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Quantum reflection is a physical phenomenon involving the reflection of a matter wave from an attractive potential. In classical mechanics, such a phenomenon is not possible; for instance when one magnet is pulled toward another, the observer does not expect one of the magnets to suddenly (i.e. before the magnets 'touch') turn around and retreat in the opposite direction.
Contents
Definition
Quantum reflection became an important branch of physics in the 21st century. 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 is diffuse rather than specular, and so this component of the reflection is easy to distinguish. Indeed 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 the non-relativistic approximation to quantum mechanics is all that is required.
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 (say
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. If, in accordance with this approximation we write the wavelength of the gross motion of the atom system toward the surface as a quantity local to every region along the
where
That is, in regions of space where the variation of the atomic wavelength is significant over its own length (i.e. the gradient of
Experiments with grazing incidence
Practically, in many experiments with quantum reflection from Si, the grazing incidence angle is used (figure A). The set-up is mounted in a vacuum chamber to provide a several-meter path free of atoms; a good vacuum (at the level of 10−7 Torr or 6996129999999999999♠130 µPa) is required. The magneto-optical trap (MOT) is used to collect cold atoms, usually excited He or Ne, approaching the point-like source of atoms. The excitation of atoms is not essential for the quantum reflection but it allows the efficient trapping and cooling using optical frequencies. In addition, the excitation of atoms allows the registration at the micro-channel plate (MCP) detector (bottom of the figure). Movable edges are used to stop atoms which do not go toward the sample (for example a Si plate), providing the collimated atomic beam. The He-Ne laser was used to control the orientation of the sample and measure the grazing angle
In the experiments with Ne atoms, usually just fall down, when the MOT is suddenly switched off. Then, the speed of atoms is determined as
In the case with He, the additional resonant laser could be used to release the atoms and provide them an additional velocity; the delay since the release of the atoms till the registration allowed to estimate this additional velocity; roughly,
Although the scheme at the figure looks simple, the extend facility is necessary to slow atoms, trap them and cool to millikelvin temperature, providing a micrometre size source of cold atoms. Practically, the mounting and maintaining of this facility (not shown in the figure) is the heaviest job in the experiments with quantum reflection of cold atoms. The possibility of an experiment with the quantum reflection with just a pinhole instead of MOT are discussed in the literature.
Casimir and van der Waals attraction
Despite this, there is some doubt as to the physical origin of quantum reflection from solid surfaces. As was briefly mentioned above, the potential in the intermediate region between the regions dominated by the Casimir-Polder and Van der Waals interactions requires an explicit Quantum Electrodynamical calculation for the particular state and type of atom incident on the surface. Such a calculation is very difficult. Indeed, there is no reason to suppose that this potential is solely attractive within the intermediate region. Thus the reflection could simply be explained by a repulsive force, which would make the phenomenon not quite so surprising. Furthermore, a similar dependence for reflectivity on the incident velocity is observed in the case of the adsorption of particles in vicinity of a surface. In the simplest case, such absorption could be described with a non-Hermitian potential (i.e. one where probability is not conserved). Until 2006, the published papers interpreted the reflection in terms of a Hermitian potential
this assumption allows to build a quantitative theory .
Efficient quantum reflection
A qualitative estimate for the efficiency of quantum reflection can be made using dimensional analysis. Letting
should be compared to the potential,
which shows good agreement with experimental data for excited neon and helium atoms, reflected from a flat silicon surface (fig.1), see and references therein. Such a fit is also in good agreement with a single-dimensional analysis of the scattering of atoms from an attractive potential,. Such agreement indicates, that, at least in the case of noble gases and Si surface, the quantum reflection can be described with single-dimensional hermitian potential, as the result of attraction of atoms to the surface.
Ridged mirror
The effect of quantum reflection can be enhanced using ridged mirrors . If one produces a surface consisting of a set of narrow ridges then the resulting non-uniformity of the material allows the reduction of the effective van der Waals constant; this extends the working ranges of the grazing angle. For this reduction to be valid, we must have small distances,
Similar enhancement of quantum reflection takes place where one has particles incident on an array of pillars . This was observed with very slow atoms (Bose–Einstein condensate) at almost normal incidence.
Application of quantum reflection
Quantum reflection makes the idea of solid-state atomic mirrors and atomic-beam imaging systems (atomic nanoscope) possible. The use of quantum reflection in the production of atomic traps has also been suggested. Up to year 2007, no commercial application of quantum reflection was reported.