Introduction and review of quantum mechanics: Review of Quantum Mechanics.- The Density Matrix.- Force on Two-Level Atoms.- Multi-Level Atoms.- General Properties Concerning Laser Cooling. Cooling and Trapping: Deceleration of an Atomic Beam.- Optical Molasses.- Cooling Below the Doppler Limit.- The Dipole Force.- Magentic Trapping of Neutral Atoms.- Optical Traps for Neutral Atoms.- Evaporative Cooling. Applications: Newtonian Atom Optics.- Ultra-Cold Collisions.- deBrooglie-Wave Optics.- Optical Lattices.- Bose -Einstein Condensation.- Dark States.
Introduction and review of quantum mechanics: Review of Quantum Mechanics.- The Density Matrix.- Force on Two-Level Atoms.- Multi-Level Atoms.- General Properties Concerning Laser Cooling. Cooling and Trapping: Deceleration of an Atomic Beam.- Optical Molasses.- Cooling Below the Doppler Limit.- The Dipole Force.- Magentic Trapping of Neutral Atoms.- Optical Traps for Neutral Atoms.- Evaporative Cooling. Applications: Newtonian Atom Optics.- Ultra-Cold Collisions.- deBrooglie-Wave Optics.- Optical Lattices.- Bose -Einstein Condensation.- Dark States.
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.
Slowing down atoms using laser cooling, together with techniques like magnetic trapping and evaporative cooling, has led to numerous exciting results over the last decade [1], with the realization of Bose-Einstein condensation as the most spectacular achievement [2]. Laser-cooling schemes are applicable to atoms since closed multilevel systems can be realized and many consecutive absorptionemission cycles can be induced. This leads to a significant momentum transfer from the photons of the laser to the atom, resulting in a change of the velocity of the atom. There currently is a great interest in producing cold molecules for the study of cold molecule-molecule collisions, molecular quantum collective effects, Doppler-free spectroscopy, frequency standards, as well as many other applications already realized for atoms [3]. Slowing down of neutral molecules, a prerequisite for being able to trap them, has proven to be considerably more difficult to be achieved, however. The above-mentioned laser-cooling scheme cannot be applied to slow down molecules as no simple closed-level systems can be found; the unavoidable off-resonant radiative decay of molecules from the excited state to other vibrational levels in the electronic ground state hampers efficient momentum transfer [4]. Once molecules are present at sufficiently low kinetic energies, below a fraction of a cm21, they can be trapped in various ways. Trapping of neutral molecules in inhomogeneous magnetic [3] and electric fields [5] and trapping based on the use of evanescent fields close to the dielectricvacuum interface have been proposed [6]. It has also been suggested that extremely high laser powers might be used to induce a dipole moment in polarizable molecules, leading to trapping of these molecules in the laser beam [7]. Other methods to produce slow molecules have been put forward and have recently been successfully applied to produce the first samples of trapped molecules. By injecting molecules in a cold buffer gas, sufficiently low kinetic energies of the injected molecules can be obtained after thermalization that they can subsequently be trapped in an inhomogeneous magnetic field. This has recently been demonstrated for CaH injected in 3He buffer gas at temperatures of around 0.3 K [8]. Associative collisions between ultracold trapped atoms [9] have proven to be
The force acting on a two-level atom in a low-intensity standing laser wave is calculated. On account of this force, atoms can be trapped at the loops (antinodes) of the field. By quantizing the atomic motion near the bottom of the sinusoidal potential, we have studied the atomic behavior when they are trapped in bound states as well as when they are in the free state. Laser cooling of neutral atoms was first suggested by T. Hansh and A. Schawlow in 1975. The principle involves the Doppler effect in a detuned laser beam. The absorption rate of a photon depends on the apparent frequency of the photon that is shifted ωv/c from ω, where ω is the frequency of the laser, v is the velocity of the atom, and c is the velocity of light. For a single laser beam detuned slightly below an atomic resonance frequency, the apparent frequency for atoms moving toward the laser is closer to resonance, which causes a higher absorption rate. And these atoms lose momentum when they absorb a photon from the beam. The velocity of atoms can be decreased from 10$\sp5$ cm/sec, the velocity they have when they escape from an oven, to 10$\sp2$ cm/sec (about 1mK) by a laser beam. For further cooling, counterpropagating beams are necessary. In this study we propose a new mechanism for supercooling, that is, cooling well below the Doppler cooling limit. Within a standing laser wave there exists a force called a "dipole force", which has a sinusoidal spatial dependence. Once atoms are trapped by the potential, their motion around the minimum of the potential well is that of a simple harmonic oscillator. Restricting our attention to the two lowest quantized states, we calculate transition rates between free states and bound states, from which the average residence times in the bound states can be obtained. This first quantum treatment of an atom trapped in the sinusoidal potential is restricted to the one-dimensional case. Generalization to higher dimensions is left for future research.
Abstract That the laser cooling and trapping of neutral atoms are interrelated has already been said in the introduction to Chapter 5. We shall, therefore, now consider various techniques whereby cold atoms can be trapped. All the known techniques for trapping laser-cooled neutral atoms can be classified according to a few basic methods. These basic methods are optical trapping using the forces of the electric dipole interaction between atoms and laser fields, magnetic trapping based on the use of the forces of the magnetic dipole interaction, mixed magneto-optical trapping using simultaneous interaction between atoms and magnetic and laser fields, and mixed gravitooptical and gravito-magnetic trapping. Traps for neutral atoms can have a wide variety of geometries and dimensions: (a) macroscopic traps with a size of a »λ, (b) microscopic traps with a size of a ≃λ/2, (c) various combinations of macroscopic and microscopic traps (one-, two-, and three-dimensional) in the case of optical lattices, and finally (d) nanoscopic traps with a size of a «λ/2.
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.).
In order to confine any object, it is necessary to exchange kinetic for potential energy in the trapping field, and in neutral atom traps, the potential energy must be stored as internal atomic energy. Thus practical traps for ground-state neutral atoms are necessarily very shallow compared with thermal energy because the energy level shifts that result from conveniently sized fields are typically considerably smaller than k B T , even for T = 1 K. Neutral atom trapping therefore depends on substantial cooling of a thermal atomic sample, and is often connected with the cooling process. In most practical cases, atoms are loaded from magneto-optical traps, where they have been efficiently accumulated and cooled to mK temperatures (see Sec. 20.3), or from optical molasses, where they have been optically cooled to μK temperatures (see Sec. 19.4). The small depth of typical neutral atom traps dictates stringent vacuum requirements, because an atom cannot remain trapped after a collision with a thermal energy background gas molecule. Since these atoms are vulnerable targets for thermal energy background gas, the mean free time between collisions must exceed the desired trapping time. The cross-section for destructive collisions is quite large because even a gentle collision (i.e. large impact parameter) can impart enough energy to eject an atom from a trap. At pressure P sufficiently low to be of practical interest, the trapping time is ~(10 -8 / P ) s, where P is in torr. This chapter begins with a discussion of ordinary, single-center traps, but also considers arrays of traps. Such “optical lattices” are playing an increasingly important role in research in atomic physics, so discussion of their properties is an appropriate part of the education of a student of the subject. Dipole force optical traps Single-beam optical traps for two-level atoms The simplest imaginable optical trap consists of a single, strongly focused Gaussian laser beam (see Fig. 20.1) [214, 215] whose intensity at the focus varies transversely with r as where is the beam waist size. Such a trap has a well-studied and important macroscopic classical analog in a phenomenon called optical tweezers (see App. 1.C) [216–218].