field. In this paper we will describe results on the latter two effects. We will start with the discussion of resonance fluorescence. 1. RESONANCE FLUORESCENCE The resonant interaction of laser light with atomic systems has received considerable theoretical and experimental attention over the past decade. Until the advent of the laser light sources for spectroscopy consisted of ordinary spectral lamps excited by DC or RF discharges and produced light having a very broad spectral width and hence very short correlation time and a relatively low intensity. For such fields both the experimental and theoretical results are in general well understood. However the development of the laser made available light sources which are sufficiently intense that an atomic (or molecular) transition can be very easily saturated. In addition the lasers are highly monochromatic having a coherence time much greater than typical natural lifetimes of excited atomic states and finally tunable making it possible to selectively excite particular atomic transitions. The theoretical analysis of this physical situation requires the use of techniques more general than
Modern methods of laser spectroscopy allow the study of single atoms or ions in an unperturbed environment. This has opened up interesting new experiments, an among them is the detailed study of radiation-atom coupling. This chapter reviews the following two experiments of this type: the single-atom maser and the study of the resonance fluorescence of a single stored ion. The simplest and most fundamental system for studying radiation-matter coupling is a single two-level atom interacting with a single mode of an electromagnetic field in a cavity. There is another aspect of the single-atom maser which is very interesting: the non-classical statistics of the photons in the cavity. The results obtained for the single-atom maser also give a new insight into the statistical properties of masers and lasers. A problem in radiation-matter interaction which has received a lot of interest is resonance fluorescence. The experiments to investigate antibunching in resonance fluorescence have been performed by means of laser-excited collimated atomic beams.
The phenomenon of resonance fluorescence provides an interesting manifestation of the quantum theory of light and is a “real world” application of the material of the Chapters 8 and 9. In this process, a two-level atom is typically driven by a resonant continuous-wave laser field and the spectral and quantum statistical properties of the fluorescent light emitted by the atom are measured. Experimentally this can be achieved by scattering a laser off a collimated atomic beam such that the directions of the laser beam, atomic beam, and detector axis are mutually perpendicular as shown in Fig. 10.1. If the driving field is monochromatic, then at low excitation intensity the atom absorbs a photon at the excitation frequency and reemits it at the same frequency as a consequence of conservation of energy. The spectral width of the fluorescent light is therefore very narrow. The situation, however, is considerably more complicated when the excitation intensity increases and the Rabi frequency associated with the driving field becomes comparable to, or larger than, the atomic linewidth. At such intensity levels, the Rabi oscillations show up as a modulation of the quantum dipole moment and sidebands start emerging in the spectrum of the emitted radiation. This so-called dynamic Stark splitting is an interesting feature of the atom–field interaction. In addition to that, the fluorescent light exhibits certain nonclassical properties including photon antibunching and squeezing. In this chapter, we develop a theory of resonance fluorescence to explain these phenomena.
The review describes and interprets the basic phenomena recently observed in the interaction between free atoms and laser radiation. Some of these have been known for a long time in magnetic resonance but in the optical range, the situation is strongly modified because of spontaneous emission and the Doppler effect. Therefore, particular attention is paid to resonance fluorescence and Doppler-free spectroscopy but without dwelling on applications. Transient effects are also discussed, but all the phenomena which characterize, not specifically the interaction between atoms and fields, but the free evolution of atoms after coherent excitation are ignored. Pulse propagation experiments are described in detail and multiphoton processes are considered, with special emphasis on Doppler-free multiphoton excitation and resonant multiphoton ionization.
An atomic electron, in the vacuum of photons, can emit and reabsorb photons of any frequency. Such processes give rise to well known radiative corrections (Lamb—shift, g — 2, natural width of excited states...). We review in this paper similar effects which can be induced by the interaction of an atomic electron with an incident electromagnetic wave, and we try to get some physical insight in radiative processes by comparing these two types of « spontaneous » and « induced » effects. Optical pumping methods have been very useful for studying how atoms are perturbed by optical or RF photons. The Zeeman sublevels of an atomic ground state are broadened and shifted by a resonant or quasiresonant optical irradiation. The corresponding light-shifts (or « Lamp-shifts » as A. Kastler called them) are due to virtual absorptions and reemissions of incident photons. Another example of an induced effect is the modification of the magnetic properties of an atomic level due to a high frequency non resonant RF irradiation. The Larmor precession is slowed down and becomes anisotropic. The two previous examples correspond to two situations leading to simple calculations. For a resonant or quasiresonant excitation, a single atomic transition needs to be considered. Non perturbative treatments can be given which include the effect of the atom field coupling to all orders. For example, the « dressed atom » approach allows a unified treatment of various effects such as light shifts, Autler-Townes doublets resonance fluorescence triplets... On the other hand, for a high frequency irradiation, all atomic transitions must be included. It is possible in this case to derive an effective hamiltonian describing, to lowest order in the fine structure constant α, how electronic energy levels are perturbed in the presence of N photons ω. The remaining part of the paper is devoted to the analysis of such a situation. The terms of the effective hamiltonian proportional to the number N of incident photons correspond to the induced effects. They can be fully interpreted in semiclassical terms and they describe how the slow motion of the electron in the external static fields is modified by the high frequency vibration in the incident monochromatic wave. For example, the vibrating electron averages the static potential over a finite length, the angular oscillation of the spin reduces the effective magnetic moment. The remaining terms, which are independent of N, exist even in the vacuum of photons (N = 0) and describe the contribution of the mode ω to spontaneous radiative corrections. It is possible to split them into two parts. The first one has the same structure as the N-dependent terms, with N replaced by 1/2. It describes the corrections due to the vibration of the electron in vacuum fluctuations which have a spectral power density ħω/2 per mode. The second part represents the effect of radiation reaction, i.e. the interaction of the electron with its self field. Such an interpretation is confirmed by a Heisenberg equations approach where the total force acting upon the electron is split into two physical (i.e. hermitian) parts representing respectively the effect of the vacuum « free » field and the effect of the « source » field produced by the electron itself. These considerations are finally applied to the problem of the positive sign of g - 2. The g-factor can be written as 2 ωL/ωc, where ω L is the Larmor frequency of the spin and ωc the cyclotron frequency of the charge for an electron in a weak static field B 0. In the absence of radiative corrections, g = 2, and ω L = ωc. To lowest order in 1/c (order zero), radiation reaction slows down ωc but not ωL (a charge is more coupled to its self field than a magnetic moment). The effect of vacuum fluctuations appears only at order 2 in 1/c and corresponds to relativistic and magnetic effects which slow down both ωL and ωc. Therefore, it appears that, in the non relativistic domain, the main effect is a reduction of ωc by radiation reaction and this explains why 2 ωL/ωc becomes larger than 2. A complete relativistic calculation (to all orders in 1/ c, but to lowest order in α) does not change this conclusion since the contribution of non relativistic modes (ħω < mc2) is predominant in the integral giving g — 2.
In this chapter, we discuss a purely quantum approach to the interaction between an atom and the electromagnetic field. In this treatment, the atom and electromagnetic field form a single quantum system, whose evolution is handled globally within a unified formalism. This will thus have the merit of being fully consistent from the theoretical standpoint. But the main advantage in an entirely quantum approach is that it can treat the full range of matter–radiation interaction phenomena. In particular, it provides a rigorous description of the spontaneous emission of light by an excited atom , something that falls outside the scope of the semi-classical framework applied in Chapters 2 and 3, where the lifetime of an excited atomic state had to be fed in phenomenologically. It can describe other phenomena of the same type, such as parametric fluorescence by a nonlinear crystal subjected to pumping radiation (see Chapter 7), which underlies many recent developments in quantum optics. The fully quantum approach also has the merit of allowing a simple interpretation in terms of photons for the various matter–radiation interaction processes, such as absorption, stimulated emission, scattering, and also the basic processes of nonlinear optics. Indeed, it provides a unified framework for both stimulated and spontaneous processes. Finally, it can be used to tackle completely new situations where matter and radiation interact, which lie outside the scope of any semi-classical description, such as cavity quantum electrodynamics or the production of single-photon or entangled-photons states .
. In this paper experiments performed with the one-atom maser are reviewed. Furthermore, possible experiments to test basic quantum physics are discussed. Introduction, the One-Atom-Maser The most promising avenue to study the generation process of radiation in lasers and masers is to drive a maser consisting of a single mode cavity by single atoms. This system, at first glance, seems to be another example of a Gedanken-experiment treated in the pioneering work of Jaynes and Cummings (1963), but such a one-atom maser (Meschede, Walther and Müller, 1985) really exists and can in addition be used to study the basic principles of radiation-atom interaction. The advantages of the system are: it is the first maser which sustains oscillations with less than one atom on the average in the cavity, this setup allows to study in detail the conditions necessary to obtain nonclassical radiation, especially radiation with sub-Poissonian photon statistics in a maser system directly in a Poissonian pumping process, and it is possible to study a variety of phenomena of a quantum field including the quantum measurement process. What are the tools that make this device work: It was the enormous progress in constructing superconducting cavities together with the laser preparation of highly excited atoms – Rydberg atoms – that have made the realization of such a one-atom maser possible.