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arXiv:1905.02755 · Journal of Optics

Interference of axially-shifted Laguerre–Gaussian beams and their interaction with atoms

K Koksal, Vasileios E Lembessis, J Yuan, M Babiker

Published Sep 3, 2019• 9 citations

Abstract

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.

DOI: 10.1088/2040-8986/ab411f

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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.

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.

We investigate the possibility of strong localization, of the Lamb–Dicke type, for cold atoms trapped by a far off-resonant Ferris wheel optical dipole potential. This optical dipole potential light field is created when a light field generated by the superposition of two similar co-propagating Laguerre–Gaussian beams, with opposite winding numbers, interacts with a two-level atom. We show that strong confinement of atoms in such a light field is possible when the light field is tightly focused, for low values of the winding number and relatively high values of power. We show that a combination of a Ferris wheel with an ordinary axial Gaussian optical lattice provides 3D cylindrically symmetric optical lattices in which the Lamb–Dicke limit can be reached for typically used experimental parameter values.

New counterpropagating geometries are presented for localizing ultracold atoms in the dark regions created by the interference of Laguerre-Gaussian laser beams. In particular dark helices, an "optical revolver," axial lattices of rings, and axial lattices of ring lattices of rings are considered and a realistic scheme for achieving phase stability is explored. The dark nature of these traps will enable their use as versatile tools for low-decoherence atom interferometry with zero differential light shifts.

Standing waves generated by the interference of Laguerre-Gaussian (LG) beams can be used for dipole trap. We propose a scheme to create a nanometer (nm) scale ring lattice based on the interference of two high order LG beams without decrease the wavelength. Both of the two LG beams have a monocyclic intensity distribution, and they have the same orbital angular momentum (OAM) quantum number on the order of

10^6

. We are able to theoretically demonstrate a dipole potential along angular direction with the period of $\sim$1 nm , given the waist of the Gaussian beams to be $\sim$0.8

μ

m. The atoms in this lattice can be trapped along the radial and azimuthal direction in the potential wells of with $\sim$100 nm and $\sim$0.85 nm distance. The proposed method opens up a convenient pathway towards sub-wavelength atom traps that could directly lead to overlap of wave function of atoms in adjacent wells and the formation of molecular bonds.

The total internal reflection of a light with phase singularity, such as Laguerre–Gaussian (LG) light, can generate an evanescent wave. The distribution of this type of light is firmly localized in the vicinity above the dielectric surface and displays a rotational character. Any atom approaching the surface from the vacuum region interacts with evanescent wave and produces interesting rotational effects. Recent studies have established the coupling of LG beams to both electric atomic transitions; dipole and quadrupole according to the selection rules of each, permitted and prohibited. Due to the small magnitude of the quadrupole interaction compared to the dipole interaction, we chose the two counter-propagating beams configuration to generate the doubling Rabi frequencies with more stable surface optical forces. We describe the essential rotational features and discuss how they can be used to influence atoms. Atom confinement and dynamics in the interaction of surface optical vortices with the two different atomic transitions are illustrated using typical experimentally accessible parameters for the case of the Cs atom interacts with the LG10 mode.

We propose a versatile optical ring lattice suitable for trapping cold and quantum degenerate atomic samples. We demonstrate the realisation of intensity patterns from pairs of Laguerre-Gauss (exp(i??) modes with different ? indices. These patterns can be rotated by introducing a frequency shift between the modes. We can generate bright ring lattices for trapping atoms in red-detuned light, and dark ring lattices suitable for trapping atoms with minimal heating in the optical vortices of blue-detuned light. The lattice sites can be joined to form a uniform ring trap, making it ideal for studying persistent currents and the Mott insulator transition in a ring geometry.