physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, a quantum mirage is a peculiar result in

quantum chaos Quantum chaos is a branch of physics which studies how chaos theory, chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship betwee ...

. Every system of quantum

dynamical billiards A dynamical billiard is a dynamical system in which a particle alternates between free motion (typically as a straight line) and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed ( ...

will exhibit an effect called ''

scarring A scar (or scar tissue) is an area of fibrous tissue that replaces normal skin after an injury. Scars result from the biological process of wound repair in the skin, as well as in other organs, and tissues of the body. Thus, scarring is a na ...

'', where the quantum probability density shows traces of the paths a classical

billiard ball A billiard ball is a small, hard ball used in cue sports, such as carom billiards, pool, and snooker. The number, type, diameter, color, and pattern of the balls differ depending upon the specific game being played. Various particular ball p ...

would take. For an elliptical arena, the scarring is particularly pronounced at the foci, as this is the region where many classical trajectories converge. The scars at the foci are colloquially referred to as the "quantum mirage". The quantum mirage was first experimentally observed by Hari Manoharan, Christopher Lutz and Donald Eigler at the IBM

Almaden Research Center IBM Research is the research and development division for IBM, an American multinational information technology company headquartered in Armonk, New York, with operations in over 170 countries. IBM Research is the largest industrial research org ...

in San Jose, California in 2000. The effect is quite remarkable but in general agreement with prior work on the quantum mechanics of dynamical billiards in elliptical arenas.

Quantum corral

The mirage occurs at the foci of a quantum corral, a ring of atoms arranged in an arbitrary shape on a substrate. The quantum corral was demonstrated in 1993 by Lutz, Eigler, and Crommie using an

elliptical Elliptical may mean: * having the shape of an ellipse, or more broadly, any oval shape ** in botany, having an elliptic leaf shape ** of aircraft wings, having an elliptical planform * characterised by ellipsis (the omission of words), or by conc ...

ring of

iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...

atoms on a

copper Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...

surface using the tip of a low-temperature

scanning tunneling microscope A scanning tunneling microscope (STM) is a type of microscope used for imaging surfaces at the atomic level. Its development in 1981 earned its inventors, Gerd Binnig and Heinrich Rohrer, then at IBM Zürich, the Nobel Prize in Physics in 1986. ...

to manipulate individual atoms. The

ferromagnetic Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...

iron atoms reflected the surface electrons of the copper inside the ring into a wave pattern, as predicted by the theory of

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

. Quantum corrals can be viewed as artificial atoms that even show similar chemical bonding properties as real atoms. The size and shape of the corral determine its quantum states, including the energy and distribution of the electrons. To make conditions suitable for the mirage the team at Almaden chose a configuration of the corral which concentrated the electrons at the foci of the ellipse. When scientists placed a magnetic cobalt atom at one focus of the corral, a mirage of the atom appeared at the other focus. Specifically the same electronic properties were present in the electrons surrounding both foci, even though the cobalt atom was only present at one focus. In scanning tunneling microscopy, an atomically sharp metal tip is advanced towards the atomically flat sample surface until electron tunneling out of the atom and into the advancing tip becomes effective. Using the sharp tip we can also arrange atoms adsorbed on the surface into unique shapes; for example, 48 adsorbed iron atoms on Cu(111) arranged into a 14.26 nm diameter circle. The electrons on the copper surface are trapped inside the circle formed by the iron atoms. A standing wave pattern emerges with a large peak at the center due to the constructive interference of electrons on the copper surface as they scatter off the adsorbed iron atoms.

Applications

IBM scientists are hoping to use quantum mirages to construct atomic scale processors in the future.

References

External links

"Quantum Mirage" may enable atom-scale circuits, IBM Research Almaden, 3rd Feb 2000

Theory of Quantum Corrals and Quantum Mirages
* Microscopic theory for quantum mirages in quantum corrals {{Use dmy dates, date=March 2018 Quantum electronics