The techniques of optical trapping and manipulation of neutral particles by lasers provide unique means to control the dynamics of small particles. These new experimental methods have played a revolutionary role in areas of the physical and biological sciences. This paper reviews the early developments in the field leading to the demonstration of cooling and trapping of neutral atoms in atomic physics and to the first use of optical tweezers traps in biology. Some further major achievements of these rapidly developing methods also are considered.

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Optical trapping and manipulation of neutral particles using lasers

https://link.aps.org/pdf/10.1103/RevModPhys.70.721

Nobel Lecture: Laser cooling and trapping of neutral atoms

The development of wave optics for light brought many new insights into our understanding of physics, driven by fundamental experiments like the ones by Young, Fizeau, Michelson-Morley and others. Quantum mechanics, and especially the de Broglie’s postulate relating the momentum p of a particle to the wave vector k of an matter wave: k = 2 λ = p/ℏ, suggested that wave optical experiments should be also possible with massive particles (see table 1), and over the last 40 years electron and neutron interferometers have demonstrated many fundamental aspects of quantum mechanics [1].

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Optics and interferometry with atoms and molecules

We present two cooling mechanisms that lead to temperatures well below the Doppler limit. These mechanisms are based on laser polarization gradients and work at low laser power when the optical-pumping time between different ground-state sublevels becomes long. There is then a large time lag between the internal atomic response and the atomic motion, which leads to a large cooling force. In the simple case of one-dimensional molasses, we identify two types of polarization gradient that occur when the two counterpropagating waves have either orthogonal linear polarizations or orthogonal circular polarizations. In the first case, the light shifts of the ground-state Zeeman sublevels are spatially modulated, and optical pumping among them leads to dipole forces and to a Sisyphus effect analogous to the one that occurs in stimulated molasses. In the second case (σ+−σ− configuration), the cooling mechanism is radically different. Even at very low velocity, atomic motion produces a population difference among ground-state sublevels, which gives rise to unbalanced radiation pressures. From semiclassical optical Bloch equations, we derive for the two cases quantitative expressions for friction coefficients and velocity capture ranges. The friction coefficients are shown in both cases to be independent of the laser power, which produces an equilibrium temperature proportional to the laser power. The lowest achievable temperatures then approach the one-photon recoil energy. We briefly outline a full quantum treatment of such a limit.

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Laser cooling below the Doppler limit by polarization gradients: simple theoretical models

Publisher Summary This chapter discusses the orbital angular momentum of light, outlines the theoretical basis for the orbital angular momentum of beams within the paraxial approximation, and indicates the unapproximated theory, based on the full set of Maxwell equations. The chapter discusses the problems associated with the separation and identification of spin and orbital contributions to the angular momentum properties of a field, the properties of Laguerre–Gaussian beams, which are physically realizable in the laboratory, and the ways in which the beams may be generated. It reviews the phenomenological behavior of beams possessing orbital angular momentum and their interaction with matter in bulk. The chapter also describes the measurement of the rotational Doppler shift, which arises when beams possessing orbital and spin angular momenta are rotated. The dipole-interaction of atoms with the orbital angular momentum of light beams is considered. The roles of spin and orbital angular momentum are also compared and contrasted.

IV The Orbital Angular Momentum of Light

A theoretical analysis is given for laser cooling of a two-level atom with magnetic sublevels in the presence of polarization gradients. The optical Bloch equations for the multilevel system are solved numerically for four combinations of polarizations in one-dimensional optical molasses. The light-pressure force on the atom as given by a simple two-level theory is recovered in the absence of polarization gradients, whereas a spatial variation of the polarization is found to lead to a strong cooling force for slow atoms. The increased cooling force is responsible for the recent observations of atoms cooled in optical molasses to temperatures an order of magnitude below the Doppler limit.

Optical molasses and multilevel atoms: theory

Stimulated Raman transitions between the ground-level hyperfine states of atoms have been used to manipulate slowly moving atoms in an atomic fountain. An ensemble of sodium atoms with an inferred velocity spread along one dimension of 270 \ensuremath{\mu}m/sec has been prepared by this technique. We also show that this velocity-selection method is effective in measuring ultracold temperatures of laser-cooled atoms in a regime where traditional ballistic methods fail.

Atomic velocity selection using stimulated Raman transitions

We have created an atomic fountain starting with a sample of laser cooled Na atoms. Excitation of the atoms between the F=1, mF=0 and F=2, mF=0 ground states have an observed linwidth of 2.0 Hz at ν = 1,772,626,129. +1/−10 Hz using the Ramsey resonance technique.

RF Spectroscopy in an Atomic Fountain

Laser-cooled sodium atoms pushed up on a vertical trajectory by radiation pressure are observed to turn around due to gravity. The reatively long time the atoms spent freely falling in this ``atomic fountain'' allowed the ground-state hyperfine splitting to be measured with a linewidth of 2 Hz. After a 1000-s integration time, the center of the line was resolved to \ifmmode\pm\else\textpm\fi{}10 mHz. The absolute splitting was measured to be 1 771 626 129(2) Hz.

rf spectroscopy in an atomic fountain.

The cooling mechanisms for laser cooling of atoms in optical molasses have been investigated experimentally. A significant simplification over the usual three-dimensional geometry has been obtained by studying the optical molasses in one or two dimensions only. By proper choice of polarizations the behavior of a pure two-level system as well as the more complicated effects of polarization gradients on laser cooling of a multilevel atom were observed.

Erling Riis

Papers

Optical molasses and multilevel atoms: theory

Atomic velocity selection using stimulated Raman transitions

RF Spectroscopy in an Atomic Fountain

rf spectroscopy in an atomic fountain.

Optical molasses and multilevel atoms: experiment