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Physical Review A

Spin-orbit coupling in free-space Laguerre-Gaussian light beams

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

Published May 1, 1996• 58 citations
Publisher

Abstract

The expression for the azimuthal force on an atom in a circularly polarized Laguerre-Gaussian beam is shown to contain a term that depends upon the coupling of the intrinsic spin and orbital angular momenta of the light. Consequently, the state of polarization of the light affects the gross motion of the atom and not simply its internal dynamics. The effect arises from the spin-orbit coupling exhibited in the linear momentum density of the free-space mode.

DOI
10.1103/physreva.53.r2937

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The expression for the azimuthal force on an atom in a circularly polarized Laguerre-Gaussian beam is shown to contain a term that depends upon the coupling of the intrinsic spin and orbital angular momenta of the light. Consequently, the state of polarization of the light affects the gross motion of the atom and not simply its internal dynamics. The effect arises from the spin-orbit coupling exhibited in the linear momentum density of the free-space mode.
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 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.
Abstract We theoretically discover that the spin angular momentum (SAM) enables to modulate the orbital torque through the inter-particle light-induced force (IP-LIF). Laguerre - Gaussian beam with the orbital angular momentum (OAM) can induce the orbital motion for the optically trapped objects. In addition, the SAM can also accelerate or decelerate the orbital motion due to the IP-LIF. Our discovery provides a new physical aspect, i.e. the IP-LIF plays an important role in the many-body dynamics of nanoparticles via the SAM-OAM coupling.
We examine the use of Laguerre-Gaussian (LG) laser beams in the tripod scheme to create the coupling between spin and orbital angular momentum in a Bose–Einstein condensate (BEC) confined by a harmonic trap. We derive and solve the Gross-Pitaeskii equation numerically to obtain the density distribution of the BEC. Orbital angular momentum from the LG beam is transferred to the BEC, inducing the formation of a giant vortex at the BEC’s centre. The macroscopic flow of spinor BEC around the vortex leads to a persistent spin current in the BEC.