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).
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).
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.
POPULATION RATE EQUATIONS From the discussion in the preceding chapter, it is clear that population inversion is the basic condition for an optical gain. For any system in its normal state in thermal equilibrium, a low-energy level is always more populated than a high-energy level, hence there is no population inversion. Population inversion in a system can only be accomplished through a process called pumping by actively exciting the atoms in a low-energy level to a high-energy level. If left alone, the atoms in a system relax to thermal equilibrium. Therefore, population inversion is a nonequilibrium state that cannot be sustained without active pumping. To keep a constant optical gain, continuous pumping is required to maintain population inversion. This condition is clearly consistent with the law of conservation of energy: amplification of an optical wave leads to an increase in optical energy, which is possible only if the required energy is supplied by a source. Pumping is the process that supplies energy to the gain medium for the amplification of an optical wave. There are many different pumping techniques, including optical excitation, electric current injection, electric discharge, chemical reaction, and excitation with particle beams. The use of a specific pumping technique depends on the properties of the gain medium being pumped. The lasers and optical amplifiers of particular interest in photonic systems are made of either dielectric solid-state media doped with active ions, such as Nd:YAG and Er:glass fiber, or direct-gap semiconductors, such as GaAs and InP. For a dielectric gain medium, the most commonly used pumping technique is optical pumping using either an incoherent light source, such as a flashlamp or a light-emitting diode, or a coherent light source from another laser. A semiconductor gain medium can also be optically pumped, but it is usually pumped by electric current injection. In this section, we consider the general conditions for pumping to achieve population inversion. Detailed pumping mechanisms and physical setups are not addressed here because they depend on the specific gain medium used in a particular application. The net rate of increase of the population density in a given energy level is described by a rate equation. As we shall see below, pumping for population inversion in any practical gain medium always requires the participation of more than two energy levels.
In the preceding chapters, we discussed the manipulation and observation of atomic variables associated with the internal degrees of freedom. A complete separation between internal and external degrees of freedom, like position and momentum, is not always possible, however. It therefore appears appropriate to include a discussion of the mechanical effects of light, which have received increasing attention in recent years. The transfer of momentum between photons and atoms, first observed more than sixty years ago, had to wait for the wide availability of lasers to become a useful experimental tool. In particular the cooling of atoms and atomic ions to very low temperatures has found numerous applications. Light-induced forces That light exerts mechanical forces on massive particles like atoms may appear surprising. To motivate the existence of such an effect two different approaches are possible. The first approach considers the light as a collection of photons that carry, apart from energy and angular momentum, linear momentum as well. Photons interacting with atoms can therefore change the momentum of the atoms. The second approach considers light as a wave, i.e., an inhomogeneous electromagnetic field interacting with the atomic dipole moment. Both approaches provide a possible description for the numerous phenomena that can occur in this context, but in many situations, one of them turns out to be more intuitive or more useful for calculations than the other.
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).
The two- and three-level model systems considered in the preceding sections can describe a wide range of phenomena. On the other hand, these models are purely mathematical constructs that lack physical content. The connection to physical systems is arbitrary and must be made separately in each case. In this chapter, we take the first step in this direction: We discuss the internal degrees of freedom that an atom has available. By far the most important ones are the electric dipole moment, which is responsible for the coupling to external fields, and the angular momentum, which determines the selection rules for the optical transitions and couples to magnetic fields. Rotational symmetry Motivation The number of energy levels that contribute to the dynamics of a quantum mechanical system is a direct measure of the number of degrees of freedom required for a full description of the system. The systems in which we are interested always include electric dipole moments – the degrees of freedom that couple to the radiation field. The second most important contribution is the magnetic dipole moment associated with the atomic angular momentum. Electric and magnetic dipole moments are those degrees of freedom that couple to external fields. Other degrees of freedom do not couple strongly to external fields but they may still modify the behaviour of the system and its optical properties.