Quantum reflection is a uniquely quantum phenomenon in which an object, such as a neutron or a small molecule, reflects smoothly and in a wavelike fashion from a much larger surface, such as a pool of mercury. A classically behaving neutron or molecule will strike the same surface much like a thrown ball, hitting only at one atomic-scale location where it is either absorbed or scattered. Quantum reflection provides a powerful experimental demonstration of particle-wave duality, since it is the extended quantum wave packet of the particle, rather than the particle itself, that reflects from the larger surface. It is similar to reflection high-energy electron diffraction, where electrons reflect and diffraction from surfaces, and grazing incidence atom scattering, where the fact that atoms (and ions) can also be waves is used to diffract from surfaces.
Definition In a workshop about quantum reflection, the following definition of quantum reflection was suggested:
Quantum reflection is a classically counterintuitive phenomenon whereby the motion of particles is reverted "against the force" acting on them. This effect manifests the wave nature of particles and influences collisions of ultracold atoms and interaction of atoms with solid surfaces.
Observation of quantum reflection has become possible thanks to recent advances in trapping and cooling atoms.
Reflection of slow atoms Although the principles of quantum mechanics apply to any particles, usually the term "quantum reflection" means reflection of atoms from a surface of condensed matter (liquid or solid). The full potential experienced by the incident atom does become repulsive at a very small distance from the surface (of order of size of atoms). This is when the atom becomes aware of the discrete character of material. This repulsion is responsible for the classical scattering one would expect for particles incident on a surface. Such scattering can be diffuse rather than specular, so this component of the reflection is easy to distinguish. To reduce this part of the physical process, a grazing angle of incidence is used; this enhances the quantum reflection. This requirement of small incident velocities for the particles means that a non-relativistic approximation to quantum mechanics is appropriate.
Single-dimensional approximation So far, one usually considers the single-dimensional case of this phenomenon, that is when the potential has translational symmetry in two directions ( y {\displaystyle y} and z {\displaystyle z} ), such that only a single coordinate ( x {\displaystyle x} ) is important. In this case one can examine the specular reflection of a slow neutral atom from a solid state surface . Where one has an atom in a region of free space close to a material capable of being polarized, a combination of the pure van der Waals interaction, and the related Casimir-Polder interaction attracts the atom to the surface of the material. The latter force dominates when the atom is comparatively far from the surface, and the former when the atom comes closer to the surface. The intermediate region is controversial as it is dependent upon the specific nature and quantum state of the incident atom. The condition for a reflection to occur as the atom experiences the attractive potential can be given by the presence of regions of space where the WKB approximation to the atomic wave-function breaks down. In accordance with this approximation the wavelength of the gross motion of the atom system toward the surface as a quantity local to every region along the x {\displaystyle x} axis is,
λ ( x ) = h 2 m ( E − V ( x ) ) {\displaystyle \lambda \left(x\right)={\frac {h}{\sqrt {2m\left(E-V\left(x\right)\right)}}}}
where m {\displaystyle m} is the atomic mass, E {\displaystyle ~E~} is its energy, and V ( x ) {\displaystyle ~V(x)~} is the potential it experiences; then it is clear that we cannot give meaning to this quantity where,
| d λ ( x ) d x | ∼ 1 {\displaystyle \left|{\frac {d\lambda \left(x\right)}{dx}}\right|\sim 1}
That is, in regions of space where the variation of the atomic wavelength is significant over its own length (i.e. the gradient of V ( x ) {\displaystyle V(x)} is steep), there is no meaning in the approximation of a local wavelength. This breakdown occurs irrespective of the sign of the potential, V ( x ) {\displaystyle ~V(x)~} . In such regions part of the incident atom wave-function may become reflected. Such a reflection may occur for slow atoms experiencing the comparatively rapid variation of the Van der Waals potential near the material surface. This is just the same kind of phenomenon as occurs when light passes from a material of one refractive index to another of a significantly different index over a small region of space. Irrespective of the sign of the difference in index, there will be a reflected component of the light from the interface. Indeed, quantum reflection from the surface of solid-state wafer allows one to make the quantum optical analogue of a mirror - the atomic mirror - to a high precision.
Experiments with grazing incidence
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