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Journal of Optics

Superweak momentum transfer near optical vortices

Stephen Mark Barnett, Michael Berry

Published Oct 18, 2013• 68 citations
Publisher

Abstract

Near a vortex in a monochromatic light beam, the length of the local wavevector (phase gradient) can exceed the wavenumber in any of the plane waves in the superposition representing the beam. One way to detect these ‘superweak’ momenta could be by ‘superkicks’ imparted to a small particle located near the vortex, by absorbing individual large-momentum photons from the beam. A model for this process is a two-level atom with a transition resonant with the light beam. A semiclassical analysis shows that the momentum distribution of the atom is shifted by interaction with the vortex beam, by amounts that can almost reach the target superkicks and are usually greater than the momenta in the plane waves comprising the beam.

DOI
10.1088/2040-8978/15/12/125701

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Near a vortex in a monochromatic light beam, the length of the local wavevector (phase gradient) can exceed the wavenumber in any of the plane waves in the superposition representing the beam. One way to detect these ‘superweak’ momenta could be by ‘superkicks’ imparted to a small particle located near the vortex, by absorbing individual large-momentum photons from the beam. A model for this process is a two-level atom with a transition resonant with the light beam. A semiclassical analysis shows that the momentum distribution of the atom is shifted by interaction with the vortex beam, by amounts that can almost reach the target superkicks and are usually greater than the momenta in the plane waves comprising the beam.
An atom placed in an optical vortex close to the axis may, upon absorbing a photon, acquire a transverse momentum much larger than the transverse momentum of any plane-wave component of the vortex lightfield. Although this surprising phenomenon dubbed superkick has been clarified in terms of the atom wave packet evolution in the field of optical vortex, a fully quantum treatment is still lacking. Here, we study the effect within the quantum field theoretical framework. We consider collision of a Bessel twisted wave with a compact Gaussian beam focused to a small focal spot σ\sigmaσ located at distance b from the twisted beam axis. Through a qualitative discussion supported by exact analytical and numerical calculations, we recover the superkick phenomenon for σ≪b\sigma \ll bσ≪b and explore its limits when σ\sigmaσ becomes comparable to b. We also comment on the recent suggestions to observe this effect in nuclear or high-energy physics.
We investigate absorption and scattering of structured light by atoms, treating the photon and the atomic center of mass as spatially localized wave packets. We show that vortex photons can transfer orbital angular momentum (OAM) to the atomic center of mass with near-perfect efficiency in head-on collisions when the impact parameter bbb is smaller than the atomic transverse coherence length σσσ, which ranges from nanometers to sub-micrometer scales. Larger offsets result in a shifted mean OAM and a finite variance, both controlled by the ratio b/σb/σb/σ. The wave-packet nature of light enables electronic transitions that violate standard selection rules, albeit with a clear hierarchy where the dipole transition dominates. For femtosecond pulses, the finite spatial coherence of the photon leads to measurable shaping of the resonant absorption lines. We demonstrate a transverse recoil of the atom in a vicinity of the photonic vortex, dubbed "the superkick", and its dual effect - "the selfkick" - when an initially twisted atomic packet experiences recoil upon absorbing a gaussian photon. These phenomena are within reach of experimental capabilities using structured light in combination with cold atomic beams and ions in Penning traps, providing a route to the controlled generation and manipulation of non-gaussian atomic packets.
We investigate absorption and scattering of structured light by atoms, treating the photon and the atomic center of mass as spatially localized wave packets. We show that vortex photons can transfer orbital angular momentum (OAM) to the atomic center of mass with near-perfect efficiency in head-on collisions when the impact parameter b is smaller than the atomic transverse coherence length σ , which ranges from nanometers to sub-micrometer scales. Larger offsets result in a shifted mean OAM and a finite variance, both controlled by the ratio b / σ . The wave-packet nature of light enables electronic transitions that violate standard selection rules, albeit with a clear hierarchy where the dipole transition dominates. For femtosecond pulses, the finite spatial extent of the photon leads to measurable shaping of the resonant absorption lines. We demonstrate a transverse recoil of the atom in a vicinity of the photonic vortex, dubbed “the superkick,” and its dual effect—“the selfkick”—when an initially twisted atomic packet experiences recoil upon absorbing a Gaussian photon. These phenomena are within reach of experimental capabilities using structured light in combination with cold atomic beams and ions in Penning traps, providing a route to the controlled generation and manipulation of non-Gaussian atomic packets.
Photons carry one unit of angular momentum associated with their spin~\cite{Beth1936}. Structured vortex beams carry additional orbital angular momentum which can also be transferred to matter~\cite{Allen1992}. This extra twist has been used for example to drive motion of microscopic particles in optical tweezers as well as to create vortices in degenerate quantum gases~\cite{He1995,Andersen2006}. Here we demonstrate the transfer of optical orbital angular momentum from the transverse spatial structure of the beam to the internal (electronic) degrees of freedom of an atom. Probing a quadrupole transition of a single trapped 40^{40}40Ca+^++ ion localized at the center of the vortex, we observe strongly modified selection rules, accounting for both the photon spin and the vorticity of the field. In particular, we show that an atom can absorb two quanta of angular momentum from a single photon even when rotational symmetry is conserved. In contrast to previous findings~\cite{Araoka2005,Loeffler2011a,Mathevet2013}, our experiment allows for conditions where the vorticity of the laser beam determines the optical excitation, contributing to the long-standing discussion on whether the orbital angular momentum of photons can be transferred to atomic internal degrees of freedom~\cite{VanEnk1994,Babiker2002,Jauregui2004, Schmiegelow2012, Mondal2014, Scholz-Marggraf2014} and paves the way for its use to tailor light-matter interactions.
Photons can carry angular momentum, not only due to their spin, but also due to their spatial structure. This extra twist has been used, for example, to drive circular motion of microscopic particles in optical tweezers as well as to create vortices in quantum gases. Here we excite an atomic transition with a vortex laser beam and demonstrate the transfer of optical orbital angular momentum to the valence electron of a single trapped ion. We observe strongly modified selection rules showing that an atom can absorb two quanta of angular momentum from a single photon: one from the spin and another from the spatial structure of the beam. Furthermore, we show that parasitic ac-Stark shifts from off-resonant transitions are suppressed in the dark centre of vortex beams. These results show how light's spatial structure can determine the characteristics of light-matter interaction and pave the way for its application and observation in other systems.
Singular optical beams have been studied for many years after the pioneering work where the wave function of the laser radiation is presented as a steady-state solution of the wave equation for a harmonic oscillator. A major step in understanding the nature of singular beams has been made by introducing the concept of the angular momentum of light and analyzing local energy transfer in a vortex beam. It is now well accepted that the orbital angular momentum of light is an intrinsic feature of the optical vortex. However, the orbital angular momentum was always analyzed for travelling modes and the important issue of the orbital angular momentum associated with standing waves still remains open. The main motivation of our work is to reveal the structure of the orbital angular momentum in a standing wave formed by the counter-propagating optical vortices and study its suitability for an optical trapping and guiding. In this work we show that a superposition of two (or more) vortex beams generates a field structure which has a form of a standing wave in both the radial and longitudinal directions, but it is rotating simultaneously along the tangential direction. We demonstrate that then field of this optical vortex structure could be used as an optical trap and simultaneously transfer the angular momentum of the electromagnetic wave to an object inside the area of vortex localisation. We believe this study provides a basis for developing a novel concept of three-dimensional optical traps where vortices could be created in a local volume by a direct transfer of the angular orbital momentum of the electromagnetic wave to trapped objects.