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Motion of Atoms in a Laser Field

Z. Ficek, Mohamed Ridza Wahiddin

Published Apr 19, 2016• 0 citations
Publisher

Abstract

In quantum optical problems involving the interaction of atoms with laser fields, the atoms are usually considered being stationary during the interaction. Since every photon has a momentum, the atomic momentum (motion) can be changed in the process of absorption and emission of photons. This may force a stationary atom to move or to change momentum of an already moving atom. Therefore, the dynamical behaviour of atoms can be varied by the interaction with a radiation field. For a weak driving field, the influence of this field on the atomic motion can be neglected. However, the intensities of laser fields are generally very strong, and then the motion of the atoms can be considerably changed by the laser field. Here, we discuss this aspect, especially the effect of a driving field on the motion of atoms and the atomic momentum distribution. In particular, we will consider diffraction of atoms by a standing-wave laser field due to an exchange of momentum with the photons of the wave, and radiation force on atoms driven by a running-or standing-wave laser field.

DOI
10.1201/b16875-26

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In quantum optical problems involving the interaction of atoms with laser fields, the atoms are usually considered being stationary during the interaction. Since every photon has a momentum, the atomic momentum (motion) can be changed in the process of absorption and emission of photons. This may force a stationary atom to move or to change momentum of an already moving atom. Therefore, the dynamical behaviour of atoms can be varied by the interaction with a radiation field. For a weak driving field, the influence of this field on the atomic motion can be neglected. However, the intensities of laser fields are generally very strong, and then the motion of the atoms can be considerably changed by the laser field. Here, we discuss this aspect, especially the effect of a driving field on the motion of atoms and the atomic momentum distribution. In particular, we will consider diffraction of atoms by a standing-wave laser field due to an exchange of momentum with the photons of the wave, and radiation force on atoms driven by a running-or standing-wave laser field.
This chapter discusses the basic physics of atom diffraction. Starting with a short review on the diffraction of light, we describe the absorption of photons by an atom and its subsequent emission, where the atom to changes its momentum and internal state. Assuming a two-level atom, we describe the coherent interactions of atoms with light, showing its effect on the ground state of the atoms. We further illustrate how the light impacts forces on the atom that can be used for trapping it in the light field. Next, we discuss Bragg diffraction of atoms, where the internal state of an atom is unchanged after diffraction. Here the external motional state of the atom is put in a linear superposition of its movement. Finally, we describe the diffraction of atoms by Raman pulses, where the internal state of the atom is changed after diffraction, while achieving directed motion.
This work discusses the effect of a high-intensity standing wave laser field on the motion of neutral atoms moving with a relatively high velocity. The analysis involves a detailed calculation of the force acting on the atoms and the calculation of the diffusion tensor associated with the fluctuations of the quantum force operator. The high-intensity laser field limit corresponds to a Rabi frequency much greater than the natural rate of the atom. The general results are valid for any atomic velocity. Results are then specialized to the case of slow and fast atoms where the Doppler shift of the laser frequency due to the atomic motion is either smaller or larger than the natural decay rate of the atom. The results obtained for the force and diffusion tensor are applied to a particular ideal experiment that studies the evolution of a fast atomic beam crossing a high-intensity laser beam. The theories developed previously, for a similar laser configuration, discuss only the low atomic velocities case and not the more realistic case of fast atoms. Here, an approximate solution of the equation for the distribution is obtained. Starting from the approximate distribution function, the deflection angle and dispersion angle for themore » atomic beam with respect to the free motion are calculated.« less
The effect of field fluctuations on the motion of a two-level atom in resonant laser radiation is investigated theoretically. The internal motion of the atom is treated quantum mechanically (optical Bloch equations); the translational motion, which is coupled to the internal motion, is treated classically (Ehrenfest's theorem); and the fluctuating radiation is treated as a classical electromagnetic wave with stochastic phase (phase-diffusion model). An expression for the radiation force and equations of motion for the ensemble-averaged Bloch vector are derived and used to calculate (i) the radiation force in a plane running wave, (ii) the steady-state radiation force in a general standing wave, and (iii) the dissipative force in a plane standing wave in the limit of strong phase fluctuations. In case (iii) it is found that the atomic velocity is damped when the radiation is tuned above resonance, which is opposite to the case of a weak coherent standing wave, in which damping occurs for radiation tuned below resonance. It is shown that fluctuations have a substantial effect on the radiation force only when the spectral width of the radiation approaches or exceeds the spontaneous emission rate.
The momentum exchange between a standing wave laser field and an atomic center-of-mass is dominated by the internal dynamics of an atomic electron in the exciting laser field. Rydberg atoms are one of the simplest physical systems where the dependence of this radiative force on the electronic dynamics can be investigated in detail. The characteristics of the momentum transfer between an atomic center-of-mass and a standing wave laser field strongly depend on whether the “particle” or the “wave” aspect of the electronic dynamics prevail. In this review recent theoretical advances in the description of the mechanical action of laser light on Rydberg atoms are discussed. These advances have become possible by the application of semiclassical path integral techniques with respect to the electronic dynamics which clearly exhibit the “particle” and “wave” aspects of this momentum transfer.
The momentum diffusion coefficient, as a function of position and velocity, is discussed for two-state atoms travelling through a standing-wave laser field. Equations leading to the force and diffusion coefficient have been obtained by Minogin. The authors present an alternative derivation, based on moments of the Wigner function and give numerical solutions in terms of matrix continued fractions. In strong fields, the discussion is supplemented by a derivation of the diffusion coefficient within the dressed-atom basis, and a picture of the diffusion mechanism emerges which is quite different from the one at low intensities. Calculated forces and diffusion coefficients are used in a Fokker-Planck equation to obtain stationary atomic velocity distributions.