Efimov state

Last updated

The Efimov effect is an effect in the quantum mechanics of few-body systems predicted by the Russian theoretical physicist V. N. Efimov [1] [2] in 1970. Efimov's effect is where three identical bosons interact, with the prediction of an infinite series of excited three-body energy levels when a two-body state is exactly at the dissociation threshold. One corollary is that there exist bound states (called Efimov states) of three bosons even if the two-particle attraction is too weak to allow two bosons to form a pair. A (three-particle) Efimov state, where the (two-body) sub-systems are unbound, is often depicted symbolically by the Borromean rings. This means that if one of the particles is removed, the remaining two fall apart. In this case, the Efimov state is also called a Borromean state.

Contents

Theory

A computer depiction of the quantum effect predicted by Efimov, said to resemble "Russian nesting dolls". Visual Representation of Efimov state - scaling.gif
A computer depiction of the quantum effect predicted by Efimov, said to resemble "Russian nesting dolls".

Efimov predicted that, as the pair interactions among three identical bosons approach resonance—that is, as the binding energy of some two-body bound state approaches zero or the scattering length of such a state becomes infinite—the three-body spectrum exhibits an infinite sequence of bound states whose scattering lengths and binding energies each form a geometric progression

where the common ratio

is a universal constant (OEIS OEIS:  A242978 ). [1] Here

is the order of the imaginary-order modified Bessel function of the second kind that describes the radial dependence of the wavefunction. By virtue of the resonance-determined boundary conditions, it is the unique positive value of satisfying the transcendental equation

.

Experimental results

In 2005, for the first time the research group of Rudolf Grimm and Hanns-Christoph Nägerl from the Institute for Experimental Physics at the University of Innsbruck experimentally confirmed such a state in an ultracold gas of caesium atoms. In 2006, they published their findings in the scientific journal Nature. [3] Further experimental proof for the existence of the Efimov state has been given recently by independent groups. [4] Almost 40 years after Efimov's purely theoretical prediction, the characteristic periodic behavior of the states has been confirmed. [5] [6]

The most accurate experimental value of the scaling factor of the states has been determined by the experimental group of Rudolf Grimm at Innsbruck University as 21.0(1.3), [7] being very close to Efimov's original prediction.

The interest in the "universal phenomena" of cold atomic gases is still growing, especially because of the long-awaited experimental results. [8] [9] The discipline of universality in cold atomic gases near the Efimov states is sometimes referred to as "Efimov physics". [10]

In 2014, the experimental group of Cheng Chin of the University of Chicago and the group of Matthias Weidemüller of the University of Heidelberg have observed Efimov states in an ultracold mixture of lithium and caesium atoms, [11] [12] which extends Efimov's original picture of three identical bosons.

An Efimov state existing as an excited state of a helium trimer was observed in an experiment in 2015. [13]

Usage

The Efimov states are independent of the underlying physical interaction and can in principle be observed in all quantum mechanical systems (i.e. molecular, atomic, and nuclear). The states are very special because of their "non-classical" nature: The size of each three-particle Efimov state is much larger than the force-range between the individual particle pairs. This means that the state is purely quantum mechanical. Similar phenomena are observed in two-neutron halo-nuclei, such as lithium-11; these are called Borromean nuclei. (Halo nuclei could be seen as special Efimov states, depending on the subtle definitions.)

See also

Related Research Articles

<span class="mw-page-title-main">Bose–Einstein condensate</span> State of matter

In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which microscopic quantum mechanical phenomena, particularly wavefunction interference, become apparent macroscopically.

<span class="mw-page-title-main">Positronium</span> Bound state of an electron and positron

Positronium (Ps) is a system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom, specifically an onium. Unlike hydrogen, the system has no protons. The system is unstable: the two particles annihilate each other to predominantly produce two or three gamma-rays, depending on the relative spin states. The energy levels of the two particles are similar to that of the hydrogen atom. However, because of the reduced mass, the frequencies of the spectral lines are less than half of those for the corresponding hydrogen lines.

<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">Top quark</span> Type of quark

The top quark, sometimes also referred to as the truth quark, is the most massive of all observed elementary particles. It derives its mass from its coupling to the Higgs Boson. This coupling is very close to unity; in the Standard Model of particle physics, it is the largest (strongest) coupling at the scale of the weak interactions and above. The top quark was discovered in 1995 by the CDF and DØ experiments at Fermilab.

<span class="mw-page-title-main">Technicolor (physics)</span> Hypothetical model through which W and Z bosons acquire mass

Technicolor theories are models of physics beyond the Standard Model that address electroweak gauge symmetry breaking, the mechanism through which W and Z bosons acquire masses. Early technicolor theories were modelled on quantum chromodynamics (QCD), the "color" theory of the strong nuclear force, which inspired their name.

<span class="mw-page-title-main">Negative temperature</span> Physical systems hotter than any other

Certain systems can achieve negative thermodynamic temperature; that is, their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. This should be distinguished from temperatures expressed as negative numbers on non-thermodynamic Celsius or Fahrenheit scales, which are nevertheless higher than absolute zero. A system with a truly negative temperature on the Kelvin scale is hotter than any system with a positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system. A standard example of such a system is population inversion in laser physics.

In physics, a Feshbach resonance can occur upon collision of two slow atoms, when they temporarily stick together forming an unstable compound with short lifetime. It is a feature of many-body systems in which a bound state is achieved if the coupling(s) between at least one internal degree of freedom and the reaction coordinates, which lead to dissociation, vanish. The opposite situation, when a bound state is not formed, is a shape resonance. It is named after Herman Feshbach, a physicist at MIT.

<span class="mw-page-title-main">Rudolf Grimm</span> Austrian physicist (born 1961)

Rudolf Grimm is an experimental physicist from Austria. His work centres on ultracold atoms and quantum gases. He was the first scientist worldwide who, with his team, succeeded in realizing a Bose–Einstein condensation of molecules.

In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle. The magnetic moment, also called magnetic dipole moment, is a measure of the strength of a magnetic source.

<span class="mw-page-title-main">Belle experiment</span>

The Belle experiment was a particle physics experiment conducted by the Belle Collaboration, an international collaboration of more than 400 physicists and engineers, at the High Energy Accelerator Research Organisation (KEK) in Tsukuba, Ibaraki Prefecture, Japan. The experiment ran from 1999 to 2010.

<span class="mw-page-title-main">Optical lattice</span> Atomic-scale structure formed through the Stark shift by opposing beams of light

An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congregate at the potential extrema. The resulting arrangement of trapped atoms resembles a crystal lattice and can be used for quantum simulation.

<span class="mw-page-title-main">Vitaly Efimov</span> Russian physicist

Vitaly N. Efimov is a Russian theoretical physicist. He proposed the existence of a novel and exotic state of matter now dubbed the Efimov State as a researcher in A. F. Ioffe Physico-Technical Institute, USSR Academy of Sciences, Leningrad, USSR in his 1970 paper "Energy levels arising from resonant two-body forces in a three-body system". It was announced in 2006 that the existence of this state of matter had been confirmed.

The Bose–Hubbard model gives a description of the physics of interacting spinless bosons on a lattice. It is closely related to the Hubbard model that originated in solid-state physics as an approximate description of superconducting systems and the motion of electrons between the atoms of a crystalline solid. The model was introduced by Gersch and Knollman in 1963 in the context of granular superconductors. The model rose to prominence in the 1980s after it was found to capture the essence of the superfluid-insulator transition in a way that was much more mathematically tractable than fermionic metal-insulator models.

In condensed matter physics, an ultracold atom is an atom with a temperature near absolute zero. At such temperatures, an atom's quantum-mechanical properties become important.

R is the ratio of the hadronic cross section to the muon cross section in electron–positron collisions:

<span class="mw-page-title-main">Ultracold neutrons</span> Free neutrons stored in very small traps

Ultracold neutrons (UCN) are free neutrons which can be stored in traps made from certain materials. The storage is based on the reflection of UCN by such materials under any angle of incidence.

<span class="mw-page-title-main">Superfluidity</span> Fluid which flows without losing kinetic energy

Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two isotopes of helium when they are liquefied by cooling to cryogenic temperatures. It is also a property of various other exotic states of matter theorized to exist in astrophysics, high-energy physics, and theories of quantum gravity. The theory of superfluidity was developed by Soviet theoretical physicists Lev Landau and Isaak Khalatnikov.

<span class="mw-page-title-main">Borromean nucleus</span>

A Borromean nucleus is an atomic nucleus comprising three bound components in which any subsystem of two components is unbound. This has the consequence that if one component is removed, the remaining two comprise an unbound resonance, so that the original nucleus is split into three parts.

<span class="mw-page-title-main">Free neutron decay</span> Decay of a neutron when outside a nucleus

When embedded in an atomic nucleus, neutrons are (usually) stable particles. Outside the nucleus, free neutrons are unstable and have a mean lifetime of 877.75+0.50
−0.44
 s
or 879.6±0.8 s. Therefore, the half-life for this process is 611±1 s.

The term Dirac matter refers to a class of condensed matter systems which can be effectively described by the Dirac equation. Even though the Dirac equation itself was formulated for fermions, the quasi-particles present within Dirac matter can be of any statistics. As a consequence, Dirac matter can be distinguished in fermionic, bosonic or anyonic Dirac matter. Prominent examples of Dirac matter are Graphene, topological insulators, Dirac semimetals, Weyl semimetals, various high-temperature superconductors with -wave pairing and liquid Helium-3. The effective theory of such systems is classified by a specific choice of the Dirac mass, the Dirac velocity, the Dirac matrices and the space-time curvature. The universal treatment of the class of Dirac matter in terms of an effective theory leads to a common features with respect to the density of states, the heat capacity and impurity scattering.

References

  1. 1 2 Ефимов, В. И. (1970). Слабосвязанные состояния трех резонансно взаимодействующих частиц[Weakly Bound States of Three Resonantly Interacting Particles]. Ядерная Физика[Nuclear Physics] (in Russian). 12 (5): 1080–1090.
  2. Efimov, V. (1970). "Energy levels arising from resonant two-body forces in a three-body system". Physics Letters B . 33 (8): 563–564. Bibcode:1970PhLB...33..563E. doi:10.1016/0370-2693(70)90349-7.
  3. T. Kraemer; M. Mark; P. Waldburger; J. G. Danzl; C. Chin; B. Engeser; A. D. Lange; K. Pilch; A. Jaakkola; H.-C. Nägerl; R. Grimm (2006). "Evidence for Efimov quantum states in an ultracold gas of caesium atoms". Nature. 440 (7082): 315–318. arXiv: cond-mat/0512394 . Bibcode:2006Natur.440..315K. doi:10.1038/nature04626. PMID   16541068. S2CID   4379828.
  4. Knoop, S.; Ferlaino, F.; Mark, M.; Berninger, M.; Schöbel, H.; Nägerl, H. -C.; Grimm, R. (2009). "Observation of an Efimov-like trimer resonance in ultracold atom–dimer scattering". Nature Physics. 5 (3): 227. arXiv: 0807.3306 . Bibcode:2009NatPh...5..227K. doi:10.1038/nphys1203. S2CID   108288673.
  5. Zaccanti, M.; Deissler, B.; D’Errico, C.; Fattori, M.; Jona-Lasinio, M.; Müller, S.; Roati, G.; Inguscio, M.; Modugno, G. (2009). "Observation of an Efimov spectrum in an atomic system". Nature Physics. 5 (8): 586. arXiv: 0904.4453 . Bibcode:2009NatPh...5..586Z. doi:10.1038/nphys1334. S2CID   118384878.
  6. Pollack, S. E.; Dries, D.; Hulet, R. G.; Danzl, J. G.; Chin, C.; Engeser, B.; Lange, A. D.; Pilch, K.; Jaakkola, A.; Naegerl, H. -C.; Grimm, R. (2009). "Universality in Three- and Four-Body Bound States of Ultracold Atoms". Science. 326 (5960): 1683–1685. arXiv: 0911.0893 . Bibcode:2009Sci...326.1683P. doi:10.1126/science.1182840. PMID   19965389. S2CID   6728520.
  7. Huang, Bo; Sidorenkov, Leonid A.; Grimm, Rudolf; Hutson, Jeremy M. (2014). "Observation of the Second Triatomic Resonance in Efimov's Scenario". Physical Review Letters. 112 (19): 190401. arXiv: 1402.6161 . Bibcode:2014PhRvL.112s0401H. doi:10.1103/PhysRevLett.112.190401. PMID   24877917. S2CID   16378280.
  8. Braaten, E.; Hammer, H. (2006). "Universality in few-body systems with large scattering length". Physics Reports. 428 (5–6): 259–390. arXiv: cond-mat/0410417 . Bibcode:2006PhR...428..259B. doi:10.1016/j.physrep.2006.03.001. S2CID   14450309.
  9. Thøgersen, Martin (2009). "Universality in Ultra-Cold Few- and Many-Boson Systems". arXiv: 0908.0852 [cond-mat.quant-gas]. Ph.D. thesis.
  10. Naidon, Pascal; Endo, Shimpei (2017). "Efimov Physics: a review". Reports on Progress in Physics. 80 (5). 056001. arXiv: 1610.09805 . Bibcode:2017RPPh...80e6001N. doi:10.1088/1361-6633/aa50e8. PMID   28350544. S2CID   206095127. pp. 3–4: the Efimov effect gives rise to a broad class of phenomena that have been referred to as Efimov physics. ... [The term] is however not clearly defined and somewhat subjective.
  11. Shih-Kuang Tung; Karina Jiménez-García; Jacob Johansen; Colin V. Parker; Cheng Chin (2014). "Geometric Scaling of Efimov States in a Li6−Cs133 Mixture". Physical Review Letters. 113 (24): 240402. arXiv: 1402.5943 . Bibcode:2014PhRvL.113x0402T. doi:10.1103/PhysRevLett.113.240402. PMID   25541753. S2CID   21807523.
  12. R. Pires; J. Ulmanis; S. Häfner; M. Repp; A. Arias; E. D. Kuhnle; M. Weidemüller (2014). "Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance". Physical Review Letters. 112 (25): 250404. arXiv: 1403.7246 . Bibcode:2014PhRvL.112y0404P. doi:10.1103/PhysRevLett.112.250404. PMID   25014797. S2CID   24371722.
  13. Kunitski, Maksim; Zeller, Stefan; Voigtsberger, Jörg; Kalinin, Anton; Schmidt, Lothar Ph. H.; Schöffler, Markus; Czasch, Achim; Schöllkopf, Wieland; Grisenti, Robert E.; Jahnke, Till; Blume, Dörte; Dörner, Reinhard (May 2015). "Observation of the Efimov state of the helium trimer". Science. 348 (6234): 551–555. arXiv: 1512.02036 . Bibcode:2015Sci...348..551K. doi:10.1126/science.aaa5601. PMID   25931554. S2CID   206635093.