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Journal of the Optical Society of America B

Atoms in axially shifted tightly focused counter-propagating beams: the role of the Gouy and curvature phases

Koray Köksal, V. E. Lembessis, Jun Tang Yuan, M. Babiker

Published Jul 7, 2020• 3 citations
Publisher

Abstract

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.

DOI
10.1364/josab.396097

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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.
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.
A novel optical set-up which enables cold atoms to be trapped in a finite set of miniature (sub-wavelength) bottle traps is highlighted. These bottle traps are formed when the atoms interact with a tightly focused standing wave due to two-counter propagating optical vortex beams possessing the same winding number ℓ=±1\ell=\pm1ℓ=±1 and the same circular polarization (σ=∓1)\sigma=\mp 1)σ=∓1). Tight focusing generates strong longitudinal field components which become responsible for an on-axis standing wave. The resulting optical potential leads to the axial confinement of far blue-detuned atoms. This completes the formation of the bottle trap, since the off-axis radial confinement is, as usual, provided by the optical potential due to the interference of the transverse components of the light. The main characteristics of the bottle traps are illustrated using typical experimentally-accessible parameters. Due to the spin-orbit coupling the trap parameters are tunable by changing the ellipicity of the light.
A novel optical set-up which enables cold atoms to be trapped in a finite set of miniature (sub-wavelength) bottle traps is highlighted. These bottle traps are formed when the atoms interact with a tightly focused standing wave due to two-counter propagating optical vortex beams possessing the same winding number ℓ=±1\ell=\pm1ℓ=±1 and the same circular polarization (σ=∓1)\sigma=\mp 1)σ=∓1). Tight focusing generates strong longitudinal field components which become responsible for an on-axis standing wave. The resulting optical potential leads to the axial confinement of far blue-detuned atoms. This completes the formation of the bottle trap, since the off-axis radial confinement is, as usual, provided by the optical potential due to the interference of the transverse components of the light. The main characteristics of the bottle traps are illustrated using typical experimentally-accessible parameters. Due to the spin-orbit coupling the trap parameters are tunable by changing the ellipicity of the light.
Laguerre-Gaussian (LG) light modes with large values of the radial index ppp and the azimuthal index lll are considered. We give special emphasis on the mechanical effects on atoms arising from the Gouy phase and the phase due to the curvature of such light. It is shown that the additional phase terms for highly twisted light can lead to mechanical effects based on the substantial reduction of the axial wavenumber. As a consequence, axial recoil effects are diminished in the processes of stimulated emission and absorption of the light by the atoms. Both the scattering force and the momentum diffusion are affected by the inclusion of these normally ignored additional phase terms. The magnitudes of the effects are explored using order of magnitude analysis with typical parameters due to the atoms and the light.
A light beam tightly focused by a high numerical-aperture lens system contains longitudinal components with polarization parallel to the propagation axis. By numerically analyzing the polarization distribution around the focal region in one pair of confocally aligned counter-propagating tightly focused light beams with orthogonal linear polarizations, we found that there exists a three-dimensional polarization gradient pattern similar to that used in cooling neutral atoms. This can be used to three-dimensionally cool atoms trapped in a far-off-resonant trap with only one pair of counter-propagating beams in one dimension. This new cooling scheme can be used to individually cool single atoms in an addressable two-dimensional single-atom array for quantum information processing and be applied to perform readouts of qubit encoded in these atoms without losing them.
We describe a relatively large volume dipole laser trap for the confinement of sodium atoms. Two counterpropagating beams, tuned below resonance, with foci separated by approximately one con focal parameter, provide radial confinement via the dipole force and axial confinement by balancing the radiation pressures of the two beams.1 Identical circular polarization for both beams prevents optical pumping and serves to maintain a two-state system. Alternation of the two beams2 is necessary to avoid the effects of standing-wave heating. Additionally, the trapping cycle is alternated with a Doppler cooling cycle2 to achieve low temperatures and long confinement times. Trapping beams of 100 mW focused to 50-μm spot radii and detuned ~2 GHz below the F = 2 to F′= 3 transition of the D2 line provide a well depth of 50 mK and a confinement volume of 10-4 cm3. Analysis of atomic motion and escape mechanisms as well as progress toward the experimental realization of this trap is presented.