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Physical Review A

Atomic motion in resonant fluctuating laser radiation

R. J. Cook

Published Jan 1, 1980• 26 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.21.268

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Modern Physics Letters B•Aug 10, 2000•2 citations
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 motion of an atom in an intense resonant standing laser wave is studied using the Ehrenfest-Bloch equations. Two approaches are taken to determine the radiation or light pressure force on the atom. The first, an attempt to find a Fourier series solution to the optical Bloch equations failed, but Fourier coefficient recursion formulas were found. The second, a numerical calculation of the Bloch variables and the radiation force was successful in obtaining plots of the instantaneous values. The effect of assuming constant atomic velocity is studied, and Fast Fourier Transform discrete harmonic frequency spectra of one of the Bloch variables and the light pressure force are obtained. Finally, the Ehrenfest-Bloch equations are compared with other theories of resonant radiation pressure. (Thesis).
The influence on atomic motion of quantum-mechanical fluctuations of the resonance-radiation force is investigated theoretically. Fluctuations due to both induced and spontaneous absorption-emission processes give rise to diffusion of atomic momentum, here described by a Fokker-Planck equation. It is shown that quantum-mechanical fluctuations of the radiation force place a lower bound on the temperature achievable by radiation cooling, inhibit cooling in a strong standing wave, and lead to finite, often short, confinement times for atoms in radiation traps.
A general theory of the motion of a two-level atom in a resonant or near-resonant electromagnetic wave of arbitrary amplitude and phase, including effects of radiative relaxation due to interaction with the quantized vacuum field, is developed from first principles. Particular emphasis is placed on the effects of quantum-mechanical fluctuations of the radiation force and on the associated diffusion of atomic momentum due to spontaneous and induced absorption and emission processes. Analytic results and numerical examples are presented for (1) the lower bound on the temperature achievable by radiation cooling in a standing wave tuned below resonance, (2) the heating rate in a strong resonant standing wave, (3) the maximum confinement time for an atom in a Gaussian radiation trap, (4) the deflection and spreading of an atomic beam transversely illuminated by a strong resonant running wave, and (5) the transverse cooling of an atomic beam by a strong running wave tuned below resonance.
We present a theoretical model for the interaction of a beam of two-level atoms with a resonant laser beam. It is shown that the radiation force, while averaging to zero at resonance, produces a transverse spread of the atomic velocities. If radiative damping is ignored, this spread increases linearly with time and finally saturates towards a steady value. Although the spread has a quantum-mechanical origin, we show that it is possible, in the limit $\ensuremath{\hbar}k\ensuremath{\rightarrow}0$, to describe the phenomenon in terms of differential equations of motion for the atomic translational variables, as in the classical case. In this model it is also possible to describe the effects of radiative damping, as well as other additional effects, which may occur in a real experiment. Finally a comparison of our results with experimental data, recently obtained on an Na atomic beam, has been made. Although an order-of-magnitude fit of the experimental data could be obtained, the weights of the different causes, reducing the spread, were found to be ambiguous and have been left partly open.
An effect of phase fluctuations of a driving laser field on dissipative and dipolar forces of two-level atom is considered. The phase fluctuations are treated by a phase diffusion model where phase fluctuations follow Wiener–Levy process. An exact master equation for the relevant density operator is obtained and solved in the steady state. Optical forces are calculated. The effect of phase fluctuations on angular momentum imparted by a Laguerre–Gaussian beam and an ideal Bessel beam to the atom is investigated.