Atom focusing by far-detuned and resonant standing wave fields: Thin lens regime

Evolving from the initial experiments [1,2], the study of atom focusing using standing wave (SW) light fields has developed into a broad area of research in atom optics. A standing wave field acts as a lens as a result of a spatially-dependent light shift, focusing atoms into a periodic set of lines or dots having widths of the order of tens of nanometers and distanced from one another by λ/2, where λ is the wave length of the light. Focusing by thick lenses and atomic deposition on a substrate have been observed for beams of Na [1,3–7], metastable He [2], and Cr [8–10]. The latest achievements in this area are summarized in a recent review article [11]. Perhaps even more significantly, lithographic techniques have been developed to create nanosurfaces in semiconductors and metals using metastable atoms as a pattern template for selective etching [12]. Similarly, cold, trapped atoms can be subjected to SW light pulses [13,14], creating a periodic wave packet which will focus along the field propagation direction at specific times following the atom-field interaction. Previous experiments with atomic beams have been carried out in a thick lens regime for which the atoms focus within the laser beam. Since the substrate surface is typically placed near the plane of peak intensity of the thick SW lens and mechanically fixed to the retroreflecting mirror, in some sense these experiments are easier to set up when compared to thin lens experiments. The classical and quantum motion through a thick lens have been numerically simulated and compared to experimental data in Refs. [7,15–18]. The classical motion and lens parameters after thick and thin lenses have also been studied in detail within a ray optics formalism [19]. For that work the lens characteristics and aberrations beyond the parabolic lens approximation were simulated numerically as were the effects of different atomic velocity distributions. However, a comprehensive theoretical study of the thin SW lens from a quantum perspective that details corrections to the lens parameters as a result of spherical aberration, chromatic aberration, and angular beam divergence has not appeared previously.