Matter wave optics

The atom mirror is the key element of matter-wave optics. An electromagnetic mirror for neutral atoms was suggested by Cook and Hill (1982). The idea was to use the radiation force of an evanescent laser wave outside a dielectric surface to repel slow atoms. This evanescent-wave atomic mirror was realized experimentally by Balykin et al. (1988a). 

However, the theorem of reciprocity is a wave optical argument that does not consider intensities where we easily find the differences. For example, if one thinks of a STEM as an inverted HRTEM one would not detect any intensity in an image since it is an inherent property of a point detector to collect no intensity. On the other extreme side, the ability to form an intense and focused probe is a valuable ability that boosts local spectroscopy. Obviously, the best choice of tools cannot be a matter of exclusion but must relate to the problem at hand that needs solving . 

Quantum theory was developed primarily to find an explanation for the stability of atomic matter, specifically the planetary model of the hydrogen atom. In the Schrodinger formulation the correct equation was obtained by recognizing the wave-like properties of an electron. The first derivation by Schrodinger [30] was done by analogy with the relationship that was known to exist between wave optics and geometrical optics in the limit where the index of refraction, n does not change appreciably over distances of order A. This condition leads to the eikonal equation (T3.15)... 

Keywords Quantum optics, matter waves, molecule interferometry, decoherence, fullerenes... 

In principle, the diffraction patterns can be quantitatively understood within the Fraunhofer approximation of Kirchhoff s diffraction theory as described in any optics textbook (e.g., [Hecht 1994]). However, Fraunhofer s optical diffraction theory misses an important point of our experiments with matter waves and material gratings the attractive interaction between the molecule and the wall results in an additional phase of the molecular wavefunction [Grisenti 1999], Although the details of the calculations are somewhat involved2, the qualitative effect of this attractive force on far-field diffraction can be understood as a narrowing of the real slit width to an effective slit width [Briihl 2002], For our fullerene molecules the reduction can be as big as 20 nm for the unselected molecular beam and almost 30 nm for the slower, velocity selected beam. The stronger effect on slower molecules is due to the longer and therefore more influential interaction between the molecules and the wall. 

Matthias Freybvurger, Alois M. Herjkommer, Daniel S. Km, Erwin Mayr, and Wolfgang P. Schleich Atom Waveguides, Victor I. Balykin Atomic Matter Wave Amplification by Optical Pumping, UlfJanicke and Martin Wilkens... 

Figure 1. A binary optical multilayer (a) together with its quantum mechanical counterpart a particle with energy Ep = hco (co being the de Broglie frequency in terms of matter waves [6]) in ID periodic (b) and non-periodic (c) binary stepwise potential. The potential u replaces the refractive index n. Elementary wells are defined as fragments (m, di), i = 1,2.

Fig. 9.70 Optical Ramsey scheme of an atomic beam passing through four traveling laser fields, interpreted as matter-wave interferometer. Solid lines represent the high-frequency recoil components, dotted lines the low-frequency components (only those traces leading to Ramsey resonances in the fourth zone are drawn) [1290]...

Ginsberg NS, Gamer SR, and Hau LV. Coherent control of optical information with matter wave dynamics. Nature 2007 Feb 8 445 623-626. 

A beam of slow atoms can be manipulated in many ways. This is performed within the field of atom optics [9.445-9.447]. An atomic beam can be bent or focused using laser fields. An atomic beam can also be reflected at an optical surface using the evanescent optical field from a laser beam reflected from the other side of the surface. The atom version of the Yoimg double-slit experiment has been performed, even with monochromatic thermal atoms, showing clearly the existence of matter waves [9.448]. Beam splitters for slow atomic beams can be optically achieved to build atomic interferometers based on de Broglie wave interference. The thermal de Broglie wavelength... 

F. Riehle, Th. Kisteers, A. White, J. Helmecke, Ch.J. Borde Optical Ramsey spectroscopy in a rotating frame Sagnac effect in a matter-wave interferometer. Phys. Rev. Lett. 67, 177 (1991)... 

Negretti A, Benseny A, Mompart J, Calarco T (2013) Speeding up the spatial adiabatic passage of matter waves in optical microtraps by optimal control. Quantum Inf Process... 

Wave optics deals with the propagation of light waves and their interaction with matter. 

Given the advanced state of wave-profile detectors, it seems safe to recognize that the descriptions given by such an apparatus provide a necessary, but overly restricted, picture. As is described in later chapters of this book, shock-compressed matter displays a far more complex face when probed with electrical, magnetic, or optical techniques and when chemical changes are considered. It appears that realistic descriptive pictures require probing matter with a full array of modern probes. The recovery experiment in which samples are preserved for post-shock analysis appears critical for the development of a more detailed defective solid scientific description. 

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