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Physical Review A

Atomic motion in light beams possessing orbital angular momentum

W. L. Power, L. Allen, M. Babiker, V. E. Lembessis

Published Jul 1, 1995• 81 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.52.479

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We show that a two-level atom moving in a Laguerre-Gaussian beam is subject to a light-induced torque, $T$, about the beam axis which is directly proportional to $l$, the orbital angular momentum quantum number of the mode. The torque, which has a Lorentzian frequency response which includes an azimuthal $l$-dependent Doppler shift in the detuning term, reduces in the saturation limit to the simple form $T\ensuremath{\approx}\ensuremath{\hbar}l\ensuremath{\Gamma}$, where $2\ensuremath{\Gamma}$ is the decay rate of the excited state.

Physical Review Letters•Aug 29, 1994•185 citations
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 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.
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.
The time evolution of the radiation pressure forces due to the action of laser light on matter in the form of neutral molecules, atoms, and ions is considered when the frequency of the light is comparable to a dipole-allowed transition frequency. We find that the transient regime, applicable from the instant the laser is switched on, is important for the gross motion, provided that the upper-state lifetime ${\ensuremath{\Gamma}}^{\ensuremath{-}1}$ is relatively long, while the steady-state regime, formally such that $t⪢{\ensuremath{\Gamma}}^{\ensuremath{-}1}$, is appropriate for the evaluation of the forces and the dynamics for large $\ensuremath{\Gamma}$. With a focus on the orbital-angular-momentum-endowed laser light, the light-induced time-dependent forces and torques are determined and their full time dependence utilized to determine trajectories. Marked differences are found in both translational and rotational features in comparison with the results emerging when the steady-state forces are assumed from the outset. Intricate and detailed atom trajectories are plotted for Laguerre-Gaussian light at near resonance for a transition of Eu3+{\mathrm{Eu}}^{3+}Eu3+ that has a particularly small $\ensuremath{\Gamma}$. The implications of the results for trapping and manipulating atoms and ions using laser light are pointed out and discussed.
The exchange of orbital angular momentum between a Laguerre-Gaussian beam of light and the center-of-mass motion of an atom or molecule is well known. We show that the orbital angular momentum of light can also be transferred to the internal electronic or rotational motion of an atom or a molecule provided the internal and center-of-mass motions are coupled. However, this transfer does not happen directly to the internal motion, but via center-of-mass motion. If atoms or molecules are cooled down to the recoil limit, then an exchange of angular momentum between the quantized center-of-mass motion and the internal motion is possible during the interaction of cold atoms or molecules with the Laguerre-Gaussian beam. The orientation of the exchanged angular momentum is determined by the sign of the winding number of the Laguerre-Gaussian beam. We present selective results of numerical calculations for the quadrupole transition rates in the interaction of the Laguerre-Gaussian beam with an atomic Bose-Einstein condensate to illustrate the underlying mechanism of light orbital angular momentum transfer. We discuss how the alignment of diatomic molecules will facilitate exploration of the effects of light orbital angular momentum on the electronic motion of molecules.
We show that a two-level atom moving in a Laguerre-Gaussian beam is subject to a light-induced torque, TTT, about the beam axis which is directly proportional to lll, the orbital angular momentum quantum number of the mode. The torque, which has a Lorentzian frequency response which includes an azimuthal lll-dependent Doppler shift in the detuning term, reduces in the saturation limit to the simple form $T\ensuremath{\approx}\ensuremath{\hbar}l\ensuremath{\Gamma}$, where $2\ensuremath{\Gamma}$ is the decay rate of the excited state.