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.
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.
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.
Introduction The theoretical foundations for describing the influence of twisted light on atoms, ions and molecules are essentially the same as those leading to their cooling and trapping by ordinary plane wave laser light [1–4]. A third of a century has passed since the Doppler mechanism was first put forward by Wineland and Dehmelt as a mechanism for cooling ions [5], and then by Hänsch and Schawlaw for neutral atoms [6]. The key role played by the Doppler mechanism is best illustrated by the simplest case of one-dimensional optical molasses, where a two-level atom is subject to two identical counter-propagating plane waves of a frequency near to resonance with the atomic transition frequency. In terms of a classical description, at small velocities the atom experiences a friction force F = −α v , where v is the velocity vector of the atomic centre of mass parallel to the common axis of the light beams, and α is a friction coefficient. The friction force gradually cools the atoms to progressively smaller, albeit limited, velocities and can be made to operate in all three dimensions by use of multiple beams. The cooling technique based on the Doppler mechanism has been superseded by more effective cooling mechanisms, especially evaporative and Sisyphus cooling mechanisms, culminating, with the achievement of super-cooling, in the realisation of Bose-Einstein condensates (BECs) [7]. Nevertheless, the Doppler mechanism remains important as a mechanism for the early stages of cooling and still plays a key role in the interaction of atomic systems with laser light.
Chapter 11 presents the simplest and most intuitive approach to atom-optical interactions: the atom is modelled as a damped harmonic oscillator with spontaneous emission as the damping agent. The semiclassical viewpoint, in which the atom is treated as a quantum object but the fields are classical, is adopted throughout the chapter. Next, the two-level atom is introduced, which sets the stage for establishing light forces at the atomic level: the dipole-gradient force and the radiation pressure force. The Einstein B coefficient is revisited as stimulated dipole emission. Finally, the optical Bloch equations are used to reformulate more generally the appearance of optical forces and to describe the existence of atom Doppler cooling.
The dipole force, which avoids the closed cycle of pumping and spontaneous emission that renders laser cooling unsuitable for molecules, is conservative: without dissipation, particles entering a trap retain the energy to escape. Fortunately, dissipation need not involve spontaneous emission if it instead results from the decoherence or decay of the optical trapping field that is coupled to the particle. To enhance the weak attraction of an atom to its reflection, cavity-mediated cooling recycles light through multiple reflections, amplifying the force and the retardation - a process related to the mechanical amplification in a near confocal cavity [5]. Resonant cavities and structures can increase the retardation, but not the intensity, even when the atoms or particles lie outside them - e.g. when the cavity is the narrow-band coating of a single mirror. Plasmon resonances of a structured metal can enhance both the delay and the optical intensity. Such processes, possible with arrays of micromirrors, resemble speckle field cooling [6], except that spontaneous emission is again replaced by decay of the optical field, and offer a new class of cooling mechanisms in which weak cooling is extended over a broad array, rather than concentrated at the centre of a single external cavity.
Beams of atoms and molecules (N.F. Ramsey). Momentum exchange between matter and light (S. Stenholm). Quantum effects in atomic optics (D.F. Walls). New laser cooling mechanisms (C. Cohen-Tannoudji). Laser cooling configurations (G. Nienhuis). Velocity-selective coherent population trapping in one and two dimensions (E. Arimondo). Coupled-pendulum model of the forces on three-level atoms (M. Prentiss et al.). Laser cooling and manipulation of atoms and selected applications (S. Chu). Laser cooling and trapping of neutral atoms (W.D. Phillips). Search for montional quantization of laser-cooled atoms (R. Gupta, S. Padua, T. Bergeman, H. Metcalf). The low (temperature) road toward Bose-Einstein condensation in optically and magnetically trapped cesium atoms (Ch. Monroe, E. Comell, C. Wieman). Manipulation of atoms by laser light (W. Ertmer). Laser manipulation of helium: the limits of the semi-classical description (A. Aspect et al.). Light manipulation of atoms (V.1. Balykin). Atom traps and atom optics (D.E. Pritchard and W. Ketterle). Electromagnetic traps for, charged and neutral particles (W. Paul). Laser cooling of trapped ions (W.M. Itano et al.). High-resolution atomic spectroscopy of laser-cooled ions (D.J. Wineland et al.).