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Physical Review A

Beaming matter waves from a subwavelength aperture

Antonio I. Fernández‐Domínguez, Esteban Moreno, Luis Martín-Moreno, Francisco José García-Vidal

Published Aug 17, 2006• 11 citations
Publisher

Abstract

We show theoretically that the shape of a beam of matter waves (cold atoms) emerging from one subwavelength aperture pierced in a film can be collimated within a few degrees. By means of an external laser field, a potential well for the atoms in the direction perpendicular to the surface is created. In this way, a running surface matter wave can be excited when atoms diffract from the aperture. If the aperture is surrounded with a finite array of indentations, coherent scattering of the surface matter wave with these indentations molds the angular distribution of the matter wave in the far field.

DOI
10.1103/physreva.74.021601

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We show theoretically that the shape of a beam of matter waves (cold atoms) emerging from one subwavelength aperture pierced in a film can be collimated within a few degrees. By means of an external laser field, a potential well for the atoms in the direction perpendicular to the surface is created. In this way, a running surface matter wave can be excited when atoms diffract from the aperture. If the aperture is surrounded with a finite array of indentations, coherent scattering of the surface matter wave with these indentations molds the angular distribution of the matter wave in the far field.
We study in detail the appearance of the phenomenon of resonant transmission of matter waves (cold noninteracting atoms) through subwavelength apertures. We show how the emergence of this effect, first reported for electromagnetic waves, is associated with the excitation of surface matter waves, the analog of surface plasmon polaritons in the electromagnetic case. We describe the similarities and differences for the one-dimensional (array of slits) and two-dimensional (array of holes) cases. In this last structure, extraordinary transmission of matter waves is theoretically predicted. Finally, we also study the existence of the beaming effect for matter waves in single apertures flanked by periodic corrugations.
Recently, it has been observed that transmission of light through subwavelength apertures, which is usually negligible, can be significantly enhanced when surface plasmons are resonantly excited. Here we introduce the idea that similar effects can be expected for cold atoms in structures supporting surface matter waves. We show that surface matter waves are possible in properly designed structures, and then we theoretically demonstrate 100% transmission of rubidium atoms through an array of slits much narrower than the de Broglie wavelength of the atoms. Our results open up the possibility of using surface matter waves to control the flow of neutral atoms.
A simple focusing device is proposed for de Broglie matter-waves - a diffractive lens, based on the optical effect of diffractive multifocal focusing of radiation. This matter-wave lens consists of two co-axial circular apertures in which the second aperture of smaller diameter is located where the Fresnel number of the first aperture is unity. It is shown that diffraction of a de Broglie matter wave by a system of two pinholes on an optical axis exhibits the multifocal focusing effect of matter waves in the near-field (Fresnel) zone. The focusing, defocusing and refocusing phenomenon is explained as resulting from periodic phase changes at singular points, which are points where the intensity is zero and the phase is undefined. It is shown that the proposed matter-wave lens could create a very intense, spatially-localized beam of atoms. Theoretical predictions for the focusing efficiency of a neutral atomic beam by the diffractive lens are: the spot diameter is ~ 0.1 &mgr;m, the ratio of focal and incident intensities is ~ 15, the focal length of the diffractive lens is in the range ~ 0.13.6 cm, the focusing depth is in the range ~ 15.30 cm, and the energy transmitting efficiency is ~ 30%. For the relatively-large diameters of the pinholes, ⩾ 5.0 &mgr;m, the proposed configuration acts as a matter-wave lens with a large focal length and a long focusing depth.
We develop a versatile theoretical approach to the study of ultracold atom diffractive scattering from light-field gratings by combining calculations of the optical near field generated by evanescent waves close to the surface of periodic nanostructured arrays with atom wavepacket propagation techniques. Nanometric one dimensional (1D) and 2D arrays with subwavelength periodicity deposited on a transparent surface and optically coupled to an evanescent wave source exhibit intensity and polarization gradients on the length scale of the object and can produce strong near-field periodic modulation in the optical potential above the structure. As a specific and experimentally practical example we calculate the diffraction of cold Cs atoms dropped onto a periodic optical potential crafted from a 2D nanostructure array. For an ``out-of-plane'' configuration we calculate a wide diffraction angle $(\ensuremath{\simeq}2\ifmmode^\circ\else\textdegree\fi{})$ and about 6060%60 of the initial atom flux in diffraction orders $\ifmmode\pm\else\textpm\fi{}1,$ an encouraging result for future experiments.
Atom laser experiments with Bose–Einstein condensates (BECs) performed in ground-based laboratories feature a coherent and directed beam of atoms which is accelerated by gravity. In microgravity the situation is fundamentally different because the dynamics is entirely determined by the repulsive interaction between the atoms and not by the gravitational force. As a result, the output of a space atom laser is a spherical wave slowly expanding away from the initial BEC. We present a thorough theoretical study of this new source of matter waves based on rf outcoupling which exhibits an isotropic distribution both in position and momentum even for an initially anisotropic trap. The unique geometry of such a freely expanding, shell-shaped BEC offers new possibilities for matter waves in microgravity and is complementary to other matter-wave sources prepared by delta-kick collimation or adiabatic expansion. Our work paves the way for the upcoming experimental realization of a space atom laser making use of NASA's Cold Atom Laboratory on the International Space Station.
This work has theoretically studied the optical properties, such as the object-image relation and the focal length of the atom-optical lens created by far red-detuned Gaussian laser beam perpendicular to the propagation direction of the atomic cloud. Furthermore we have thoroughly studied the collimation effect when the cold atomic clouds passing through the laser beam. The effective transverse temperature can reach tens nanokelvin, which is far smaller than that by 1D polarization gradient cooling.