After the discussion of ionic solids we shift our attention to atomic vapours. Here, we discuss the dynamics of microscopic order within the angular momentum substates under the influence of light and magnetic fields. For this purpose, we combine optical pumping as outlined in Chapter 5 to prepare the ordered states, and polarisation-selective detection introduced in Chapter 6 for its observation. In contrast to the introductory sections, we no longer discuss these dynamics as mathematical models, but for specific physical systems, using experimental data to illustrate the theoretical description. The systems we use for this illustration are vapours of alkali metal atoms, in particular sodium. These one-electron systems allow the most direct application of the theoretical models developed above. In addition, we concentrate on electronic ground states, whose long lifetimes permit long observation times and correspondingly precise observations. Experimental arrangement General considerations Laser-induced dynamics This chapter surveys the coherent evolution of coherences between angular momentum sublevels. Optical pumping excites this microscopic order, and it evolves under the influence of external magnetic fields and the laser radiation. The primary goal of this section is to show how the mathematical models developed in the preceding sections apply to real physical systems. We discuss how the observed signals arise and by which parameters the experimenter can control the dynamics of these systems.
After the discussion of ionic solids we shift our attention to atomic vapours. Here, we discuss the dynamics of microscopic order within the angular momentum substates under the influence of light and magnetic fields. For this purpose, we combine optical pumping as outlined in Chapter 5 to prepare the ordered states, and polarisation-selective detection introduced in Chapter 6 for its observation. In contrast to the introductory sections, we no longer discuss these dynamics as mathematical models, but for specific physical systems, using experimental data to illustrate the theoretical description. The systems we use for this illustration are vapours of alkali metal atoms, in particular sodium. These one-electron systems allow the most direct application of the theoretical models developed above. In addition, we concentrate on electronic ground states, whose long lifetimes permit long observation times and correspondingly precise observations. Experimental arrangement General considerations Laser-induced dynamics This chapter surveys the coherent evolution of coherences between angular momentum sublevels. Optical pumping excites this microscopic order, and it evolves under the influence of external magnetic fields and the laser radiation. The primary goal of this section is to show how the mathematical models developed in the preceding sections apply to real physical systems. We discuss how the observed signals arise and by which parameters the experimenter can control the dynamics of these systems.
In all preceding chapters, we have tried to separate the effect of the light on the atoms from the reverse effect, the modification of the light by the atomic medium. In most cases this allows an explicit solution of the equations of motion and provides stable stationary states. In recent years, another approach to the interaction between light and matter has appeared, which emphasises strong coupling between the two. It uses the interactions as a tool to study general aspects of nonlinear dynamics. This chapter provides an introduction to this field, without trying to give a complete summary. Overview Resonant vapours as optically nonlinear media Mutual interactions So far, we have considered the effect of the laser on the atomic medium separately from the measurement of microscopic dynamics by the polarisation selective detection of transmitted light. In this approximation, the pump laser drives the atoms without suffering significant attenuation or polarisation changes. Conversely, the probe beam, which monitors the optical properties of the atomic medium, changes the microscopic state of the atoms only infinitesimally. This approach guarantees, e.g., that the response of the medium to the probe beam is linear. As stressed before, this assumption of one-sided interactions is always an approximation, since the conservation of energy and angular momentum make it impossible to change either of the two partial systems without compensating changes in the other part.
The ground electronic state of even such simple atoms as those of alkali elements has the set of sublevels. These sublevels are hyperfine (HF) components and magnetic sublevels. The collisions with particles of nonmagnetic buffer gas or even with walls (when walls have proper coating) do not mix practically the populations of ground state HF sublevels, if the orbital moment of electrons in the ground state is equal to zero. Due to this reason these sublevels may be extremely long lived. Because of this, for instance, the so-called effects of optical orientation and optical pumping are apparent in atoms of alkali metals. The radiation can pump practically all the atoms (with which there is effective interaction) to a single HF component. In a situation in which optical pumping is a minor effect, the monochromatic absorption line consists of separate lines corresponding to intra-atomic transitions. The optical pumping is not significant, for example, if the radiation intensity is so low that now pumping between HF sublevels occurs in the time it takes the atom to traverse the light beam. Under the conditions of optical pumping and when other nonlinear effects are present, the absorption line profile can undergo considerable alteration. Many theoretical and experimental investigations have been done in the laser spectroscopy of resonant transitions of atoms (atoms of alkali metals) under the conditions of optical pumping within ground state HF structure. A characteristic feature of all such investigations is the velocity-selective excitation of absorbing atoms. Also, as a rule, the value of HF splitting is not very big in comparison to Doppler broadening in these experiments. Under such conditions, the absorption spectra consists of Doppler- broadened lines with nonlinear resonances, which emerge when two fields of different frequencies or different propagation directions are employed. When only one monochromatic traveling wave is employed, optical pumping leads to formation of a single smooth absorption line occupying a position between the resonant transitions frequencies associated with HF components. As HF splitting grows, the line profile remains smooth, its width is approximately equal to the size of the HF splitting. The strength of the optical pumping from one ground state HF component to another is greater for greater HF splitting in comparison to the Doppler width. In this regard, Cs and Rb are the most typical of the alkali atoms (the HF splitting exceeds the Doppler width by a factor close to 20). This is the qualitative picture of the absorption line profile (particularly for a monochromatic radiation) under the conditions of optical pumping between the HF sublevels of the electronic ground state, this qualitative picture had formed by now.
After the brief discussion of the internal degrees of freedom of atomic systems, we give an overview of how these variables can acquire nonvanishing average values in an ensemble of atoms. Optical pumping was one of the first experimental schemes that allowed physical systems to be pushed far from equilibrium through the interaction with light, a direct consequence of angular momentum conservation and the symmetry properties of the interaction between atoms and radiation. Principle and overview Phenomenology Optical pumping (Happer 1972) is one of the earliest examples wherein optical radiation qualitatively modifies the properties of a material system. In its original implementation, it corresponds to a selective population of specific angular momentum states, starting from thermal equilibrium. In the idealised process depicted in Figure 5.1, the light brings the atomic system from the initially disordered state, in which the populations of degenerate levels are equal, into an ordered state where the internal state of all atoms is the same. If we consider only the material system, it appears as if the evolution from the initially disordered state into an ordered state, where the population of one level is higher than that of another level, violated the second law of thermodynamics. This process does not proceed spontaneously, however. It is the interaction with polarised light that drives the system and increased disorder in the radiation field compensates for the increase in the population difference in the material system (Enk and Nienhuis 1992).
This book provides a thorough introduction to the interaction of atoms and atomic ions with optical and magnetic fields. Particular emphasis is placed on the wealth of important multilevel effects, where atomic vapours exhibit anisotropic behaviour. As well as covering the classic two-level atom approach to light-atom interactions, a general multi-level formalism is also described in detail, and used to discuss optical pumping, two-dimensional spectroscopy and nonlinear optical dynamics. The final chapter deals with the mechanical effects of light, including the cooling and trapping of atoms. With full theoretical and experimental coverage, and over 250 illustrations, the book will be of great interest to graduate students of laser spectroscopy, quantum electronics and quantum optics, and to researchers in these fields.
Abstract A century ago Einstein introduced the notion of the linear momentum of a photon, h k, and analyzed its transfer to an atom (and back) in the establishment of thermodynamic equilibrium between black-body radiation and matter. In addition to a linear momentum, the photon also possesses an angular momentum, ħ, directed parallel (or antiparallel) to its propagation direction (the OZ axis in Fig. 4.1), depending on its polarization direction (left- or right-handed). This angular momentum is due to the spin of the photon, equal to 1. Half a century later, Kastler (1950) considered the use of the transfer of the angular momentum of a polarized photon to the angular momentum of an atom as a method of optical orientation of atoms. In essence, this was the first method to control atomic motion by means of low-intensity light, developed even before the advent of the laser; it which found widespread application in investigating and then using spin polarization effects in atomic physics. But even after lasers had made their appearance, the method of optical orientation of atoms (or pumping of certain magnetic sublevels in atoms) proved very important, specifically in the laser cooling of atoms (Chapter 5).
Two-dimensional spectroscopy is an extension of conventional spectroscopic methods that characterises resonant systems as a function of two frequency variables. We use this technique to improve on the characterisation of atomic media along the lines discussed in the preceding chapter. On a microscopic level, the most important physical process for two-dimensional spectroscopy is the transfer of coherence between different transitions. We introduce the basics of the technique and discuss a few specific examples to outline its potential. Fundamentals Motivation and principle Motivation The preceding chapter showed how light drives the internal dynamics of resonant atomic media and how the measurement of optical anisotropies allows us to monitor these dynamics. The experiments discussed in the preceding chapter, however, can provide only limited information about the system. Most physical systems have more degrees of freedom than we can observe by measurements on transmitted light. As another limitation, we have primarily considered atoms that evolve under their internal Hamiltonian, only weakly perturbed by the probe laser beam. The example of light-induced spin nutation showed that the dynamics of optically pumped atoms differ significantly from those of a free atom. Although it is possible to observe spin nutation for systems with more than two ground-state sublevels, such an experiment suffers from the damping that accompanies optical pumping. The damping drives the system rapidly to an equilibrium, too fast for detailed dynamical observations.