1. Introduction
Matter-wave optics refers to coherent manipulations of a matter-wave. In 1924, the postulation of wave nature of matter by de Broglie broke new ground for matter-wave optics. Subsequent observation of electron reflection from a crystal surface have confirmed his hypothesis [1] and opened up the possibility of developing new techniques using matter-waves. For example, the development of electron wave optics including electromagnetic lens has motivated electron microscopy, which still remains an indispensable device to reveal the ultrastructure such as microorganism [ref]. Thus, matter-wave-based instruments have been achieved based on the matter-wave optical elements such as a mirror, beam splitter, and lens.
\cite{Oberst_2005}\cite{Galiffi_2017}
In the past few decades, a new type of matter-wave microscopy has been developed by using neutral He atoms as a probe source, known as a neutral He atom microscopy. By taking advantages of He atoms’ low energy (5-100 meV) and chemical inertness, it has drawn attention as a surface sensitive microscopy capable of imaging not only fragile structures but also insulating materials without damaging target samples[ref]. However, the He atom microscopy is still challenging to commercialize due to the technical limitation on atom optical elements and detectors. Atomic mirrors and zone plates have been proposed as a focusing element of the He atom microscopy through years of efforts, yet neutral He atom microscopy has been limited by the low intensity and resolution [ref].
In my introduction, I outline briefly about atom optics along with the technical development first. Studies on atom optics been motivated by the achievement of atomic sources and elements. Amongst the optical elements, atomic mirrors are dealt with in this thesis as a key component of matter-wave microscopy. Several underlying physical principles for atomic reflection (i.e., classical, quantum reflections and edge diffraction from an array of half plane) with consequent atomic mirrors will follow. Finally, a summary of this project is described.
1.1 Atom optics
The early stage of atom optics was in need of further steps while electron and neutron optics were on a fast track [ref]. 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 the next 40 years. One of the obstacles for the realization of atom optics was a lack of intense and coherent atomic source. Without a 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 the 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]. Thus, the 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 technological 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 laser-cooling and -trapping techniques in the late 20th century. By exploiting such techniques to atoms, ultracold atoms (below \(\mu K\)) are produced, providing a high-flux and much slower atomic source. It made a significant advance in atomic mirrors: 1) normal incidence atomic reflection from the evanescent wave mirror has been achieved [ref]; 2) the atomic reflection from an external magnetic field, known as a magnetic mirror, has been performed for the first time [in evanescent thesis]. Furthermore, since ultracold atoms have low kinetic energy, their de Broglie wavelength is much larger than 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. As described below, the quantum reflection has provided a major breakthrough in the discovery of solid atomic mirror (see 1.2.2).
1.2 Atomic mirror