Atom traps Light forces It is well known that a light beam carries momentum and that the scattering of light by an object produces a force. This property of light was first demonstrated by Frish [139] through the observation of a very small transverse deflection (3 × 10 –5 rad) in a sodium atomic beam exposed to light from a resonance lamp. With the invention of the laser, it became easier to observe effects of this kind because the strength of the force is greatly enhanced by the use of intense and highly directional light fields, as demonstrated by Ashkin [20, 21] with the manipulation of transparent dielectric spheres suspended in water. The results obtained by Frish and Ashkin raised the possibility of using light forces to control the motion of neutral atoms. Although the understanding of light forces acting on atoms was already established by the end of the 1970s, unambiguous demonstration of atom cooling and trapping was not accomplished before the mid 1980s. In this section we discuss some fundamental aspects of light forces and schemes employed to cool and trap neutral atoms. The light force exerted on an atom can be of two types: a dissipative, spontaneous force and a conservative, dipole force. The spontaneous force arises from the impulse experienced by an atom when it absorbs or emits a quantum of photon momentum.
Atom traps Light forces It is well known that a light beam carries momentum and that the scattering of light by an object produces a force. This property of light was first demonstrated by Frish [139] through the observation of a very small transverse deflection (3 × 10 –5 rad) in a sodium atomic beam exposed to light from a resonance lamp. With the invention of the laser, it became easier to observe effects of this kind because the strength of the force is greatly enhanced by the use of intense and highly directional light fields, as demonstrated by Ashkin [20, 21] with the manipulation of transparent dielectric spheres suspended in water. The results obtained by Frish and Ashkin raised the possibility of using light forces to control the motion of neutral atoms. Although the understanding of light forces acting on atoms was already established by the end of the 1970s, unambiguous demonstration of atom cooling and trapping was not accomplished before the mid 1980s. In this section we discuss some fundamental aspects of light forces and schemes employed to cool and trap neutral atoms. The light force exerted on an atom can be of two types: a dissipative, spontaneous force and a conservative, dipole force. The spontaneous force arises from the impulse experienced by an atom when it absorbs or emits a quantum of photon momentum.
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.
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.
The development of laser cooling has an important impact on many aspects of atomic physics and quantum optics. The efforts to understand the various types of force exerted on atoms by laser light have led to some interesting physics and it is now possible for extremely cold clouds of atoms to be produced, which can be confined in atom traps or formed into very monoenergetic atomic beams. There are many new possibilities to explore in this ultra-cold regime where quantum effects are significant, in addition to the potential for great improvements in precision measurements made by r.f. and laser spectroscopy.
We present a simple review of the basic physical processes allowing one to control, with laser beams, the velocity and the position of neutral atoms. The control of the velocity corresponds to a cooling of atoms, that is, a reduction of the atomic velocity spread around a given value. The control of the position means a trapping of atoms in real space. The best present performances will be given, in terms of the lowest temperatures and the highest densities. The corresponding highest quantum degeneracy will also be estimated. It is imposed by fundamental limits, which will be described briefly. We also give the general trends in this field of research and outline the new directions which look promising for observing quantum statistical effects in laser cooled atomic samples, but which are for the moment restricted by unsolved problems. Introducing the Simple Schemes The radiative forces acting on atoms in a light field can be split into two parts, a reactive one and a dissipative one. The dissipative force (radiation pressure), which basically involves scattering processes, is velocity dependent. We will see that this dependence leads to the Doppler cooling scheme and to the concept of optical molasses, and we will give the corresponding minimal achievable temperature. The dissipative force can be made position dependent, through a gradient of the magnetic field, so that the atoms are also trapped in the so-called magneto-optical trap.
We propose several ideas for neutral atom traps which utilize spontaneous light forces produced by static laser beams. Although the “optical Earnshaw theorem”1 would seem to prohibit such traps, the theorem does not apply if the proportionality constant between force and light intensity is made to vary with position. We suggest possible ways to accomplish this: Zeeman tuning the atom’s resonant frequency by applying a changing magnetic field; varying the quantization axis of the system via a magnetic field cork-screw; utilizing optical pumping effects which arise from matrix element imbalances between hyperfine sublevels in certain atoms. These traps are true in the sense that they provide a potential energy minimum in three dimensions, as well as dissipative cooling. Compared with gradient force light traps, these traps are many times deeper, a million times larger, and can be operated cw.
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.