Trojan wave packet

Last updated
Trojan wavepacket evolution animation Trojan wavepacket hue.gif
Trojan wavepacket evolution animation
Classical simulation of the Trojan wavepacket on 1982 home ZX Spectrum microcomputer. The packet is approximated by the ensemble of points initially randomly localized within the peak of a Gaussian and moving according to the Newton equations. The ensemble stays localized. For the comparison the second simulation follows when the strength of the circularly polarized electric (rotating) field is equal to zero and the packet (points) fully spreads around the circle. Z80Trojan.gif
Classical simulation of the Trojan wavepacket on 1982 home ZX Spectrum microcomputer. The packet is approximated by the ensemble of points initially randomly localized within the peak of a Gaussian and moving according to the Newton equations. The ensemble stays localized. For the comparison the second simulation follows when the strength of the circularly polarized electric (rotating) field is equal to zero and the packet (points) fully spreads around the circle.

A trojan wave packet is a wave packet that is nonstationary and nonspreading. It is part of an artificially created system that consists of a nucleus and one or more electron wave packets, and that is highly excited under a continuous electromagnetic field. Its discovery as one of significant contributions to the Quantum Theory was awarded the 2022 Wigner Medal for Iwo Bialynicki-Birula [1]

Contents

The strong, polarized electromagnetic field, holds or "traps" each electron wave packet in an intentionally selected orbit (energy shell). [2] [3] They derive their names from the trojan asteroids in the Sun–Jupiter system. [4] Trojan asteroids orbit around the Sun in Jupiter's orbit at its Lagrangian equilibrium points 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 liquids, Wigner crystals and Bose–Einstein condensates. [5] This ability to manipulate the quantum properties directly is key to the 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. [6]

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. [7]

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., with 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. [8] [9] 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. [10]

Beyond single electron wave packets

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 constructively only over a small region of space, and destructively elsewhere. Wave packet (dispersion).gif
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 constructively only over a small region of space, and destructively elsewhere.

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. [12] [13]

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. [14] In 2012 an essential experimental step was undertaken not only generating but locking the Trojan wavepackets on adiabatically changed frequency and expanding the atoms as once predicted by Kalinski and Eberly. [15] It will allow to create two electron Langmuir Trojan wave packets in Helium by the sequential excitation in adiabatic Stark field able to produce the circular one-electron aureola over He+
first and then put the second electron in similar state. [16]

See also

Related Research Articles

<span class="mw-page-title-main">Ionization</span> Process by which atoms or molecules acquire charge by gaining or losing electrons

Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected.

<span class="mw-page-title-main">Roton</span> Collective excitation in superfluid helium-4 (a quasiparticle)

In theoretical physics, a roton is an elementary excitation, or quasiparticle, seen in superfluid helium-4 and Bose–Einstein condensates with long-range dipolar interactions or spin-orbit coupling. The dispersion relation of elementary excitations in this superfluid shows a linear increase from the origin, but exhibits first a maximum and then a minimum in energy as the momentum increases. Excitations with momenta in the linear region are called phonons; those with momenta close to the minimum are called rotons. Excitations with momenta near the maximum are called maxons.

<span class="mw-page-title-main">Supersolid</span> State of matter

In condensed matter physics, a supersolid is a spatially ordered material with superfluid properties. In the case of helium-4, it has been conjectured since the 1960s that it might be possible to create a supersolid. Starting from 2017, a definitive proof for the existence of this state was provided by several experiments using atomic Bose–Einstein condensates. The general conditions required for supersolidity to emerge in a certain substance are a topic of ongoing research.

An atom interferometer is an interferometer which uses the wave character of atoms. Similar to optical interferometers, atom interferometers measure the difference in phase between atomic matter waves along different paths. Today, atomic interference is typically controlled with laser beams. Atom interferometers have many uses in fundamental physics including measurements of the gravitational constant, the fine-structure constant, the universality of free fall, and have been proposed as a method to detect gravitational waves. They also have applied uses as accelerometers, rotation sensors, and gravity gradiometers.

In condensed matter physics, Anderson localization is the absence of diffusion of waves in a disordered medium. This phenomenon is named after the American physicist P. W. Anderson, who was the first to suggest that electron localization is possible in a lattice potential, provided that the degree of randomness (disorder) in the lattice is sufficiently large, as can be realized for example in a semiconductor with impurities or defects.

An electron bubble is the empty space created around a free electron in a cryogenic gas or liquid, such as neon or helium. They are typically very small, about 2 nm in diameter at atmospheric pressure.

In physics, an atomic mirror is a device which reflects neutral atoms in a way similar to the way a conventional mirror reflects visible light. Atomic mirrors can be made of electric fields or magnetic fields, electromagnetic waves or just silicon wafer; in the last case, atoms are reflected by the attracting tails of the van der Waals attraction. Such reflection is efficient when the normal component of the wavenumber of the atoms is small or comparable to the effective depth of the attraction potential. To reduce the normal component, most atomic mirrors are blazed at the grazing incidence.

Quantum reflection is a uniquely quantum phenomenon in which an object, such as a neutron or a small molecule, reflects smoothly and in a wavelike fashion from a much larger surface, such as a pool of mercury. A classically behaving neutron or molecule will strike the same surface much like a thrown ball, hitting only at one atomic-scale location where it is either absorbed or scattered. Quantum reflection provides a powerful experimental demonstration of particle-wave duality, since it is the extended quantum wave packet of the particle, rather than the particle itself, that reflects from the larger surface. It is similar to reflection high-energy electron diffraction, where electrons reflect and diffraction from surfaces, and grazing incidence atom scattering, where the fact that atoms can also be waves is used to diffract from surfaces.

Atom optics "refers to techniques to manipulate the trajectories and exploit the wave properties of neutral atoms". Typical experiments employ beams of cold, slowly moving neutral atoms, as a special case of a particle beam. Like an optical beam, the atomic beam may exhibit diffraction and interference, and can be focused with a Fresnel zone plate or a concave atomic mirror.

The dihydrogen cation or hydrogen molecular ion is a cation with formula H+
2
. It consists of two hydrogen nuclei (protons) sharing a single electron. It is the simplest molecular ion.

In theoretical physics, the logarithmic Schrödinger equation is one of the nonlinear modifications of Schrödinger's equation. It is a classical wave equation with applications to extensions of quantum mechanics, quantum optics, nuclear physics, transport and diffusion phenomena, open quantum systems and information theory, effective quantum gravity and physical vacuum models and theory of superfluidity and Bose–Einstein condensation. Its relativistic version was first proposed by Gerald Rosen. It is an example of an integrable model.

Double ionization is a process of formation of doubly charged ions when laser radiation is exerted on neutral atoms or molecules. Double ionization is usually less probable than single-electron ionization. Two types of double ionization are distinguished: sequential and non-sequential.

In quantum mechanics Langmuir states are certain quantum states of Helium that in the classical limit correspond to two parallel circular orbits of electrons one above the other and with the nucleus in between. They are constructed in analogy to circular states of Hydrogen when the electron has the maximum angular momentum and moves on the circle. Because of the magic value of the Helium nucleus charge 2e the triangle nucleus-electron-electron which sweeps the configuration space during the circular motion is equilateral.

Quantum microscopy allows microscopic properties of matter and quantum particles to be measured and imaged. Various types of microscopy use quantum principles. The first microscope to do so was the scanning tunneling microscope, which paved the way for development of the photoionization microscope and the quantum entanglement microscope.

<span class="mw-page-title-main">Peter E. Toschek</span> German physicist (1933–2020)

Peter E. Toschek was a German experimental physicist who researched nuclear physics, quantum optics, and laser physics. He is known as a pioneer of laser spectroscopy and for the first demonstration of single trapped atoms (ions). He was a professor at Hamburg University.

Spin squeezing is a quantum process that decreases the variance of one of the angular momentum components in an ensemble of particles with a spin. The quantum states obtained are called spin squeezed states. Such states have been proposed for quantum metrology, to allow a better precision for estimating a rotation angle than classical interferometers.

<span class="mw-page-title-main">Rydberg polaron</span>

A Rydberg polaron is an exotic state of matter, created at low temperatures, in which a very large atom contains other ordinary atoms in the space between the nucleus and the electrons. For the formation of this atom, scientists had to combine two fields of atomic physics: Bose–Einstein condensates and Rydberg atoms. Rydberg atoms are formed by exciting a single atom into a high-energy state, in which the electron is very far from the nucleus. Bose–Einstein condensates are a state of matter that is produced at temperatures close to absolute zero.

<span class="mw-page-title-main">Carlos Stroud</span> American physicist

Carlos Ray Stroud, Jr. is an American physicist and an educator. Working in the field of quantum optics, Stroud has carried out theoretical and experimental studies in most areas of the field from its beginnings in the late 1960s, studying the fundamentals of the quantum mechanics of atoms and light and their interaction. He has authored over 140 peer-reviewed papers and edited seven books. He is a fellow of the American Physical Society and the Optical Society of America, as well as a Distinguished Traveling Lecturer of the Division of Laser Science of the American Physical Society. In this latter position he travels to smaller colleges giving colloquia and public lectures.

<span class="mw-page-title-main">Electron-on-helium qubit</span> Quantum bit

An electron-on-helium qubit is a quantum bit for which the orthonormal basis states |0⟩ and |1⟩ are defined by quantized motional states or alternatively the spin states of an electron trapped above the surface of liquid helium. The electron-on-helium qubit was proposed as the basic element for building quantum computers with electrons on helium by Platzman and Dykman in 1999. 

References

  1. Bialynicki-Birula, Iwo; Kalinski, Matt; Eberly, J. H. (1994). "Lagrange Equilibrium Points in Celestial Mechanics and Nonspreading Wave Packets for Strongly Driven Rydberg Electrons" (PDF). Physical Review Letters. 73 (13): 1777–1780. Bibcode:1994PhRvL..73.1777B. doi:10.1103/PhysRevLett.73.1777. PMID   10056884.
  2. Bialynicka-Birula, Zofia; Bialynicki-Birula, Iwo (1997). "Radiative decay of Trojan wave packets" (PDF). Physical Review A. 56 (5): 3623. Bibcode:1997PhRvA..56.3623B. doi:10.1103/PhysRevA.56.3623.
  3. Kalinski, Maciej; Eberly, JH (1996). "Trojan wave packets: Mathieu theory and generation from circular states". Physical Review A. 53 (3): 1715–1724. Bibcode:1996PhRvA..53.1715K. doi:10.1103/PhysRevA.53.1715. PMID   9913064.
  4. Kochański, Piotr; Bialynicka-Birula, Zofia; Bialynicki-Birula, Iwo (2000). "Squeezing of electromagnetic field in a cavity by electrons in Trojan states". Physical Review A. 63 (1): 013811. arXiv: quant-ph/0007033v1 . Bibcode:2000PhRvA..63a3811K. doi:10.1103/PhysRevA.63.013811. S2CID   36895794.
  5. Andrews, M. R.; C. G. Townsend; H.-J. Miesner; D. S. Durfee; D. M. Kurn; W. Ketterle (1997). "Observation of Interference Between Two Bose Condensates". Science. 275 (5300): 637–641. CiteSeerX   10.1.1.38.8970 . doi:10.1126/science.275.5300.637. PMID   9005843. S2CID   38284718.
  6. Maeda, H. & Gallagher, T. F. (2004). "Nondispersing Wave Packets". Phys. Rev. Lett. 92 (13): 133004. Bibcode:2004PhRvL..92m3004M. doi:10.1103/PhysRevLett.92.133004. PMID   15089602.
  7. Maeda, H.; D. V. L. Norum; T. F. Gallagher (2005). "Microwave Manipulation of an Atomic Electron in a Classical Orbit". Science. 307 (5716): 1757–1760. Bibcode:2005Sci...307.1757M. doi:10.1126/science.1108470. PMID   15705805. S2CID   12153532.Originally published in Science Express on 10 February 2005
  8. Stroud, C. R. Jr. (2009). "An astronomical solution to an old quantum problem". Physics. 2 (19): 19. Bibcode:2009PhyOJ...2...19S. doi: 10.1103/Physics.2.19 .
  9. Murray, C. D.; Dermot, S. F. (2000). Solar System Dynamics. Cambridge, United Kingdom: Cambridge University Press. ISBN   978-0-521-57597-3.
  10. Metcalf Research Group (2004-11-08). "Rydberg Atom Optics". Stoney Brook University. Archived from the original on August 26, 2005. Retrieved 2008-07-30.
  11. Joy Manners (2000). Quantum Physics: An Introduction. CRC Press. pp. 53–56. ISBN   978-0-7503-0720-8.
  12. Brodsky, M.; Zhitenev, NB; Ashoori, RC; Pfeiffer, LN; West, KW (2000). "Localization in Artificial Disorder: Two Coupled Quantum Dots". Physical Review Letters. 85 (11): 2356–9. arXiv: cond-mat/0001455 . Bibcode:2000PhRvL..85.2356B. doi:10.1103/PhysRevLett.85.2356. PMID   10978009. S2CID   22967562.
  13. Berman, D.; Zhitenev, N.; Ashoori, R.; Shayegan, M. (1999). "Observation of Quantum Fluctuations of Charge on a Quantum Dot". Physical Review Letters. 82 (1): 161–164. arXiv: cond-mat/9803373 . Bibcode:1999PhRvL..82..161B. doi:10.1103/PhysRevLett.82.161. S2CID   26475397.
  14. Kalinski, Matt; Hansen, Loren; David, Farrelly (2005). "Nondispersive Two-Electron Wave Packets in a Helium Atom". Physical Review Letters. 95 (10): 103001. Bibcode:2005PhRvL..95j3001K. doi:10.1103/PhysRevLett.95.103001. PMID   16196925.
  15. Kalinski, M.; Eberly, J. (1997). "Guiding electron orbits with chirped light". Optics Express. 1 (7): 216–20. Bibcode:1997OExpr...1..216K. doi:10.1364/OE.1.000216. PMID   19373404.
  16. Wyker, B.; Ye, S.; Dunning, F. B.; Yoshida, S.; Reinhold, C.O.; Burgdörfer, J. (2012). "Creating and Transporting Trojan Wave Packets" (PDF). Physical Review Letters. 108 (4): 043001. Bibcode:2012PhRvL.108d3001W. doi: 10.1103/PhysRevLett.108.043001 . PMID   22400833.

Further reading

Books

Journal articles