Trojan wave packet
Encyclopedia
A Trojan wave packet is a wave packet
that is nonstationary and nonspreading. It is part of an artificially created system, which consists of a nucleus
, and one or more electron wave packets, of a highly excited atom
.
A strong, polarized electromagnetic field
, holds or "traps" each electron wave packet in an intentionally selected orbit (energy shell). They derive their names from the Trojan asteroid
s in the Sun-Jupiter system. Trojan asteroids orbit around the sun in Jupiter
's orbit at its Lagrangian equilibrium point
s L4 and L5, where they are phase-locked and protected from collision with each other, and this phenomenon is analogous to the way the wave packet is held together.
s, Wigner crystal
s and Bose-Einstein condensates.
This ability to manipulate the quantum properties directly is key to the real life development of applicable nanodevices
such as quantum dots and microchip traps. In 2004 it was shown that it is possible to create a trap which is actually a single atom. Within the atom, the behavior of an electron can be manipulated.
During experiments in 2004 using lithium atoms in an excited state, researchers were able to localize an electron in a classical orbit for 15,000 orbits (900 ns). It was neither spreading nor dispersing. This “classical atom” was synthesized by “tethering” the electron using a microwave field to which its motion is phase locked. The phase lock of the electrons in this unique atomic system is, as mentioned above, analogous to the phase locked asteroids of Jupiter's orbit.
The techniques explored in this experiment are a solution to a problem that dates back to 1926. Physicists at that time realized that any initially localized wave packet will inevitably spread around the orbit of the electrons. Physicist noticed that "the wave equation is dispersive for the atomic Coulomb potential." In the 1980s several groups of researchers proved this to be true. The wave packets spread all the way around the orbits and coherently interfered with themselves. Recently the real world innovation realized with experiments such as Trojan wave packets, is localizing the wave packets, i.e., no dispersion. Applying a polarized circular EM field, at microwave frequencies, synchronized with an electron wave packet, intentionally keeps the electron wave packets in a Lagrange type orbit.
The Trojan wave packet experiments built on previous work with lithium atoms in an excited state. These are atoms, which respond sensitively to electric and magnetic fields, have decay periods that are relatively prolonged, and electrons, which for all intents and purposes actually operate in classical orbits. The sensitivity to electric and magnetic fields is important because this allows control and response by the polarized microwave field.
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The next logical step is to attempt to move from single electron wave packets to more than one electron wave packet
. This had already been accomplished in barium
atoms, with two electron wave packets. These two were localized. However, eventually, these created dispersion
after colliding near the nucleus. Another technique employed a nondispersive pair of electrons, but one of these had to have a localized orbit close to the nucleus. The nondispersive two-electron Trojan wave packets demonstration changes all that. These are the next step analogue of the one electron
Trojan wave packets - and designed for excited helium atoms.
As of July 2005, atoms with coherent, stable two-electron, nondispersing wave packets had been created. These are excited helium-like atoms, or quantum dot
helium (in solid-state
applications), and are atomic (quantum) analogues to the three body problem of Newton's classical physics
, which includes today's astrophysics
. In tandem, circularly polarized electromagnetic and magnetic fields stabilize the two electron configuration in the helium atom
or the quantum dot helium (with impurity center). The stability is maintained over a broad spectrum
, and because of this, the configuration of two electron wave packets is considered to be truly nondispersive. For example, with the quantum dot helium, configured for confining electrons in two spatial dimensions, there now exists a variety of trojan wave packet configurations with two electrons
, and as of 2005, only one in three dimensions.
Recently the patent was filed proposing the usage of the positron
-electron Trojan wavepackets
to store the antimatter positrons for very long time when the Gaussian wave functions do not
overlap significantly and the recombination
of positronium
is greatly extended to days which may be the solution to realistic antimatter
inerstellar propulsion engines working on direct miligrams
of relativistic mass.
Wave packet
In physics, a wave packet is a short "burst" or "envelope" of wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere...
that is nonstationary and nonspreading. It is part of an artificially created system, which consists of a nucleus
Atomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
, and one or more electron wave packets, of a highly excited atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...
.
A strong, polarized electromagnetic field
Electromagnetic field
An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...
, holds or "traps" each electron wave packet in an intentionally selected orbit (energy shell). They derive their names from the Trojan asteroid
Trojan (astronomy)
In astronomy, a Trojan is a minor planet or natural satellite that shares an orbit with a larger planet or moon, but does not collide with it because it orbits around one of the two Lagrangian points of stability , and , which lie approximately 60° ahead of and behind the larger body,...
s in the Sun-Jupiter system. Trojan asteroids orbit around the sun in Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...
's orbit at its Lagrangian equilibrium point
Lagrangian point
The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects...
s L4 and L5, where they are phase-locked and protected from collision with each other, and this phenomenon is analogous to the way the wave packet is held together.
Concepts and research
The concept of the Trojan wave packet is derived from a flourishing area of physics which manipulates atoms and ions at the atomic level creating ion traps. Ion traps allow the manipulation of atoms and are used to create new states of matter including ionic liquidIonic liquid
An ionic liquid is a salt in the liquid state. In some contexts, the term has been restricted to salts whose melting point is below some arbitrary temperature, such as . While ordinary liquids such as water and gasoline are predominantly made of electrically neutral molecules, ILs are largely made...
s, Wigner crystal
Wigner crystal
A Wigner crystal is the solid phase of electrons first predicted by Eugene Wigner in 1934. A gas of electrons moving in 2D or 3D in a uniform, inert, neutralizing background will crystallize and form a lattice if the electron density is less than a critical value...
s and Bose-Einstein condensates.
This ability to manipulate the quantum properties directly is key to the real life development of applicable nanodevices
Nanotechnology
Nanotechnology is the study of manipulating matter on an atomic and molecular scale. Generally, nanotechnology deals with developing materials, devices, or other structures possessing at least one dimension sized from 1 to 100 nanometres...
such as quantum dots and microchip traps. In 2004 it was shown that it is possible to create a trap which is actually a single atom. Within the atom, the behavior of an electron can be manipulated.
During experiments in 2004 using lithium atoms in an excited state, researchers were able to localize an electron in a classical orbit for 15,000 orbits (900 ns). It was neither spreading nor dispersing. This “classical atom” was synthesized by “tethering” the electron using a microwave field to which its motion is phase locked. The phase lock of the electrons in this unique atomic system is, as mentioned above, analogous to the phase locked asteroids of Jupiter's orbit.
The techniques explored in this experiment are a solution to a problem that dates back to 1926. Physicists at that time realized that any initially localized wave packet will inevitably spread around the orbit of the electrons. Physicist noticed that "the wave equation is dispersive for the atomic Coulomb potential." In the 1980s several groups of researchers proved this to be true. The wave packets spread all the way around the orbits and coherently interfered with themselves. Recently the real world innovation realized with experiments such as Trojan wave packets, is localizing the wave packets, i.e., no dispersion. Applying a polarized circular EM field, at microwave frequencies, synchronized with an electron wave packet, intentionally keeps the electron wave packets in a Lagrange type orbit.
The Trojan wave packet experiments built on previous work with lithium atoms in an excited state. These are atoms, which respond sensitively to electric and magnetic fields, have decay periods that are relatively prolonged, and electrons, which for all intents and purposes actually operate in classical orbits. The sensitivity to electric and magnetic fields is important because this allows control and response by the polarized microwave field.
Beyond single electron wave packets
Wave packet
In physics, a wave packet is a short "burst" or "envelope" of wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere...
. This had already been accomplished in barium
Barium
Barium is a chemical element with the symbol Ba and atomic number 56. It is the fifth element in Group 2, a soft silvery metallic alkaline earth metal. Barium is never found in nature in its pure form due to its reactivity with air. Its oxide is historically known as baryta but it reacts with...
atoms, with two electron wave packets. These two were localized. However, eventually, these created dispersion
Dispersion (materials science)
In materials science, dispersion is the fraction of atoms of a material exposed to the surface. In general:where D is the dispersion, NS is the number of surface atoms and NT is the total number of atoms of the material...
after colliding near the nucleus. Another technique employed a nondispersive pair of electrons, but one of these had to have a localized orbit close to the nucleus. The nondispersive two-electron Trojan wave packets demonstration changes all that. These are the next step analogue of the one electron
Trojan wave packets - and designed for excited helium atoms.
As of July 2005, atoms with coherent, stable two-electron, nondispersing wave packets had been created. These are excited helium-like atoms, or quantum dot
Quantum dot
A quantum dot is a portion of matter whose excitons are confined in all three spatial dimensions. Consequently, such materials have electronic properties intermediate between those of bulk semiconductors and those of discrete molecules. They were discovered at the beginning of the 1980s by Alexei...
helium (in solid-state
Solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from...
applications), and are atomic (quantum) analogues to the three body problem of Newton's classical physics
Classical physics
What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics...
, which includes today's astrophysics
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
. In tandem, circularly polarized electromagnetic and magnetic fields stabilize the two electron configuration in the helium atom
Helium atom
Helium is an element and the next simplest atom to solve after the hydrogen atom. Helium is composed of two electrons in orbit around a nucleus containing two protons along with either one or two neutrons, depending on the isotope. The hydrogen atom is used extensively to aid in solving the helium...
or the quantum dot helium (with impurity center). The stability is maintained over a broad spectrum
Electromagnetic spectrum
The electromagnetic spectrum is the range of all possible frequencies of electromagnetic radiation. The "electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object....
, and because of this, the configuration of two electron wave packets is considered to be truly nondispersive. For example, with the quantum dot helium, configured for confining electrons in two spatial dimensions, there now exists a variety of trojan wave packet configurations with two electrons
, and as of 2005, only one in three dimensions.
Recently the patent was filed proposing the usage of the positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
-electron Trojan wavepackets
to store the antimatter positrons for very long time when the Gaussian wave functions do not
overlap significantly and the recombination
Annihilation
Annihilation is defined as "total destruction" or "complete obliteration" of an object; having its root in the Latin nihil . A literal translation is "to make into nothing"....
of positronium
Positronium
Positronium is a system consisting of an electron and its anti-particle, a positron, bound together into an "exotic atom". Being unstable, the two particles annihilate each other to produce two gamma ray photons after an average lifetime of 125 ps or three gamma ray photons after 142 ns in...
is greatly extended to days which may be the solution to realistic antimatter
Antimatter
In particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...
inerstellar propulsion engines working on direct miligrams
of relativistic mass.
See also
- Atomic orbitalAtomic orbitalAn atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus...
- Dispersion (optics)Dispersion (optics)In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency.Media having such a property are termed dispersive media...
- Electron wave-packet interference
- Introduction to quantum mechanicsIntroduction to quantum mechanicsQuantum mechanics is the body of scientific principles that explains the behavior of matter and its interactions with energy on the scale of atoms and atomic particles....
- Ion GelIon GelAn Ion Gel is a relatively new material where an ionic conducting liquid is immobilized inside a polymer matrix. This allows the design of unique materials with high ionic conductivity combined with the easy handling properties of the solid state...
- Quantum mechanicsQuantum mechanicsQuantum 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...
- Rydberg state
- Simulated RealitySimulated realitySimulated reality is the proposition that reality could be simulated—perhaps by computer simulation—to a degree indistinguishable from "true" reality. It could contain conscious minds which may or may not be fully aware that they are living inside a simulation....
- Soliton wave
- Video trackingVideo trackingVideo tracking is the process of locating a moving object over time using a camera. It has a variety of uses, some of which are: human-computer interaction, security and surveillance, video communication and compression, augmented reality, traffic control, medical imaging and video editing...
- WavelengthWavelengthIn physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
- Wave function
- Wave function collapse
External links
- Glauber States (Java)
- Aharonov-Bohm Oscillations In "Trojan Electrons"
- Giant double Trojan wave packets from asteroids in Solar System - Trojan Asteroids - simulation
- Trojan wave packet for arbitrary parameters value (Java3D)
