A small crystal distortion can dramatically translate the path of an x-ray beam, an effect that could be useful in the development of x-ray optics. The first impression one gets walking into an optics lab is of the endless maze of mirrors, lenses, etc., that can bend and guide the light along practically any desired path. Controlling x rays in the same manner, however, is much harder. In a paper appearing in Physical Review Letters, Yoshiki Kohmura, Kei Sawada, and Tetsuya Ishikawa at the SPring-8 synchrotron in Hyogo, Japan, show they can displace an x-ray beam propagating inside a crystal by a drastic amount - of order a millimeter - by deforming a single crystal less than 100 nanometers. They argue that the displacement arises from a geometric, or Berry, phase picked up by the waves constituting the x ray, an effect predicted several years ago. Experimentally, much remains to be done towards a full demonstration of the geometric-phase effect on the beam propagation. This statement is not meant to be derogatory - the experiments are challenging - but rather to stimulate further work in precision x-ray optics and, at the same time, investigate further what could be a toymore » model for many other fields of physics. Berry phases appear in many contexts of physics, including quantum systems, classical oscillators, and classical wave-propagating media. In the 1980s, Michael Berry observed that a quantum system, which is described by multiple parameters, picks up a phase beyond that of its dynamical evolution if the parameters are changed slowly along a closed loop in the parameter space (where each axis represents one parameter). This additional phase depends only on the geometrical properties of the loop. In particular, the Berry phase does not depend on the time it takes to traverse the loop, as long as it is done sufficiently slowly (adiabatically). The classic example is the polarization of a light beam as it is transmitted through a twisted optical fiber. Geometric phases are closely related to another ubiquitous concept - that of avoided crossings. The term 'avoided crossings' refers to energy levels in spectroscopy that rise or fall under the influence of an external field, but the concept applies generally to interacting parameter-dependent oscillatory modes, or wave modes in a parameter-dependent medium. As parameters are varied, and two modes become similar (say, they approach the same frequency), oscillatory averaging of the interaction no longer applies. Because the modes are coupled, they can no longer be degenerate and they repel each other by splitting into two coupled-wave modes with oppositely phased contributions from the original modes.« less
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