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Journal of Vacuum Science & Technology B Microelectronics and Nanometer Structures Processing Measurement and Phenomena

Limit of resolution of a standing wave atom optical lens

Robert E. Behringer, Vasant Natarajan A, Gregory L. Timp, D. M. Tennant

Published Nov 1, 1996• 8 citations
Publisher

Abstract

Using a Gaussian standing wave at λ=589 nm as an atom optical lens, we have focused a thermal atomic sodium beam. We have examined the limits of the resolution of this focusing technique, and have made structures with linewidths of 13 nm and contrast of 6:1 with a short focal length atom optical lens. While numerical simulations predict that smaller structures should be attainable with shorter focal lengths, we find that the resolution deteriorates for focal length shorter than f≊16 μm.

DOI
10.1116/1.588647

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Using a Gaussian standing wave at λ=589 nm as an atom optical lens, we have focused a thermal atomic sodium beam. We have examined the limits of the resolution of this focusing technique, and have made structures with linewidths of 13 nm and contrast of 6:1 with a short focal length atom optical lens. While numerical simulations predict that smaller structures should be attainable with shorter focal lengths, we find that the resolution deteriorates for focal length shorter than f≊16 μm.
Summary form only given. Recently it has been demonstrated that neutral atomic beams can be focused by use of a laser as an atom-optical lens. Standing wave atom-optical (SW) lenses have been of particular interest because of the potential for both high-resolution and high-throughput lithography. In this paper, using sub-Doppler optical cooling schemes in conjunction with mechanical collimation, and a SW with /spl sigma/=56 /spl mu/m, we have been able to achieve <20 nm resolution with contrast of at least 10:1, focusing a thermal atomic sodium beam using 589-nm light corresponding to the D/sub 2/ transition.
We show that light force lenses can be used to focus a thermal beam of neutral atoms with extremely high resolution (\ensuremath{\sim}20 nm) and high contrast (\ensuremath{\sim}10:1), finally making such atom-optical lenses viable for proposed applications. Our (cylindrical) lenses for sodium atoms are created by the dipole force within each period of a standing wave. We determine the spatial distribution of the focused atoms (with nanometer resolution) by allowing the atoms to deposit on a substrate and scanning with a UHV scanning tunneling microscope. We find that the requirements for optimum focusing are very large, positive detuning; short focal lengths; and a well-collimated atomic beam. These dependences can be thoroughly understood from a simple theoretical model. \textcopyright{}1996 The American Physical Society.
The focusing of atoms to nanometer-scale dimensions by a near-resonant standing-wave light field is examined from a particle optics perspective. The classical equation of motion for atoms traveling through the lens formed by a node of the standing wave is derived and converted to a spatial trajectory equation. A paraxial solution is obtained, which results in simple expressions for the focal properties of the lens, useful for estimating its behavior. Aberrations are also discussed, and an exact numerical solution of the trajectory equation is presented. The effects on focal linewidth of angular collimation and velocity spread in the atomic beam are investigated, and it is shown that angular collimation has a much more significant effect than velocity spread, even when the velocity spread is thermal.
A near-resonant standing laser light field is used to focus a diverging beam of sodium atoms onto the atomic-beam axis. The investigations presented here distinguish between channeling of atoms with trajectories close to the axis and imaging of the atomic source. For laser detunings close to resonance, acceleration of the atoms in the transverse direction occurs. The amount of acceleration changes as either the intensity or the detuning of the standing wave is varied, thereby altering the position at which the atoms are imaged. This results in a variable focal-length lens for atoms. The experimental results are in good agreement with a theoretical model based on a continued-fraction solution for the standing-wave light forces.