Projection of diffraction patterns for use in cold-neutral-atom trapping

Scalar diffraction theory is combined with beam-propagation techniques to investigate the projection of near-field diffraction patterns to spatial locations away from the aperture for use in optically trapping cold neutral alkali-metal atoms. Calculations show that intensity distributions with localized bright and dark spots usually found within a millimeter of the diffracting aperture can be projected to a region free from optical components such as a cloud of cold atoms within a vacuum chamber. Calculations also predict that the critical properties of the optical dipole atom traps are not only maintained for the projected intensity patterns but also can be manipulated and improved by adjustment of the optical components outside the vacuum chamber.

Figure 1

Intensity distribution pattern just beyond a metallic circular aperture with a radius of 50 $\mu$m and a laser wavelength of 780 nm, normalized to the intensity incident upon the aperture. The locations of the localized bright region for the primary red-detuned trap site and the localized dark region for the primary blue-detuned trap site are noted.

Figure 2

Theoretical setup for projecting near-field diffraction patterns to an optics-free location within a MOT cloud of cold atoms. The key parameters are the aperture radius, $a$, the aperture-to-lens distance, $L$, the focal length of the lens, $f$, and the axial distance between the lens and the point of interest, $z$. Plane 0 is the axial location of the aperture, and plane 1 is an axial plane within the diffraction region.

Figure 3

Diffraction patterns for an aperture with a radius of 25 $\mu$m, where (a) is the original pattern just beyond the diffracting aperture, (b) is a projection with the aperture-to-lens distance, $L$, chosen such that the projection is approximately the same size as the original, (c) is a projection with $L$ chosen such that the projection is smaller than the original, and (d) is a projection with $L$ chosen such that the projection is larger than the original. Parts (b)–(d) are all set to the same distance scaling as (a) for direct comparison of the size differences, and (e) is an expansion of (c). All numerical intensity scaling values are normalized to the intensity incident upon the aperture.

Figure 4

(a) Original and (b) projected intensity patterns for the creation of a nanotrap. The aperture radius is 5 $\mu$m, the focal length of the lens is 40 mm, and the aperture-to-lens distance is set to 125 mm. Both intensity scaling values are normalized to the intensity incident upon the aperture.