Quantum mirage
Encyclopedia
In physics
, a quantum mirage is a peculiar result in quantum chaos
. Every system of quantum dynamical billiards
will exhibit an effect called scarring, where the quantum probability density shows traces of the paths a classical billiard ball 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
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.
, and Crommie using an ellipitical
ring of cobalt
atoms on a copper
surface. The ferromagnetic cobalt atoms reflected the surface electrons of the copper inside the ring into a wave pattern, as predicted by the theory of quantum mechanics
.
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.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, a quantum mirage is a peculiar result in quantum chaos
Quantum chaos
Quantum chaos is a branch of physics which studies how 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 between quantum mechanics and classical chaos?" The correspondence principle...
. Every system of quantum dynamical billiards
Dynamical billiards
A billiard is a dynamical system in which a particle alternates between motion in 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, where the quantum probability density shows traces of the paths a classical billiard ball 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
Donald Eigler
Donald M. Eigler is a physicist and IBM Fellow at the IBM Almaden Research Center. On September 28, 1989 he achieved a landmark in humankind’s ability to build small structures by demonstrating the ability to manipulate individual atoms with atomic-scale precision...
at the IBM
IBM Research
IBM Research, a division of IBM, is a research and advanced development organization and currently consists of eight locations throughout the world and hundreds of projects....
Almaden Research Center
Almaden Research Center
The IBM Almaden Research Center is in San Jose, California, and is one of IBM's nine worldwide research labs. Its scientists perform basic and applied research in computer science, services, storage systems, physical sciences, and materials science and technology. The center opened in 1986, and...
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, EiglerDonald Eigler
Donald M. Eigler is a physicist and IBM Fellow at the IBM Almaden Research Center. On September 28, 1989 he achieved a landmark in humankind’s ability to build small structures by demonstrating the ability to manipulate individual atoms with atomic-scale precision...
, and Crommie using an ellipitical
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
ring of cobalt
Cobalt
Cobalt is a chemical element with symbol Co and atomic number 27. It is found naturally only in chemically combined form. The free element, produced by reductive smelting, is a hard, lustrous, silver-gray metal....
atoms on a copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
surface. The ferromagnetic cobalt 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
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
.
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.