Atom trapping and dynamics in the interaction of optical vortices with quadrupole-active transitions

Abstract

Recent studies have confirmed the coupling of optical vortices, such as Laguerre-Gaussian and Bessel-Gaussian modes, to quadrupole-active atomic transitions. This interaction has been shown to be enhanced considerably in the case of Laguerre-Gaussian beams due to the gradient coupling, particularly in the case of a relatively large winding number. Here we consider the trapping and the dynamics of atoms in the optical quadrupole potential generated by two co-axial counter-propagating optical vortex beams. We focus on the atomic transition 6 2 S 1/2 → 5 2 D 5/2 in Cs which is a dipole-forbidden, but a quadrupole-allowed transition. We show how this atomic transition engages with the optical vortex fields at near-resonance, leading to atom trapping in the optical quadrupole potential well accompanied by translational motion. We set out the formalism leading to atom trapping and show how the optical forces generate the atomic motion, illustrating the results using typical experimentally accessible parameters.

Quadrupole absorption rate and orbital angular momentum transfer for atoms in optical vortices

“…In order to illustrate the main result with practical examples, we focus on a case that has recently been discussed [6,8,10,19], namely, an LG mode of winding number ℓ = 0, 1, 2 and radial number p. In the simplest case, where the mode is a doughnut mode p = 0, we find that the last terms involving the derivatives in U (R) and V (R) given by Eqs. (15) and ( 16) vanish, as L |ℓ| 0 are constants for all ℓ.…”

“…The ground and excited states of the two-level atom are {|g , |e }, with level energies E 1 and E 2 , respectively, which correspond to a transition frequency ω a = (E 2 − E 1 )/h. The interaction Hamiltonian is written as a multipolar series expansion about the center-of-mass coordinate R as [6,8,10,19]…”

“…The absorption or emission of any type of light by atoms is accompanied by the transfer of linear momentum between the light and the atoms, and this effect has been exploited in the cooling and trapping of atoms [4][5][6]. It has also been established that the application of vortex light to atoms affects the center-of-mass motion [6,7] via the dipole force, but the quadrupole force too can influence atomic motion attracting the atoms to high-or low-intensity regions of the light field [8][9][10].…”

“…Research has also dealt with the study of the mechanical forces on atoms due to the coupling of optical vortices, such as the Laguerre-Gaussian (LG) and Bessel-Gaussian modes, to quadrupole-active atomic transitions [6,10,19] and the results displayed a considerable enhancement in the case of twisted beams due to the gradient coupling, which increases with increasing winding number. Quadrupole transitions have also been observed in the case of Rb atoms by evanescent light when Rb is localized in the vicinity of an optical nanofiber [9].…”

Symmetry and Quantum Features in Optical Vortices

“…The phasor defined by Equation ( 23) is a feature of not just the electric field but also the magnetic field B. Field gradients prove to play a significant role in a wide range of quadrupole and higher multipole interactions [39,[123][124][125][126][127][128][129][130][131][132]. In molecular or dielectric materials, and especially those with a chiral structure, electronic transitions may be mediated by more than one type of multipole, and through involvement of the azimuthal phasor in twisted light, the electric quadrupole form of coupling in particular introduces a range of new and interesting features.…”