Laser Manipulation of Atoms

K. Sengstock; W. Ertmer    Institut für Quantenoptik, Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany

I Introduction

From the beginning of this century there have been extensive investigations of the internal degrees of freedom of atoms. However, for a long time it was impossible to control the external degrees of freedom. In contrast, the past decade was characterized by the development of very versatile tools to manipulate and control the motion and temperature of free atoms by light pressure forces of nearly resonant laser light. During the last few years, spectacular results have been obtained, pushing the field of laser cooling to unforeseen new developments and opening totally new fields of applications.

The theoretical discussions and experimental results of these laser cooling techniques have intensively stimulated interest in a variety of meshed fields in physics like quantum optics, atom optics, atom interferometry, atom lithography, physics of correlated quantum effects, and high-precision measurements of fundamental constants, to name a few. Even the Gedanken experiments of the early days of quantum mechanics became feasible experimentally by the new preparation techniques for atomic ensembles.

The whole field is based on the “momenta of light quanta,” discovered by Einstein (1917). Absorption and emission of these light quanta by atoms in gases may lead to a manipulation of the momentum and the momentum distribution of the atoms. In the early thirties Frisch succeeded in demonstrating experimentally for the first time the mechanical action of light pressure on atoms (Frisch, 1933). But those experiments suffered from the lack of intense, tunable and monochromatic light sources, which became available after the invention of the laser. Thus it was not surprising that in the mid-1970s the basic ideas of manipulation and cooling by laser light were derived for atoms (Hänsch and Schawlow, 1975) and ions (Wineland and Dehmelt, 1975). These first proposals introduced the so-called “Doppler cooling” mechanisms. The early theoretical discussions of laser cooling were based on the interaction of single radiative field modes with two level atoms. Under this assumption the expected lowest possible temperature is given by the “Doppler limit” (Gordon and Ashkin, 1980; Cook, 1980; Minogin, 1980) determined only by the natural linewidth of the relevant atomic transition.

Here and in the following the temperature of atoms is given by the kinetic energy distribution of the atomic ensemble. One half of the mean square of the velocity distribution v2 times the atom’s mass m corresponds to 2kBT for each degree of freedom, where kB is Boltzmann’s constant. Thus in three dimensions the temperature is defined by

2kBT=12mv2

For sodium atoms the Doppler limit gives a temperature of 240μK, corresponding to some 10 recoil velocities of single photon emissions.

It was the group of Phillips who surprisingly measured temperatures below the Doppler limit (Lett et al., 1988) on laser-cooled sodium atoms. Since this discovery, considerable theoretical and experimental effort has focused on understanding the “new” mechanisms of laser cooling. These investigations revealed the more complex interactions between the rich inner structure of degenerated atomic states and the polarization gradients of the light fields. The achievable lowest temperatures with these so-called “sub-Doppler” mechanisms correspond to only a few single photon recoil velocities, e.g., 20 μK for sodium. But even the limit of one photon recoil was underscored with techniques based on “dark resonances” (Aspect et al.,1998) or “Raman cooling” mechanisms (Kasevich and Chu, 1992).

At the current state of laser cooling it is possible to cool an ensemble of atoms in three dimensions down to temperatures of a few tens of nanokelvins. Densities of laser trapped atoms up to 1011cm- 3 and clouds with 1010 atoms are currently the standard. Today more than 200 groups all over the world operate neutral atom traps or cold beams to study further cooling techniques and an enormous variety of applications.

With the manipulation techniques realized so far, a wide range of optimized phase space distributions can be created. In most of the experiments basic manipulation techniques reduce in a first step thermal velocities of the atoms. For example, the velocity distribution of an atomic beam is nearly monochromized and reduced down to a mean velocity of a few m/s by a counterpropagating laser beam within some 10 cm (corresponding to an acceleration of 105 g). This was first demonstrated by Prodan et al. (1985) and Ertmer et al. (1985). This process is based on the so-called “spontaneous light pressure force,” by which photons from a laser beam are scattered by atoms, thus reducing the antiparallel velocity component of the atom by the momentum transfer of the individual photons. Afterward the slow atoms can be deflected (Nellessen et al., 1989b), transversely compressed (Nellessen et al., 1990), captured in an atom trap (Migdall et al., 1985; Raab et al., 1987), or a combination thereof. Also these techniques are based in principle on the spontaneous light pressure force. Once precooled and confined in a space region, the more sophisticated cooling schemes, like sub-Doppler cooling, can take over, damping atomic velocities down to the final temperature.

The main purpose of this article is to outline the development and achievements of the manipulation of atoms and to give examples for the design of optimized phase space distributions of cold atomic ensembles. Since the main emphasis of this article is an experimental point of view, only a short theoretical introduction is given in Section II with references to tutorials and reports on laser cooling theory. Section III describes, as examples for basic manipulation schemes, the deceleration and deflection of atomic beams with laser light. In Section IV principles and experimental realizations of the two- and three-dimensional confinement of neutral atoms, in particular the magnetooptical trapping configurations, are discussed. Some manipulation methods based on light gradient forces, the so-called “dipole forces,” are then presented in Section V. In Section VI we give a few examples for applications with laser-trapped atoms.

In the fast developing field of laser manipulation only a snapshot of experiments can be described. For further information about theoretical and experimental aspects the reader is referred to textbooks of summer schools about laser cooling (Dalibard et al., 1992; Arimondo et al., 1992), special issues of journals dealing with laser cooling and trapping (Metcalf and van der Straten, 1994; Foot, 1991; Special Issue, 1985, 1989), and the references therein. For an overview of related fields which will not be discussed here the reader is referred to overview and tutorial articles, for example, in atom optics (Adams et al., 1994), ion traps, and ion cooling (Walther, 1992, 1994) as well as in atom interferometry (Special Issue, 1992).

II General Principles

Laser cooling and manipulation of free atoms are based on the principles of light matter interaction, well understood in QED. Nevertheless, the numerous degrees of freedom, present in complex cooling schemes, force theory to make a clever choice of assumptions and simplifications in order to take into account the details of the actual cooling scheme. This led and will lead to the development of new calculation methods (e.g., quantum Monte Carlo calculations (Zoller et al., 1987; Dalibard et al., 1992). In the following we give a brief review of basic laser cooling theories and the corresponding regimes in which they apply.

The discussion of light pressure and atom cooling starts with the definition of the Hamiltonian of the interacting systems:

=HA+HV+VAL+VAV,

where

A=P22m+Hint

is the undisturbed atomic Hamiltonian including external degrees of freedom and Hint describes the internal structure of, for example, a two-level system:

int=ħωA|e〉〈e|.

Hv is the field Hamiltonian as the sum of the various field modes i:

V=∑ħωiai+ai+12.

The atom is coupled to the laser field modes EL, via VAL and to all other modes of the radiation field, initially empty, via VAV.

In this ansatz atom-atom interactions are neglected, although they play a central role in density and temperature limits of, for example, trapped atom clouds. Interactions like van der Waals forces and radiation-assisted atom-atom forces are typically introduced in a second step by an effective potential. A new...