Laser cooling and trapping are based on the mechanical force an electromagnetic wave (EMW) exerts upon an atom. The force is generally explained as the result of the conservation law of the linear momentum of a photon and the atom. In contrast, we have directly derived the force from primary electromagnetism in order to clarify its origin. We regarded the atom as an electric dipole moment induced by the EMW, and examined the interaction between the dipole moment and the EMW. We applied a semiclassical theory in which the atom is quantized as a two-level system but the electromagnetic field is not; no photon is introduced. The results are consistent with the commonly accepted explanation, and explicitly demonstrate the contribution of the electric and magnetic fields to the force, in particular, the significance of the longitudinal magnetic field for the dipole force in laser trapping.
Laser cooling and trapping are based on the mechanical force an electromagnetic wave (EMW) exerts upon an atom. The force is generally explained as the result of the conservation law of the linear momentum of a photon and the atom. In contrast, we have directly derived the force from primary electromagnetism in order to clarify its origin. We regarded the atom as an electric dipole moment induced by the EMW, and examined the interaction between the dipole moment and the EMW. We applied a semiclassical theory in which the atom is quantized as a two-level system but the electromagnetic field is not; no photon is introduced. The results are consistent with the commonly accepted explanation, and explicitly demonstrate the contribution of the electric and magnetic fields to the force, in particular, the significance of the longitudinal magnetic field for the dipole force in laser trapping.
The usual form of electromagnetic forces is given by but for neutral atoms q = 0. The next order of force is the dipole term, but this also vanishes because neutral atoms have no inherent dipole moment. However, a dipole moment can be induced by a field, and this is most efficient if the field is alternating near the atomic resonance frequency. Since these frequencies are typically in the optical range, dipole moments are efficiently induced by shining nearly resonant light on the atoms. Laser cooling and trapping rely on the interaction between laser light and atoms to exert a controllable force on the atoms, and many sophisticated schemes have been developed using the special properties of the interaction. This chapter begins with the simplest schemes for exerting optical forces on atoms, namely a single-frequency light field interacting with a two-level atom. Although this is the simplest possible scheme, it is pedagogically valuable because it shows many of the features that will be encountered further on. The ultimate temperature using such a scheme is limited, but lower temperatures can be achieved with multilevel atoms. This topic is addressed later in the chapter. Two kinds of optical forces When an atom absorbs nearly resonant light, it makes a transition to the excited state, and its subsequent return to the ground state can be either by spontaneous or by stimulated emission. The nature of the optical force that arises from these two different processes is quite different, and will be described separately [1]. The spontaneous emission case is different from the familiar quantum mechanical calculations using state vectors to describe the state of the system, because spontaneous emission causes the state of the system to evolve from a pure state into a mixed state (see Exercise 6.9). Spontaneous emission is an essential ingredient for the dissipative nature of the optical forces in monochromatic light, and the density matrix is needed to describe it (see Chap. 6). When an atom absorbs light, its energy excites the atom and its angular momentum changes the electron's orbit. Both of these are internal atomic properties. However, the linear momentum of the light, can change only the external, translational motion of the atom.
This review describes the methods of trapping cold atoms in electromagnetic fields and in the combined electromagnetic and gravity fields. We discuss first the basic types of the dipole radiation forces used for cooling and trapping atoms in the laser fields. We outline next the fundamentals of the laser cooling of atoms and classify the temperature limits for basic laser cooling processes. The main body of the review is devoted to discussion of atom traps based on the dipole radiation forces, dipole magnetic forces, combined dipole radiation-magnetic forces, and the forces combined of the dipole radiation-magnetic and gravity forces. Physical fundamentals of atom traps operating as waveguides and cavities for cold atoms are also considered. The review ends with the applications of cold and trapped atoms in atomic, molecular and optical physics.
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.
This thesis describes theoretical and experimental work concerning radiation forces on atoms, with particular reference to rubidium atoms confined in a magneto-optical trap. After a short history of the field of laser cooling, a review of the semiclassical theory of mechanical interactions between two-level atoms and electromagnetic radiation is given. Different formulations of the semiclassical theory are discussed, including a new formulation in terms of momentum transfer amongst the plane wave modes of the electromagnetic field. Two important applications of light forces on atoms, namely 'optical molasses' and the 'magneto-optical trap', are then described with emphasis on experimental parameters. Three sub-Doppler cooling mechanisms, 'sisyphus cooling', 'motion-induced orientation cooling' and the 'magnetically-assisted sisyphus effect', are described and their role in optical molasses and the magneto-optical trap is discussed. A new study of the polarisation gradients which occur in 3-D monochromatic light fields is presented and quantifies their relative presence in different light field configurations. Polarisation gradient parameters are developed and shown to be directly related to the relativistic spin tensor of the light field. Implications of this polarisation gradient study for laser cooling work are discussed. The design, construction from scratch, operation and testing of a magneto-optical trap for rubidium are described, including novel designs for two vacuum cells. Preliminary experiments to characterise the trap are described and results are presented; they primarily concern the number and distribution of atoms in the trap. Finally. the theory of time domain spectroscopy is reviewed. The construction and testing of a pulsed dye laser for study of coherent transients in samples of laser-cooled atoms and a proposed experiment to measure the temperature of cold atoms using coherent transients are described. Factors expected to influence the shape of coherent transients in cold atoms are discussed.
It has been known for some time that the interaction of laser light with a free atom can give rise to electromagnetic pressure forces that act on its centre of mass. These forces have been extensively examined both theoretically and experimentally: see, for example Metcalf and van der Straten (5.1) or Adams and Riis (5.2). A simple model of a two-level atom subject to a plane electromagnetic wave may be shown to give rise to two kinds of force acting on the atom centre of mass. These are, a dissipative force arising from the absorption of the light by the atom and its subsequent spontaneous emission in a random direction and a dipole force arising from the non-uniformity of the field distribution which can attract the atom to the regions of intense field. These forces underpin the manipulation of atoms by lasers in a variety of beam configurations. The dissipative force has been exploited in the Doppler cooling of the atomic motion (5.3, 5.4) and the dipole force used for trapping (5.5), while a combination of these effects has led to the realisation of Bose-Einstein condensation (5.6). These forces are, of course, closely related to the ones discussed in Section 4.
Manipulation of cold atoms by lasers has so far been studied solely within the framework of the conventional dipole approximation, and the atom-light interaction has been treated using low order perturbation theory. Laser control of atomic motions has been ascribed exclusively to the corresponding light-induced dipole forces. In this work, we present a general theory to derive the potential experienced by an atom in a monochromatic laser field in a context analogous to the Born-Oppenheimer approximation for molecules in the field-free case. The formulation goes beyond the dipole approximation and gives rise to the field-atom coupling potential terms which so far have not been taken into consideration in theoretical or experimental studies. Contrary to conventional approaches, our method is based upon the many electron Floquet theory and remains valid also for high intensity laser fields (i.e., for a strongly nonperturbative atom-light interaction). As an illustration of the developed theory, we investigate the trapping of cold atoms in optical lattices. We find that for some atoms for specific laser parameters, despite the absence of the dipole force, the laser trapping is still possible due to the electric quadrupole forces. Namely, we show that by using realistic laser parameters one can form a quadrupole optical lattice which is sufficiently strong to trap Ca and Na atoms.