The Efimov effect is an effect in the quantum mechanics of few-body systems predicted by the Russian theoretical physicistV. 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.
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
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 resultsedit
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]
Usageedit
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.)
^ abЕфимов, 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.
^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.
^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.
^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.
^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.
^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.
^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.
^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.
^Thøgersen, Martin (2009). "Universality in Ultra-Cold Few- and Many-Boson Systems". arXiv:0908.0852 [cond-mat.quant-gas]. Ph.D. thesis.
^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.
^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.
^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.
^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.
External linksedit
Press release about the experimental confirmation (2006.03.16)
Overwhelming proof for Efimov State that's become a hotbed for research some 40 years after it first appeared (2009.12.14)
Observation of the Second Triatomic Resonance in Efimov’s Scenario (2014.05.15)
December 15, 2023
efimov, state, efimov, effect, effect, quantum, mechanics, body, systems, predicted, russian, theoretical, physicist, efimov, 1970, efimov, effect, where, three, identical, bosons, interact, with, prediction, infinite, series, excited, three, body, energy, lev. 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 1 Theory 2 Experimental results 3 Usage 4 See also 5 References 6 External linksTheory edit nbsp 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 N 0 1 2 displaystyle N 0 1 2 ldots nbsp whose scattering lengths a N displaystyle a N nbsp and binding energies E N displaystyle E N nbsp each form a geometric progression a N a 0 l N displaystyle a N a 0 lambda N nbsp E N E 0 l 2 N displaystyle E N E 0 lambda 2N nbsp where the common ratio l e p s 0 22 69438 displaystyle lambda mathrm e mathrm pi s 0 22 69438 ldots nbsp is a universal constant OEIS OEIS A242978 1 Here s 0 1 0062378 displaystyle s 0 1 0062378 ldots nbsp is the order of the imaginary order modified Bessel function of the second kind K s 0 r a displaystyle tilde K s 0 r a nbsp that describes the radial dependence of the wavefunction By virtue of the resonance determined boundary conditions it is the unique positive value of s displaystyle s nbsp satisfying the transcendental equation s cosh p s 2 8 3 sinh p s 6 0 displaystyle s cosh left tfrac mathrm pi s 2 right tfrac 8 sqrt 3 sinh left tfrac mathrm pi s 6 right 0 nbsp Experimental results editIn 2005 for the first time the research group of Rudolf Grimm and Hanns Christoph Nagerl 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 Weidemuller 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 editThe 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 editThree body forceReferences edit a b Efimov V I 1970 Slabosvyazannye sostoyaniya treh rezonansno vzaimodejstvuyushih chastic Weakly Bound States of Three Resonantly Interacting Particles Yadernaya Fizika Nuclear Physics in Russian 12 5 1080 1090 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 T Kraemer M Mark P Waldburger J G Danzl C Chin B Engeser A D Lange K Pilch A Jaakkola H C Nagerl 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 Knoop S Ferlaino F Mark M Berninger M Schobel H Nagerl 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 Zaccanti M Deissler B D Errico C Fattori M Jona Lasinio M Muller 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 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 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 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 Thogersen Martin 2009 Universality in Ultra Cold Few and Many Boson Systems arXiv 0908 0852 cond mat quant gas Ph D thesis 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 Shih Kuang Tung Karina Jimenez Garcia 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 R Pires J Ulmanis S Hafner M Repp A Arias E D Kuhnle M Weidemuller 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 Kunitski Maksim Zeller Stefan Voigtsberger Jorg Kalinin Anton Schmidt Lothar Ph H Schoffler Markus Czasch Achim Schollkopf Wieland Grisenti Robert E Jahnke Till Blume Dorte Dorner 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 External links editPress release about the experimental confirmation 2006 03 16 Overwhelming proof for Efimov State that s become a hotbed for research some 40 years after it first appeared 2009 12 14 Observation of the Second Triatomic Resonance in Efimov s Scenario 2014 05 15 Retrieved from https en wikipedia org w index php title Efimov state amp oldid 1187386329, wikipedia, wiki, book, books, library,
