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In physics, a neutron interferometer is an interferometer capable of diffracting neutrons, allowing the wave-like nature of neutrons, and other related phenomena, to be explored.
Interferometry inherently depends on the wave nature of the object. As pointed out by de Broglie in his PhD thesis, particles, including neutrons, can behave like waves (the so-called wave–particle duality, now explained in the general framework of quantum mechanics). The wave functions of the individual interferometer paths are created and recombined coherently which needs the application of dynamical theory of diffraction. Neutron interferometers are the counterpart of X-ray interferometers and are used to study quantities or benefits related to thermal neutron radiation.
In 1975 Werner and Overhauser demonstrated quantum phase shifts on neutron matter waves due to gravity. The interferometer was oriented such that two paths are at different heights in Earth's gravitational field. The interferometer was sufficiently sensitive to detected the phase shift due to different acceleration. [1] The phase shift originates from time-dilation differences along the two paths. [2]
Like X-ray interferometers, neutron interferometers are typically made from a single large crystal of silicon, often 10 to 30 or more centimeters in diameter and 20 to 60 cm or more in length. Modern semiconductor technology allows large single-crystal silicon boules to be easily grown. Since the boule is a single crystal, the atoms in the boule are precisely aligned, to within small fractions of a nanometer or an angstrom, over the entire boule. The interferometer is created by removing all but three slices of silicon, held in perfect alignment by a base. (image) Neutrons impinge on the first slice, where, by diffraction from the crystalline lattice, they separate into two beams. At the second slice, they are diffracted again, with two beams continuing on to the third slice. At the third slice, the beams recombine, interfering constructively or destructively, completing the interferometer. Without the precise, angstrom-level alignment of the three slices, the interference results would not be meaningful.
The first neutron interferometer experiments were performed in the 1980s. Experiments with cold neutrons are more recent. Only recently, a neutron interferometer for cold and ultracold neutrons was designed and successfully run. [3] Neutron-optical components in this case comprise three gratings. They are artificially holographically produced, i.e., by means of a light-optic two-wave interference setup illuminating a photo-neutron-refractive polymer. Mechanical stability and count rates are crucial for such an experiment. Therefore, efficient, thermally and mechanically stable optical devices are needed. [4]
Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.
In modern physics, the double-slit experiment demonstrates that light and matter can satisfy the seemingly-incongruous classical definitions for both waves and particles, which is considered evidence for the fundamentally probabilistic nature of quantum mechanics. This type of experiment was first performed by Thomas Young in 1801, as a demonstration of the wave behavior of visible light. At that time it was thought that light consisted of either waves or particles. With the beginning of modern physics, about a hundred years later, it was realized that light could in fact show both wave and particle characteristics. In 1927, Davisson and Germer and, independently George Paget Thomson and Alexander Reid demonstrated that electrons show the same behavior, which was later extended to atoms and molecules. Thomas Young's experiment with light was part of classical physics long before the development of quantum mechanics and the concept of wave–particle duality. He believed it demonstrated that Christiaan Huygens' wave theory of light was correct, and his experiment is sometimes referred to as Young's experiment or Young's slits.
In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater intensity or lower amplitude if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.
Wave–particle duality is the concept in quantum mechanics that quantum entities exhibit particle or wave properties according to the experimental circumstances. It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects. During the 19th and early 20th centuries, light was found to behave as a wave, and then later discovered to have a particulate character, whereas electrons were found to act as particles, and then later discovered to have wavelike aspects. The concept of duality arose to name these contradictions.
Interferometry is a technique which uses the interference of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, spectroscopy, quantum mechanics, nuclear and particle physics, plasma physics, biomolecular interactions, surface profiling, microfluidics, mechanical stress/strain measurement, velocimetry, optometry, and making holograms.
Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave.
Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of the structure of the material. The technique is similar to X-ray diffraction but due to their different scattering properties, neutrons and X-rays provide complementary information: X-Rays are suited for superficial analysis, strong x-rays from synchrotron radiation are suited for shallow depths or thin specimens, while neutrons having high penetration depth are suited for bulk samples.
In physics and chemistry, Bragg's law, Wulff–Bragg's condition or Laue–Bragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a large crystal lattice. It encompasses the superposition of wave fronts scattered by lattice planes, leading to a strict relation between wavelength and scattering angle, or else to the wavevector transfer with respect to the crystal lattice. Such law had initially been formulated for X-rays upon crystals. However, it applies to all sorts of quantum beams, including neutron and electron waves at atomic distances if there are a large number of atoms, as well as visible light with artificial periodic microscale lattices.
The Michelson interferometer is a common configuration for optical interferometry and was invented by the 19/20th-century American physicist Albert Abraham Michelson. Using a beam splitter, a light source is split into two arms. Each of those light beams is reflected back toward the beamsplitter which then combines their amplitudes using the superposition principle. The resulting interference pattern that is not directed back toward the source is typically directed to some type of photoelectric detector or camera. For different applications of the interferometer, the two light paths can be with different lengths or incorporate optical elements or even materials under test.
An atom interferometer is an interferometer which uses the wave character of atoms. Similar to optical interferometers, atom interferometers measure the difference in phase between atomic matter waves along different paths. Today, atomic interference is typically controlled with laser beams. Atom interferometers have many uses in fundamental physics including measurements of the gravitational constant, the fine-structure constant, the universality of free fall, and have been proposed as a method to detect gravitational waves. They also have applied uses as accelerometers, rotation sensors, and gravity gradiometers.
The dynamical theory of diffraction describes the interaction of waves with a regular lattice. The wave fields traditionally described are X-rays, neutrons or electrons and the regular lattice are atomic crystal structures or nanometer-scale multi-layers or self-arranged systems. In a wider sense, similar treatment is related to the interaction of light with optical band-gap materials or related wave problems in acoustics. The sections below deal with dynamical diffraction of X-rays.
Atom optics "refers to techniques to manipulate the trajectories and exploit the wave properties of neutral atoms". Typical experiments employ beams of cold, slowly moving neutral atoms, as a special case of a particle beam. Like an optical beam, the atomic beam may exhibit diffraction and interference, and can be focused with a Fresnel zone plate or a concave atomic mirror.
A holographic grating is a type of diffraction grating formed by an interference-fringe field of two laser beams whose standing-wave pattern is exposed to a set of photosensitive materials. The exposure triggers chemical processes within the sample and results in the formation of a periodic structure that has the same periodicity of the recorded pattern. One of the most interesting features of these structures is their versatility and tunability as the optical response strongly depends on the blend of used materials, and their interactions with light during, and after, the recording procedure.
A common-path interferometer is a class of interferometers in which the reference beam and sample beams travel along the same path. Examples include the Sagnac interferometer, Zernike phase-contrast interferometer, and the point diffraction interferometer. A common-path interferometer is generally more robust to environmental vibrations than a "double-path interferometer" such as the Michelson interferometer or the Mach–Zehnder interferometer. Although travelling along the same path, the reference and sample beams may travel along opposite directions, or they may travel along the same direction but with the same or different polarization.
Phase-contrast X-ray imaging or phase-sensitive X-ray imaging is a general term for different technical methods that use information concerning changes in the phase of an X-ray beam that passes through an object in order to create its images. Standard X-ray imaging techniques like radiography or computed tomography (CT) rely on a decrease of the X-ray beam's intensity (attenuation) when traversing the sample, which can be measured directly with the assistance of an X-ray detector. However, in phase contrast X-ray imaging, the beam's phase shift caused by the sample is not measured directly, but is transformed into variations in intensity, which then can be recorded by the detector.
In quantum mechanics, a quantum carpet is a regular art-like pattern drawn by the wave function evolution or the probability density in the space of the Cartesian product of the quantum particle position coordinate and time or in spacetime resembling carpet art. It is the result of self-interference of the wave function during its interaction with reflecting boundaries. For example, in the infinite potential well, after the spread of the initially localized Gaussian wave packet in the center of the well, various pieces of the wave function start to overlap and interfere with each other after reflection from the boundaries. The geometry of a quantum carpet is mainly determined by the quantum fractional revivals.
A matter wave clock is a type of clock whose principle of operation makes use of the apparent wavelike properties of matter.
In 1923, American physicist William Duane presented a discrete momentum-exchange model of the reflection of X-ray photons by a crystal lattice. Duane showed that such a model gives the same scattering angles as the ones calculated via a wave diffraction model, see Bragg's Law.
Michael Allan Horne was an American quantum physicist, known for his work on the foundations of quantum mechanics.