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Optics Letters

Optimal profile for a Gaussian standing-wave atom-optical lens

Robert E. Behringer, Vasant Natarajan A, Gregory L. Timp

Published Jan 15, 1997• 10 citations
Publisher

Abstract

We have used a Gaussian standing-wave atom-optical lens to focus a thermal atomic beam. We examine the effect of variations in the intensity profile along the direction of the atomic beam on the performance of our atom-optical lens. For a constant focal-length atom-optical lens, we find that the resolution and contrast of the standing-wave lens are independent of the intensity profile.

DOI
10.1364/ol.22.000114

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We have used a Gaussian standing-wave atom-optical lens to focus a thermal atomic beam. We examine the effect of variations in the intensity profile along the direction of the atomic beam on the performance of our atom-optical lens. For a constant focal-length atom-optical lens, we find that the resolution and contrast of the standing-wave lens are independent of the intensity profile.
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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.
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.
Recently, the focusing of an atomic beam using a laser has been considered by Balykin and Letokhov.1 Their calculations explicitly assume the thin lens approximation. Here, using path integral techniques, we derive the focal length and lowest-order aberrations of the laser atomic beam lens as a function of both laser and atomic beam parameters without making the thin lens approximation. Starting from the basic form of the potential energy for an atom in a laser beam, the propagation kernel is derived for the TEM(01)* or donut mode beam. From this result the focal length and lowest-order aberrations can be found for any atomic beam profile. We consider in particular a Gaussian atomic beam. Both the full 3-D propagation kernel and its paraxial approximation are discussed. We show how the paraxial case can be obtained from the 3-D case via a stationary phase approximation of the propagation equation.
We propose a lens for atoms with reduced chromatic aberrations and calculate its focal length and spot size. In our scheme a two-level atom interacts with a near-resonant standing light wave formed by two running waves of slightly different wave vectors, and a far-detuned running wave propagating perpendicularly to the standing wave. We show that within the Raman-Nath approximation and for an adiabatically slow atom-light interaction, the phase acquired by the atom is independent of the incident atomic velocity.