Atom-Optical Calculations
An important part of applying atom optics to nanostructure fabrication is performing
theoretical estimates of the behavior of atoms in a laser field.
These estimates can range from simple analogies with ordinary optics to
full-blown trajectory calculations or even quantum Monte Carlo approaches.
Our approach to atom optics has mainly been from the point of view of
particle optics - that is, the optics of particles such as electrons or ions
traveling in an electrostatic or magnetic field. Particle optics is a highly
developed field, and we have found that many of the concepts can be directly
transferred to atom optics. In each case, after all, the problem consists of
particles moving in a (more or less) conservative potential with a geometry
that causes focusing.
Our first
use [EPG pub# 574] of the
particle optics approach was the analysis of atom focusing in the bore of a
focused, TEM01* ("doughnut"-mode) laser beam. This
geometry, first proposed by Balykin and Letokhov [Opt. Comm. 64, 157(1978)],
showed promise for very high-resolution focusing. By making a direct analogy
with the Glaser model for a magnetic electron lens, we were able to derive
first-order properties, such as focal lengths and principal plane locations, as
well as a number of aberration coefficients. With this in-depth analysis,
we showed that nanometer-scale focal spots are indeed possible with reasonable
experimental conditions.
Another important application of the particle optics approach
has been the analysis of atom focusing in a single node of a laser standing wave
[EPG pub# 649]. As seen in the
figure, the standing-wave atom lens also has the potential for nanometer-scale
resolution. We note that this calculation does not include the effects of
diffraction (based on the De Brogie wavelength of the atom). Using the diffraction
limit formula borrowed from ordinary optics, we find the predicted width to be
about 9 nm for the situation of the figure. Since this is larger than the
value for spherical aberration alone, the lens is, in effect, diffraction
limited.
A further important use of the trajectory approach is a realistic estimate of
expected linewidths, given the actual experimental conditions. We have taken
into account the thermal longitudinal velocity spread and also the residual
transverse velocity spread of the atom beam. We find these to be the major
contributors to the line width, and when they are considered, fairly good
agreement is seen.
In addition to permitting detailed analyses of the behavior of atoms in a
standing wave field, the trajectory approach has also allowed a strong
analogy with simple optics through the paraxial approximation. We have found
that focal lengths and principal plane locations depend only on a single
parameter, which is a combination of laser intensity, waist size, detuning,
and other experimental factors. This allows quick estimates of the behavior
of a lens when one is planning an experiment, or if one wishes to know what
parameter to adjust to improve a lens. A significant impact of this has been
the realization that the best way to narrow the Cr lines is to shorten the focal
length, and this is best achieved by narrowing the laser beam waist.
Laser Focusing of Atoms: A Particle Optics Approach
Atom-Optical Properties of a Standing-Wave Light Field
Jabez J. McClelland - NIST
Michael Scheinfein - Simon Fraser University
Online: May 1996
Last Updated: February 2008
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