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arXiv:1702.05410 · Journal of the Optical Society of America B

Radiation pressure on a two-level atom: an exact analytical approach

L. Podlecki, R. D. Glover, John Martin, Thierry Bastin

Published Dec 13, 2017• 7 citations
arXivHTMLPDF

Abstract

The mechanical action of light on atoms is nowadays a tool used ubiquitously in cold atom physics. In the semiclassical regime where the atomic motion is treated classically, the computation of the mean force acting on a two-level atom requires in the most general case numerical approaches. Here we show that this problem can be tackled in a pure analytical way. We provide an analytical yet simple expression of the mean force that holds in the most general case where the atom is simultaneously exposed to an arbitrary number of lasers with arbitrary intensities, wave vectors, and phases. This yields a novel tool for engineering the mechanical action of light on single atoms.

DOI
10.1364/josab.35.000127

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The mechanical action of light on atoms is nowadays a tool used ubiquitously in cold atom physics. In the semiclassical regime where the atomic motion is treated classically, the computation of the mean force acting on a two-level atom requires in the most general case numerical approaches. Here we show that this problem can be tackled in a pure analytical way. We provide an analytical yet simple expression of the mean force that holds in the most general case where the atom is simultaneously exposed to an arbitrary number of lasers with arbitrary intensities, wave vectors, and phases. This yields a novel tool for engineering the mechanical action of light on single atoms.
In a recent work, we provided a standardized and exact analytical formalism for computing in the semiclassical and asymptotic regime, the radiation force experienced by a two-level atom interacting with any number of plane waves with arbitrary intensities, frequencies, phases, and propagation directions [ J. Opt. Soc. Am. B 35 , 127 ( 2018 ) JOBPDE 0740-3224 10.1364/JOSAB.35.000127 ]. Here, we extend this treatment to the multilevel atom case, where degeneracy of the atomic levels is considered and polarization of light enters into play. A matrix formalism is developed to this aim.
Theories of radiation pressure based on rate equations and on the optical Bloch equations are developed within a common framework that allows comparison of the two. The latter method is used to determine the time dependence of the mean momentum of a two-level atom subjected to monochromatic coherent light for general values of various broadening parameters and detuning. The expression for the corresponding radiation pressure force in the limit of steady-state atomic level populations includes previous results as special cases. The rate equation method provides a fully quantum-mechanical calculation of an expression obtained by Einstein for the rate of change of mean-square atomic momentum in thermal equilibrium.
The quantum kinetic equation describing slow atomic motion in laser light is derived by an operational method which provides mathematical expressions with a transparent physical structure. The authors prove in a general way that the coefficients appearing in this equation, which is of a Fokker-Planck type, are simply related to the mean value and to the correlation functions of the Heisenberg radiative force of the semiclassical approach, where the atomic position is treated classically. They derive in particular a new theoretical expression for the damping force responsible for radiative cooling and they interpret it in terms of linear response theory. The authors also obtain a new crossed r-p derivative term, which does not appear in semiclassical treatments, but which they find to be very small in most situations. Finally, all the theoretical expressions derived are valid for any J g to J e transitions and are not restricted to two-level atoms.
We adapt an earlier semiclassical theory of laser cooling of an arbitrary multistate atom [J. Javanainen, Phys. Rev. A 44, 5857 (1991)] to the limit of low light intensity. The formal theory is implemented analytically on a computer using mathematica. Expressions of light-pressure force and diffusion are provided for j1{\mathit{j}}_{1}j1​=1/2\ensuremath{\rightarrow}j2{\mathit{j}}_{2}j2​=3/2 and j1{\mathit{j}}_{1}j1​=1\ensuremath{\rightarrow}j2{\mathit{j}}_{2}j2​=2 atoms in a one-dimensional optical confinement area in which the pair of counterpropagating waves has orthogonal polarizations. In our models the cooling temperature decreases as the level degeneracy increases.
Chapter 11 presents the simplest and most intuitive approach to atom-optical interactions: the atom is modelled as a damped harmonic oscillator with spontaneous emission as the damping agent. The semiclassical viewpoint, in which the atom is treated as a quantum object but the fields are classical, is adopted throughout the chapter. Next, the two-level atom is introduced, which sets the stage for establishing light forces at the atomic level: the dipole-gradient force and the radiation pressure force. The Einstein B coefficient is revisited as stimulated dipole emission. Finally, the optical Bloch equations are used to reformulate more generally the appearance of optical forces and to describe the existence of atom Doppler cooling.