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Stimulated light pressure on atoms and molecules in amplitude modulated counterpropagating waves

V. S. Voǐtsekhovich, M. V. Danileǐko, Анатолій Михайлович Негрійко, V. I. Romanenko, Леонід Петрович Яценко

Published May 8, 1994• 2 citations
OpenAlex

Abstract

The light pressure that results from the transfer of a momentum hk/2π to an atomic particle in the resonant scattering of photons has been studied thoroughly and is widely used to control the motion of atoms, to reduce their kinetic energy, corresponding to temperatures in the range below 1 mK and to reach in future the ultimate frequency standard. For a traveling plane wave the momentum of an atom can be changed significantly only if the interaction of the atom with a laser field can be made cyclic. This is possible if there is a transition from a ground (or metastable) state to a short lived level that decays spontaneously to the lower state. For this case the maximum force is determined by the rate 2γ of the spontaneous decay and is given by Fmax = hkγ/ 2π.

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Soviet Physics Uspekhi•Sep 30, 1985•17 citations
The light pressure that results from the transfer of a momentum hk/2π to an atomic particle in the resonant scattering of photons has been studied thoroughly and is widely used to control the motion of atoms, to reduce their kinetic energy, corresponding to temperatures in the range below 1 mK and to reach in future the ultimate frequency standard. For a traveling plane wave the momentum of an atom can be changed significantly only if the interaction of the atom with a laser field can be made cyclic. This is possible if there is a transition from a ground (or metastable) state to a short lived level that decays spontaneously to the lower state. For this case the maximum force is determined by the rate 2γ of the spontaneous decay and is given by Fmax = hkγ/ 2π.
The influence of the resonance light pressure on the motion of atoms and molecules is studied. A kinetic equation has been obtained describing the action on particles of both the mean force of light pressure and its fluctuations. The forces that are considered are due to spontaneous and stimulated transitions and also to a certain combination thereof. The kinetic equation is used to describe the scattering of atoms in conditions close to the experimental ones [16]. The temperature of atoms cooled in a standing wave with the aid of the force of light pressure of the combined type has also been found.
A theoretical investigation is made of the force acting on a two-level atom under conditions of saturation in the field of counterpropagating amplitude- and frequency-modulated waves of different intensities, which are in resonance with an atomic transition. It is shown that the resultant induced optical pressure (due to preferential absorption of light of one of the waves and subsequent stimulated emission in the form of the other wave) depends linearly on the correlation function of the amplitude of the field of one of the waves and on the rate of change of the amplitude of the other wave, and also on the correlation function of the phase of one of the waves and the rate of change of the phase of the other wave at the point where the atom is located.
The spontaneous decay rate $\ensuremath{\gamma}$ of excited atomic states limits the radiative force on atoms to $\ensuremath{\Elzxh}k\ensuremath{\gamma}/2.$ This bottleneck in the dissipative exchange of momentum between atoms and light can be overcome by coherent control of the momentum exchange interactions. The bichromatic force provides such control by using stimulated instead of spontaneous emission to produce the force, while at the same time exploiting spontaneous emission to enable a dissipative interaction. It is implemented with two counterpropagating light beams, each containing two frequencies, whose phases, amplitudes, and frequency difference are carefully chosen. We have made precise measurements of the extremely large magnitude and velocity range of this bichromatic force, and have shown that its velocity dependence near the edge of its range is suitable for atomic beam slowing and laser cooling. Our measurements have corroborated various models and calculations of this bichromatic force.
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.
The present state of research on the cooling of atomic ensembles by means of laser radiation pressure is discussed. First the basic theory of resonance radiation pressure is reviewed. The effect of recoil on the drift and fluctuations of the momentum of an atom interacting with resonance radiation is examined. There is an analysis of the forces acting on an atom in some simple light fields: a traveling plane wave, a Gaussian beam, and counterpropagating Gaussian beams. The review then focuses on the monochromatization of atoms by resonance radiation pressure and related methods for laser cooling of atoms. The roles played by the radiation pressure force and by momentum diffusion in shaping the narrow velocity distributions of the ensemble of atoms are analyzed. The lowest temperature obtainable in the radiation cooling of atoms is estimated. The basic experimental methods for laser cooling of atomic beams are described. Problems of the three-dimensional cooling of atomic ensembles and problems of localizing cold atoms in light fields, steady-state magnetic fields, and electrostatic fields are discussed. The review concludes with a discussion of some applications of cold atoms in high-precision spectroscopy, frequency standards, and atomic physics.