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Physical Review Letters

Radiation pressure vortices in two crossed standing waves

Andreas Hemmerich, Theodor W. Hänsch

Published Mar 9, 1992• 49 citations
Publisher

Abstract

We have observed the effect of microscopic radiation pressure vortices on atomic motion in two crossed, near-resonant, optical standing waves. When the two standing waves oscillate synchronously the resulting light field and the corresponding light forces possess a 90\ifmmode^\circ\else\textdegree\fi{} rotation symmetry. However, when one of the standing waves' oscillations is delayed with respect to those of the other, a vortical radiation pressure force arises which can be identified by the breaking of this symmetry. Radiation pressure vortices should play a significant role for the atomic kinematics in optical molasses and magneto-optical traps.

DOI
10.1103/physrevlett.68.1492

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We have observed the effect of microscopic radiation pressure vortices on atomic motion in two crossed, near-resonant, optical standing waves. When the two standing waves oscillate synchronously the resulting light field and the corresponding light forces possess a 90\ifmmode^\circ\else\textdegree\fi{} rotation symmetry. However, when one of the standing waves' oscillations is delayed with respect to those of the other, a vortical radiation pressure force arises which can be identified by the breaking of this symmetry. Radiation pressure vortices should play a significant role for the atomic kinematics in optical molasses and magneto-optical traps.
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).
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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.
The forces acting on a resonance particle in the fields of laser radiation sources can be large. Acceleration, heating, and cooling of atoms by using these forces are discussed. Since the forces are of a resonance type, one can employ them to separate isotopes and excited atoms from unexcited atoms. Light pressure can play an important role in the spectroscopy of narrow atomic and molecular resonances. The quantum features of the motion of particles in a standing light wave are manifested in a fine structure of the absorption coefficient. This review is concerned with analyzing the resonance light-pressure forces and discussing the application of them in optics and quantum electronics.
An overview of the theory of the magneto-optical trap is presented, along with measurements of the effect of an imbalance in the intensities of the trapping beams. This investigation tests the theory of the spring constant of the trap and confirms that the confining force at the center of the trap results from an induced orientation of the atomic ground state. The experimental results give the magnitude of this force, which has not yet been calculated accurately. We calculate the radiation field in the three-dimensional molasses, finding that the relative time phase of the orthogonal standing waves is significant, and we give some insight into the phenomenon of interference fringes when the beams are misaligned. We also discuss the limitation of the trapped atomic density resulting from photon scattering within the cloud, predicting that densities above 1013 atoms/cm3 could be achieved in a trap operating at low saturation of the atomic transition. Finally, we briefly consider collisional loss at low densities, finding an especially large contribution from resonant dipole–dipole scattering.