Atom optics

 The early stage of atom optics was in need of further steps while electron and neutron optics were on a fast track [3-7, 1994-review]. In truth, since 1930, when Stern and Estermann showed diffraction of He atoms from the crystal surface of lithium fluoride [2], following studies on atom optics were halted for next 40 years. One of the obstacles for realization of atom optics was a lack of intense and coherent atomic source. Without the proper atomic source, neither static electric or electromagnetic field nor solid materials are suitable to change their motion while preserving their coherence while both of them easily affect motions of neutrons and electrons. There are two reasons for this: 1) electric, magnetic and optical forces upon thermal neutral atoms are too weak to change their motion [8]; and 2) atoms collide with rather than penetrate through the solid material, causing diffusive scattering. 
 Development of a supersonic beam, in the 1970s, appeared to be a starting point to address the aforementioned problems [ref]. Under supersonic expansion, atoms in the high-pressure environment, pass through an orifice into low pressure or vacuum region. Their random thermal motions are, thereby, collimated, i.e.; atomic wave sources with well-defined kinetic energy become available [9]. Such supersonic beams serving as the coherent atomic source enabled various studies on the physisorption or chemisorption as well as the atomic diffraction from the crystal surface [10-18?/scattering//]. Thus, an advent of the proper atomic source played an important role in the revival of atom optics. 
 The further progress in atom optics has been accelerated by the advanced technical developments in laser and nanotechnology such as improved quality and tunability of laser and nano-fabrication technique; Enhanced coherence and intensity of the laser enabled us to observe Bragg scattering and the Kapitza-Dirac effect of atomic waves by generating a standing wave [19-22]. Besides that, intense tunable laser motivated the first approach to an evanescent wave mirror [23,24], by adjusting the detuning frequency with respect to the transition frequency of atoms. In addition, the establishment of nano-fabricated devices has served as atomic optical elements such as transmission grating [25-27] and Fresnel zone plate [28-31]. Until now, those instruments have been the basis of matter-wave interferometry [32-35] as well as atomic de Broglie microscopy [28-31].
 Moreover, attempts to utilize advanced laser technology to explore the atomic motion has led to the advent of laser-cooling and -trapping techniques in the late 20th century. By exploiting such techniques to atoms, ultracold atoms (~\(nK\)) are produced. In general, the de Broglie wavelength of the ultracold atoms is much larger than that of thermal atoms. Such a large atomic de Broglie wavelength emphasize the wave nature of atoms, giving rise to the quantum mechanical phenomena, e.g.; quantum reflection. For instance, magneto-optically trapped(MOT) metastable neon atoms has led to the first observation of a quantum reflection of the atomic wave from the solid surface [27]. It made a significant advance in atomic mirrors. Hence, such technical developments has been the key to atom optical source as well as elements. 

Atomic mirror

Reflection mechanism 1: Classical reflection

 Reflection from the surface>reflection from a repulsive potential> Classical reflection. 
 As mentioned above, earlier studies of atomic reflection has been carried out with thermal supersonic beams through He atom scattering from crystal surfaces [ref]. However, the reflection efficiency of such a mirror have been limited by its high sensitivity to the surface quality [DW]. Since atomic de Broglie wavelengths of thermal beams (around sub-angstroms) are much smaller than the characteristic surface roughness (usually 100 angstroms), the atoms are classically reflected at the repulsive potential [reference]. Under such a circumstance, the atomic reflection happens close by the outmost atoms on the surface, influenced by the local variation of the potential along the surface. Namely, surface roughness and adsorbates on the surfaces cause the incoherent reflection. For this reason, complicated surface-preparation processes like annealing and sputtering are crucial to render surfaces smooth at the atomic-level [8-10]. Furthermore, since the solid surface are easily affected by surroundings, ultra high vacuum (~10-12 mbar) are necessary during the whole experiment [ref]. Besides, even a perfectly clean surface would, nonetheless, have unexpected surface defects (i.e, surface steps, adatoms and vacancies), decreasing reflectivity [ref].
 Therefore, the initial stage of atomic mirrors has been proposed in a way that prevents atom-surface collisions because atom-surface interaction has been known to undermine coherent reflection from the surface [ref--]. For example, the evanescent wave mirror[ref] and the magnetic mirror [ref] use the evanescent wave and the magnetic field applied along the surface, respectively, to prevent atom-surface collisions. The artificial repulsive potentials induced by those field push atoms away from the surface before they collide against it. However, the delicate fabrication process and lithography technique are necessary to construct the magnetic mirror and evanescent wave mirror is only applicable to specific atoms. In addition, such mirrors are difficult to make big in size without compromising accuracy.

Reflection mechanism 2: quantum reflection

 Ultracold atoms ( ̃μK), formed by laser-cooling and trapping techniques, have provided a major breakthrough in atomic mirrors. In general, the de Broglie wavelength of the ultracold atoms is much larger than that of thermal atoms. Such a large atomic de Broglie wavelength emphasize the wave nature of atoms, giving rise to the quantum mechanical phenomena, e.g.; quantum reflection. For instance, magneto-optically trapped(MOT) metastable neon atoms has led to the first observation of a quantum reflection of the atomic wave from the solid surface [27]. It is noteworthy that their study revealed the possibility of using a bare solid material without any applied field as a decent atomic mirror through the quantum reflection. Driven by such a pioneering research, numerous studies on the quantum reflection from the surface both in theory and experiment have been carried out with various solid materials such as silicon or glass surface and even with structured surfaces [ref]. As a result of such active studies, the solid material is finally found to be the proper atomic mirror which reflectivity can reach 1 at certain conditions. Thus, the creation of ultracold atoms made a significant advance in atomic mirrors. 
 As previously stated, the quantum reflection breakthrough in discovery of solid atomic mirror, is a quantum mechanical phenomenon in which a particle is reflected by the attractive part of the atom-surface interaction, also known as Casimir-van der Waals potential. The Casimir-van der Waals potential is given by the equation below: