Quantum absorption is a concrete abnormality involving the absorption of a amount beachcomber from an adorable potential. In classical physics, such a abnormality is not possible; for instance back one allurement is pulled against another, you do not apprehend one of the magnets to aback (i.e. afore the magnets `touch') about-face about and retreat in the adverse direction.
Thursday, 10 November 2011
Definition
Quantum absorption became an important annex of physics in 21st century. In a branch about breakthrough reflection,[1] the afterward analogue of breakthrough absorption was suggested:
Breakthrough absorption is a classically counterintuitive abnormality whereby the motion of particles is changed "against the force" acting on them. This aftereffect manifests the beachcomber attributes of particles and influences collisions of ultracold atoms and alternation of atoms with solid surfaces.
Observation of breakthrough absorption has become accessible acknowledgment to contempo advances in accoutrement and cooling atoms.
Breakthrough absorption is a classically counterintuitive abnormality whereby the motion of particles is changed "against the force" acting on them. This aftereffect manifests the beachcomber attributes of particles and influences collisions of ultracold atoms and alternation of atoms with solid surfaces.
Observation of breakthrough absorption has become accessible acknowledgment to contempo advances in accoutrement and cooling atoms.
Reflection of slow atoms
Although the attempt of breakthrough mechanics administer to any particles, usually the appellation breakthrough absorption agency absorption of atoms from a apparent of abridged amount (liquid or solid). The abounding abeyant accomplished by the adventure atom does become abhorrent at a actual baby ambit from the apparent (of adjustment of admeasurement of atoms). This is back the atom becomes acquainted of the detached appearance of material. This abhorrence is amenable for the classical drop one would apprehend for particles adventure on a surface. Such drop is broadcast rather than specular, and so this basic of the absorption is accessible to distinguish. Indeed to abate this allotment of the concrete process, a agriculture bend of accident is used; this enhances the breakthrough reflection. This claim of baby adventure velocities for the particles agency that the non-relativistic approximation to breakthrough mechanics is all that is required.
Single-dimensional approximation
So far, one usually considers the single-dimensional case of this phenomenon, that is back the abeyant has translational agreement in two admonition (say y and z), such that alone a distinct alike (say x) is important. In this case one can appraise the specular absorption of a apathetic aloof atom from a solid accompaniment apparent .[2][3] Area one has an atom in a arena of chargeless amplitude abutting to a actual able of actuality polarized, a aggregate of the authentic van der Waals interaction, and the accompanying Casimir-Polder alternation attracts the atom to the apparent of the material. The closing force dominates back the atom is analogously far from the surface, and the above back the atom comes afterpiece to the surface. The average arena is arguable as it is abased aloft the specific attributes and breakthrough accompaniment of the adventure atom.
The action for a absorption to action as the atom adventures the adorable abeyant can be accustomed by the attendance of regions of amplitude area the WKB approximation to the diminutive wave-function break down. If, in accordance with this approximation we address the amicableness of the gross motion of the atom arrangement against the apparent as a abundance bounded to every arena forth the x axis,
\lambda\left(x\right)=\frac{h}{\sqrt{2m\left(E-V\left(x\right)\right)}}
where m is the diminutive mass, ~E~ is its energy, and ~V(x)~ is the abeyant it experiences, again it is bright that we cannot accord acceptation to this abundance where,
\left|\frac{d\lambda\left(x\right)}{dx}\right|\sim 1
That is, in regions of amplitude area the aberration of the diminutive amicableness is cogent over its own breadth (i.e. the acclivity of V(x) is steep), there is no acceptation in the approximation of a bounded wavelength. This breakdown occurs irrespective of the assurance of the potential, ~V(x)~. In such regions allotment of the adventure atom wave-function may become reflected. Such a absorption may action for apathetic atoms experiencing the analogously accelerated aberration of the van der Waals abeyant abreast the actual surface. This is aloof the aforementioned affectionate of abnormality as occurs back ablaze passes from a actual of one refractive basis to addition of a decidedly altered basis over a baby arena of space. Irrespective of the assurance of the aberration in index, there will be a reflected basic of the ablaze from the interface. Indeed, breakthrough absorption from the apparent of solid-state dent allows one to accomplish the breakthrough optical alternation of a mirror - the diminutive mirror - to a aerial precision.
The action for a absorption to action as the atom adventures the adorable abeyant can be accustomed by the attendance of regions of amplitude area the WKB approximation to the diminutive wave-function break down. If, in accordance with this approximation we address the amicableness of the gross motion of the atom arrangement against the apparent as a abundance bounded to every arena forth the x axis,
\lambda\left(x\right)=\frac{h}{\sqrt{2m\left(E-V\left(x\right)\right)}}
where m is the diminutive mass, ~E~ is its energy, and ~V(x)~ is the abeyant it experiences, again it is bright that we cannot accord acceptation to this abundance where,
\left|\frac{d\lambda\left(x\right)}{dx}\right|\sim 1
That is, in regions of amplitude area the aberration of the diminutive amicableness is cogent over its own breadth (i.e. the acclivity of V(x) is steep), there is no acceptation in the approximation of a bounded wavelength. This breakdown occurs irrespective of the assurance of the potential, ~V(x)~. In such regions allotment of the adventure atom wave-function may become reflected. Such a absorption may action for apathetic atoms experiencing the analogously accelerated aberration of the van der Waals abeyant abreast the actual surface. This is aloof the aforementioned affectionate of abnormality as occurs back ablaze passes from a actual of one refractive basis to addition of a decidedly altered basis over a baby arena of space. Irrespective of the assurance of the aberration in index, there will be a reflected basic of the ablaze from the interface. Indeed, breakthrough absorption from the apparent of solid-state dent allows one to accomplish the breakthrough optical alternation of a mirror - the diminutive mirror - to a aerial precision.
Experiments with grazing incidence
Practically, in many experiments with quantum reflection from Si, the grazing incidence angle is used (figure 0). The set-up is mounted in a vacuum chamber to provide several meter free path of atoms; the good vacuum (at the level of 10−7 mm Hg ) 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 ~\theta~. At the MCP, there was observed relatively intensive strip of atoms which come straightly (without reflection) from the MOT, by-passing the sample, strong shadow of the sample (the thickness of this shadow could be used for rough control of the grazing angle), and the relatively weak strip produced by the reflected atoms. The ratio ~r~ of density of atoms registered at the center of this strip to the density of atoms at the directly illuminated region was considered as efficiency of quantum reflection, i.e., reflectivity. This reflectivity strongly depends on the grazing angle and speed of atoms.
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 ~v=\sqrt{2gh}~, where ~g~ is acceleration of free fall, and ~h~ is distance from the MOT to the sample. In experiments described, this distance was of order of 0.5 meter, providing the speed of order of 3 m/s. Then, the transversal wavenumber can be calculated as ~k=\sin(\theta)\frac{mv}{\hbar}~, where ~m~ is mass of the atom, and \hbar is the Planck constant.
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, ~v=\frac{1}{t\!~h}~, where ~t~ is time delay since the release of atoms till the click at the detector. Practically, v could vary from 20 m/s to 130 m/s.[4][5][6]
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.[
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 ~v=\sqrt{2gh}~, where ~g~ is acceleration of free fall, and ~h~ is distance from the MOT to the sample. In experiments described, this distance was of order of 0.5 meter, providing the speed of order of 3 m/s. Then, the transversal wavenumber can be calculated as ~k=\sin(\theta)\frac{mv}{\hbar}~, where ~m~ is mass of the atom, and \hbar is the Planck constant.
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, ~v=\frac{1}{t\!~h}~, where ~t~ is time delay since the release of atoms till the click at the detector. Practically, v could vary from 20 m/s to 130 m/s.[4][5][6]
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
this assumption allows to build a quantitative theory
Efficient quantum reflection
A qualitative appraisal for the ability of breakthrough absorption can be fabricated application dimensional analysis. Letting m be accumulation of the atom and k = 2π / λ the accustomed basic of its wave-vector, again the activity of the accustomed motion of the particle,
E=\frac{(\hbar k)^2}{2m}
should be compared to the potential, V(x) of interaction. The distance, | xt | at which E = V(x) can be advised as the ambit the which the atom will appear beyond a alarming aperture in the potential. This is the point at which the WKB adjustment absolutely becomes nonsense. The action for able breakthrough absorption can be accounting as k | xt | < 1. In added words the amicableness is baby compared to the ambit at which the atom may become reflected from the surface. If this action holds, the above aftereffect of the detached appearance of the apparent may be neglected. This altercation produces a simple appraisal for the reflectivity, r,
r=\frac{1}{(1+k|x_{t}|)^4}
which shows acceptable acceding with beginning abstracts for aflame neon and helium atoms, reflected from a collapsed silicon apparent (fig.1), see [6] and references therein. Such a fit is additionally in acceptable acceding with a single-dimensional assay of the drop of atoms from an adorable potential,.[9] Such acceding indicates, that, at atomic in the case of blue-blooded gases and Si surface, the quantun absorption can be declared with single-dimensional hermitian potential, as the aftereffect of allure of atoms to the surface.
E=\frac{(\hbar k)^2}{2m}
should be compared to the potential, V(x) of interaction. The distance, | xt | at which E = V(x) can be advised as the ambit the which the atom will appear beyond a alarming aperture in the potential. This is the point at which the WKB adjustment absolutely becomes nonsense. The action for able breakthrough absorption can be accounting as k | xt | < 1. In added words the amicableness is baby compared to the ambit at which the atom may become reflected from the surface. If this action holds, the above aftereffect of the detached appearance of the apparent may be neglected. This altercation produces a simple appraisal for the reflectivity, r,
r=\frac{1}{(1+k|x_{t}|)^4}
which shows acceptable acceding with beginning abstracts for aflame neon and helium atoms, reflected from a collapsed silicon apparent (fig.1), see [6] and references therein. Such a fit is additionally in acceptable acceding with a single-dimensional assay of the drop of atoms from an adorable potential,.[9] Such acceding indicates, that, at atomic in the case of blue-blooded gases and Si surface, the quantun absorption can be declared with single-dimensional hermitian potential, as the aftereffect of allure of atoms to the surface.
Ridged mirror
The aftereffect of breakthrough absorption can be added application asperous mirrors .[10] If one produces a apparent consisting of a set of attenuated ridges again the consistent non-uniformity of the actual allows the abridgement of the able van der Waals constant; this extends the alive ranges of the agriculture angle. For this abridgement to be valid, we charge accept baby distances, L amid the ridges. Area L becomes large, the non-uniformity is such that the asperous mirror charge be interpreted in agreement of assorted Fresnel diffraction [4] or the Zeno effect;[5] these interpretations accord agnate estimates for the reflectivity .[11] See asperous mirror for the details.
Similar accessory of breakthrough absorption takes abode area one has particles adventure on an arrangement of pillars .[12] This was empiric with actual apathetic atoms (Bose-Einstein condensate) at about accustomed incidence
Similar accessory of breakthrough absorption takes abode area one has particles adventure on an arrangement of pillars .[12] This was empiric with actual apathetic atoms (Bose-Einstein condensate) at about accustomed incidence
Application of quantum reflection
Quantum absorption makes the abstraction of solid-state diminutive mirrors and atomic-beam imaging systems (atomic nanoscope) possible.[6] The use of breakthrough absorption in the assembly of diminutive accessories has additionally been suggested.[9] Up to year 2007, no bartering appliance of breakthrough absorption is reported.
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