Abstract One of the most remarkable achievements of laser control is the manipulation of atomic particles, their velocities, positions, etc., which is referred to as laser cooling and laser trapping . These two effects are interrelated and usually prove effective when used jointly. That this is so one can see by considering as an example the laser cooling of trapped ions and the laser trapping of laser-cooled neutral atoms (Fig. 5.1). The sequences of processes in these two situations are directly opposite. Ions can easily be trapped in an electromagnetic trap of large depth (Paul 1990) and then be cooled for a long time by laser radiation (sideband cooling) (Wineland and Dehmelt 1975; Dehmelt 1990). Neutral atoms are first slowed down and cooled by laser radiation down to millikelvin temperatures, and only then confined in an optical trap. Trapped atoms can further be cooled to microkelvin temperatures. The present chapter and Chapter 6 consider the cooling and trapping of neutral atoms, the present chapter concentrating on their cooling, and Chapter 6 on trapping. But it would be reasonable first to familiarize the reader with the history of the early ideas in this field that eventually led to the advent of a new domain of physics—the physics of ultracold atoms and molecules (Chapters 7 and 8).
The stability region of a far-off-resonance dipole-atom trap (FORT) composed of a single trapping laser beam and a ${\ensuremath{\sigma}}^{+}\ensuremath{-}{\ensuremath{\sigma}}^{\ensuremath{-}}$ cooling field configuration is discussed for the simplest
(3+5)-level atomic scheme. The ultimate parameters of the stable FORT are evaluated by extending the theory of the FORT to the fourth-order rate-equation approximation. It is shown that when the detuning of the trapping field is much larger than the detuning of the cooling field, and with a proper choice of a low optical saturation due to the trapping and cooling field, the mixing of the one-photon processes responsible for the trapping potential with the two-photon processes responsible for the sub-Doppler cooling of atoms in the trap remains weak. It is concluded that the FORT with superimposed cooling fields possesses a stability region where the diffusive heating is suppressed by the cooling processes. Numerical evaluations of the stability region for a model of a
(3+5)-level atom are given.
It is demonstrated experimentally that the anharmonic property of the quadrupole trap can be exploited to cool trapped atoms by modulating the trap potential anisotropically. This cooling effect arises from the energy-selective removal of the most energetic trapped atoms and the thermal equilibrium of the remaining atoms. The frequency dependences of the temperature and the fraction of the atoms left in the trap after the modulation are explored. It is also demonstrated that the cooling induced by parametric resonance can also increase the phase space density of the trapped atoms.