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Bulletin of the American Physical Society

Resolving Momentum and Position in a trapped gas using Laguerre-Gaussian beams

Rabin Paudel, Tara E. Drake, John Gaebler, Jayson Stewart, Deborah Jin

Published Jun 14, 2011• 0 citations
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Laser cooling and trapping has led to a revolution in Atomic and Molecular physics. Optical traps created with blue-detuned laser beams are desired for numerous studies. One method of creating such a trap is with Laguerre-Gaussian laser beams. Laguerre-Gaussian (LG) laser beams are interesting because of their orbital angular momentum and radial intensity modes. Previous methods of creating higher-order LG beams did not yield pure LG modes. In collaboration with Digital Optics Corporation diffraction optics have been manufactured that yield higher-order LG laser beams with purities consistent with 100% of the intensity in the desire mode. We then create a donut-mode LG beam with this method to confine atoms from a MOT in both a blue-detuned and a red-detuned optical dipole force trap.
Abstract Previous studies show that within paraxial limit and electric dipole approximations, the orbital angular momentum (OAM) of a Laguerre–Gaussian (LG) beam rotates the whole atom about the beam axis but does not affect the internal electronic motion. The contribution of the Gaussian part of the LG beam profile to the angular momentum exchange is not usually taken into account. In this paper, we develop a theory which shows that not only the OAM of a LG beam, but also the geometry of the beam cross section, plays an important role in the electronic lowest-order transitions in the interaction of the beam with a trapped Rydberg atom, due to the large span of its electronic wavefunctions. In this interaction, the standard dipole selection rules do not hold and our results show that the otherwise forbidden transitions can become sufficiently probable.
By employing x -Bohm theory and p -Bohm theory, we construct the position and momentum trajectories of single-mode and superposed-mode Laguerre-Gaussian (LG) beams. The dependence of divergence velocity and rotation velocity on the initial position and propagation distance is quantified, indicating that LG beams exhibit subluminal effects, even in free space. Additionally, we clarify the formation of the petal-shaped intensity distribution of the superposed-mode LG beam in terms of motion trajectory, where the particle-like trajectory and wave-like interference are “simultaneously” observed. Our work provides an intuitive way to visualize the propagation characteristics of LG beams and deepen the comprehension of Bohm-like theory.