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Physical Review A

Mechanical effects on atoms interacting with highly twisted Laguerre-Gaussian light

V. E. Lembessis, M. Babiker

Published Oct 28, 2016• 11 citations
Publisher

Abstract

Laguerre-Gaussian (LG) light modes with large values of the radial index $p$ and the azimuthal index $l$ are considered. We give special emphasis on the mechanical effects on atoms arising from the Gouy phase and the phase due to the curvature of such light. It is shown that the additional phase terms for highly twisted light can lead to mechanical effects based on the substantial reduction of the axial wavenumber. As a consequence, axial recoil effects are diminished in the processes of stimulated emission and absorption of the light by the atoms. Both the scattering force and the momentum diffusion are affected by the inclusion of these normally ignored additional phase terms. The magnitudes of the effects are explored using order of magnitude analysis with typical parameters due to the atoms and the light.

DOI
10.1103/physreva.94.043854

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Laguerre-Gaussian (LG) light modes with large values of the radial index ppp and the azimuthal index lll are considered. We give special emphasis on the mechanical effects on atoms arising from the Gouy phase and the phase due to the curvature of such light. It is shown that the additional phase terms for highly twisted light can lead to mechanical effects based on the substantial reduction of the axial wavenumber. As a consequence, axial recoil effects are diminished in the processes of stimulated emission and absorption of the light by the atoms. Both the scattering force and the momentum diffusion are affected by the inclusion of these normally ignored additional phase terms. The magnitudes of the effects are explored using order of magnitude analysis with typical parameters due to the atoms and the light.
A theory is developed that leads to the description of the internal and gross motions of an atom interacting with an arbitrary light field. The general results are then applied to the case of a Laguerre-Gaussian (LG) mode, one of a class of modes of electromagnetic radiation that possess orbital angular momentum. A number of effects are predicted, notably, an azimuthal shift in the atomic resonance, a modified radiation pressure force, and an associated torque on the atom. It is pointed out that the effects originate in the processes of the transfer of linear and orbital angular momentum from the field to the atomic gross motion. The strengths of the effects are assessed in relation to the normal axial Doppler shift and the linear light pressure force. The motion of atoms and ions subject to the LG pressure force is studied by solving the classical equation of motion. Trajectories clearly exhibiting the effects of orbital angular momentum are displayed for a free atom and for an ion in a two-dimensional trap and in a Paul trap.
The interaction of atoms and molecules with structured light, specifically laser light endowed with the property of orbital angular momentum, such as Laguerre-Gaussian light, is discussed. The primary effects of interest here are the influence of the light on the gross motion of atoms and molecules and the possibilities this motion provides for particle manipulation in cooling, heating and trapping experiments. It turns out that, in addition to the possibility of modifying translational motion, suitably structured light can facilitate the manipulation of rotational motion. The latter possibility arises from a light-induced torque that is directly attributable to the orbital angular momentum property of the light. We outline the physics responsible for these effects and consider applications to typical cases in which atoms and ions are subject to near resonant Laguerre-Gaussian beams, leading to characteristic trajectories and eventual trapping in specific regions. Details are given for optical molasses configurations based on twisted light beams arranged in one-, two- and three-dimensional counter-propagating pairs. We extend consideration to the case of liquid crystals, subject to Laguerre-Gaussian light tuned far off-resonance, and show how this leads to the twisting of the directors in the liquid crystal, coinciding with the intensity distribution of the light.
Abstract Counter-propagating co-axial Laguerre–Gaussian (LG) beams are considered, not in the familiar scenario where the focal planes coincide at z = 0, but when they are separated by a finite axial distance d . The simplest case is where both beams are doughnut beams which have the same linear polarisation. The total fields of this system are shown to display novel amplitude and phase distributions and are shown to give rise to a ring or a finite ring lattice composed of double rings and single central ring. When the beams have slightly different frequencies the ring lattice pattern becomes a finite set of rotating Ferris wheels and the whole pattern also moves axially between the focal planes. We show that the fields of such an axially shifted pair of counter-propagating LG beams generate trapping potentials due to the dipole force which can trap two-level atoms in the components of the ring lattice. We also highlight a unique feature of this system which involves the creation of a new longitudinal optical atom trapping potential due to the scattering force which arises solely when d ≠ 0 . The results are illustrated using realistic parameters which also confirm the importance of the Gouy and curvature effects in determining the ring separation both radially and axially and gives rise to the possibility of atom tunnelling between components of the double rings.
The leading radiation forces acting on an atom or ion subject to linearly polarized Laguerre-Gaussian (LG) light are studied. Particular emphasis is laid on the orbital angular momentum effects associated with LG light. The optical Bloch equations appropriate for the adiabatic approximation are derived and used to evaluate the forces and associated torque governing the atomic motion. The steady-state dynamics of the atom are explored for atoms subject to a single beam and multiple independent counterpropagating beams. The main features responsible for the dynamics of the atom, together with the dipole potentials characteristic of Laguerre-Gaussian light, are identified and discussed. The theory is illustrated by the numerical integration of the equation of motion for Mg+{\mathrm{Mg}}^{+}Mg+ ions in various beam configurations. This yields information on trajectories, velocity evolution, and vibrational frequencies at potential minima. Interesting effects involving a reciprocal interplay between motions in orthogonal directions are demonstrated. Such features are purely dependent on the orbital angular momentum property of the light. Their possible use in controlling atomic motion is investigated. \textcopyright{} 1996 The American Physical Society.
We consider the interaction of atoms with two tightly focused and axially shifted counter-propagating optical beams. At sub-wavelength focusing, we find that the scattering force potential in the three-dimensional space between the shifted focal planes changes from a feature with a saddle-point to a three-dimensional trapping potential. Further analysis shows that due to the tight focusing, the trapping depends on significant contributions arising from the Gouy and curvature phase gradients of the interfering beams. The physics and its effects are illustrated with reference to the sub-wavelength trapping of sodium atoms.