Experiments With Grazing Incidence
Practically, in many experiments with quantum reflection from Si, the grazing incidence angle is used (figure 0). The set-up is mounted in a vacuum chamber to provide several meter free path of atoms; the good vacuum (at the level of 10−7 mm Hg ) is required. The magneto-optical trap (MOT) is used to collect cold atoms, usually excited He or Ne, approaching the point-like source of atoms. The excitation of atoms is not essential for the quantum reflection but it allows the efficient trapping and cooling using optical frequencies. In addition, the excitation of atoms allows the registration at the micro-channel plate (MCP) detector (bottom of the figure). Movable edges are used to stop atoms which do not go toward the sample (for example a Si plate), providing the collimated atomic beam. The He-Ne laser was used to control the orientation of the sample and measure the grazing angle . At the MCP, there was observed relatively intensive strip of atoms which come straightly (without reflection) from the MOT, by-passing the sample, strong shadow of the sample (the thickness of this shadow could be used for rough control of the grazing angle), and the relatively weak strip produced by the reflected atoms. The ratio of density of atoms registered at the center of this strip to the density of atoms at the directly illuminated region was considered as efficiency of quantum reflection, i.e., reflectivity. This reflectivity strongly depends on the grazing angle and speed of atoms.
In the experiments with Ne atoms, usually just fall down, when the MOT is suddenly switched-off. Then, the speed of atoms is determined as, where is acceleration of free fall, and is distance from the MOT to the sample. In experiments described, this distance was of order of 0.5 meter, providing the speed of order of 3 m/s. Then, the transversal wavenumber can be calculated as, where is mass of the atom, and is the Planck constant.
In the case with He, the additional resonant laser could be used to release the atoms and provide them an additional velocity; the delay since the release of the atoms till the registration allowed to estimate this additional velocity; roughly, where is time delay since the release of atoms till the click at the detector. Practically, could vary from 20 m/s to 130 m/s.
Although the scheme at the figure looks simple, the extend facility is necessary to slow atoms, trap them and cool to millikelvin temperature, providing a micrometre size source of cold atoms. Practically, the mounting and maintaining of this facility (not shown in the figure) is the heaviest job in the experiments with quantum reflection of cold atoms. The possibility of an experiment with the quantum reflection with just a pinhole instead of MOT are discussed in the literature.
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