weak electric/magnetic and optical forces upon neutral atoms and atom-surface interaction which makes atoms stick to the surface of the material rather than being reflected or diffracted [sticking]. Besides, in the latter case, a complicated surface-preparation processes such as annealing and sputtering is necessary to prevent the incoherent reflection so that reflection or diffraction efficiency of an atomic wave can be increased [8-10].
(?), development of supersonic beam source allowed us to overcome the aforementioned problems by providing breakthrough in preparation of atomic wave sources with well-defined kinetic energy [ref].
A combination of the supersonic nozzle with advanced technical developments in laser and nanotechnology show great promise as it allows us to overcome the aforementioned problems. At an earlier stage, laser-tuning enabled us to observe Bragg scattering and Kapitza-Dirac effect of atomic waves by adjusting detuning frequency [11-14]. It motivated the first approach to the practical atomic mirror which is referred to as evanescent wave mirror [15-17]. Meanwhile, the establishment of nano-fabricated devices including transmission grating[18-20] and Fresnel zone plate [21] have served as optical elements for matter-wave. Until now, those instruments have been a basis of the matter-wave interferometry [22-26] as well as atomic de Broglie microscopy [21].
Nonetheless, previous studies carried out with thermal atomic beams had shown the efficiency limit on reflection or diffraction mainly because their de Broglie wavelengths are too short to exploit the wave nature of the matter. Atomic-cooling and -trapping techniques have provided a major breakthrough in preparation of the coherent atomic wave source as enabling us to produce ultracold atoms. Magneto-optically trapped(MOT) metastable neon atoms, for instance, has led to the first observation of a quantum reflection of the atomic wave from the solid surface in 2001 [27]. Thus, the atom optics has been developed based on those studies of controlling the motion of the atoms as well as the technical development.
Recently, the quantum reflection of a thermal atomic beam has been reported at a grazing incidence angle of a few milliradians [28-31]. Under grazing incidence condition which is another way to enhance the wave nature of the particle, the vertical component of the wave vector for a particle is decreased and corresponding de Broglie wavelength gets larger. Hence, when an incident matter-wave propagates almost parallel to a surface, even fast atoms can be coherently reflected from the surface. In such circumstances, the reflectivity from a solid surface can reach 1 as grazing incidence angle goes to 0, which is an important requisite for the practical matter-wave mirror. In other words, those fast atoms without complex preparation steps like trapping or cooling processes can ///complement/// the ultra-cold atoms as the proper matter wave sources for the atomic mirror.////
Furthermore, under the above-mentioned condition, resolved diffraction peaks have been observed from micro-fabricated reflection-gratings [ref]. Figure 1a and 1b show the schematics of matter-wave scattering from a transmission grating with the period of 100 nm and a square-wave grating whose period is 400 um, respectively. For the sake of convenience, the incidence angle \(\theta_{in}\) and the diffraction angle \(\theta_n\) of the nano-transmission grating are defined with respect to the normal line while those are determined by the angle between the incident beam and the grating-surface plane at the square-wave grating. A sign of the diffraction order is defined in a way that diffraction angles of positive orders are larger than negative orders./// In order to see the difference between two gratings, \(n\)-th-order diffraction angles over certain ranges of incidence angles from each grating are calculated by grating equation [2008-19] in Fig 1c and 1d, respectively.
Here, matter-wave de Broglie wavelength is fixed at 136 pm. Assuming the angular resolution of the atomic beam is around 100 urad, up to 5th order diffraction peaks can be observed at grazing incidence angles from the micro-fabricated reflection-grating as it can be from a nano-transmission grating at a normal incidence condition. Considering the fact that the reflection and diffraction efficiencies are increased as incidence angle goes smaller from the reflection-type grating, diffraction efficiencies from square-wave gratings are expected to be higher as much as those efficiencies from transmission grating. Therefore, micro-fabricated structures can act as a matter-wave-grating and it appears important for the generality of matter-wave elements due to its lower price and size-limit than nano-fabricated structures like the nano-transmission grating. Thus, micro-fabricated solid structures can be a good candidate for practical matter-wave optical instruments as exploiting grazing incidence condition.