Universality in few-body systems with large scattering length
TL;DR: In this paper, a thorough treatment of universality for the system of three identical bosons is presented, and the universal information that is currently available for other 3-body systems is summarized.
About: This article is published in Physics Reports.The article was published on 2006-06-01 and is currently open access. It has received 968 citations till now. The article focuses on the topics: Efimov state & Scattering length.
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TL;DR: Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases and have found numerous experimental applications, opening up the way to important breakthroughs as mentioned in this paper.
Abstract: Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
2,642 citations
01 May 2009
TL;DR: Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases and have found numerous experimental applications, opening up the way to important breakthroughs as mentioned in this paper.
Abstract: Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
1,531 citations
Cites background from "Universality in few-body systems wi..."
...The domain of universality, where scattering and bound state properties are solely characterized by the scattering length and mass, are discussed at length in recent reviews (Braaten and Hammer, 2006; Köhler et al., 2006)....
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...For bosonic atoms with large scattering length a ≫ ā and low temperatures, L3 scales generally as a4 (Braaten and Hammer, 2006; Esry et al., 1999; Fedichev et al., 1996b; Nielsen and Macek, 1999), but with additional quantum features (resonance and interference effects) as discussed in Sec....
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TL;DR: In this article, the nuclear forces can be derived using effective chiral Lagrangians consistent with the symmetries of QCD, and the status of the calculations for two and three nucleon forces and their applications in few-nucleon systems are reviewed.
Abstract: Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.
1,455 citations
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TL;DR: In this article, the authors review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures Nonrelativistic effective field theories are the suitable framework for studying hadronic molecule, and are discussed in both the continuum and finite volumes.
Abstract: A large number of experimental discoveries especially in the heavy quarkonium sector that did not at all fit to the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy Among various explanations of the internal structure of these excitations, hadronic molecules, being analogues of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty We review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules, and are discussed in both the continuum and finite volumes Also pertinent lattice QCD results are presented Further, we discuss the production mechanisms and decays of hadronic molecules, and comment on the reliability of certain assertions often made in the literature
1,016 citations
Cites background from "Universality in few-body systems wi..."
...(Braaten and Hammer, 2006)....
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...(18), the effective coupling can be expressed in terms of the scattering length g2eff 4π = 4M2 µ −aγ a+ 2/γ , (26) which reduces to −4M2/(µa) in the limit of λ2 = 0, reflecting the universality of an S-wave system with a large scattering length (Braaten and Hammer, 2006)....
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TL;DR: In this article, the Efimov trimer state was shown to exist in an ultracold gas of caesium atoms and its signature was observed as a giant three-body recombination loss when the strength of the two-body interaction is varied.
Abstract: In the bizarre world of quantum physics, three interacting particles can form a loosely bound system even if the two-particle attraction is too weak to allow for the binding of a pair. This exotic trimer state was predicted 35 years ago by Russian physicist Vitali Efimov, who found a remarkable and counterintuitive solution to the notoriously difficult quantum-mechanical three-body problem. Efimov's well known result was a landmark in theoretical few-body physics, but until now these exotic states had not been demonstrated experimentally. Now that has been achieved, in an ultracold gas of caesium atoms. The existence of this gas confirms key predictions and opens up few-body quantum systems to further experiment. The first experimental observation of Efimov's prediction confirms key theoretical predictions and represents a starting point from which to explore the universal properties of resonantly interacting few-body systems. Systems of three interacting particles are notorious for their complex physical behaviour. A landmark theoretical result in few-body quantum physics is Efimov's prediction1,2 of a universal set of bound trimer states appearing for three identical bosons with a resonant two-body interaction. Counterintuitively, these states even exist in the absence of a corresponding two-body bound state. Since the formulation of Efimov's problem in the context of nuclear physics 35 years ago, it has attracted great interest in many areas of physics3,4,5,6,7,8. However, the observation of Efimov quantum states has remained an elusive goal3,5. Here we report the observation of an Efimov resonance in an ultracold gas of caesium atoms. The resonance occurs in the range of large negative two-body scattering lengths, arising from the coupling of three free atoms to an Efimov trimer. Experimentally, we observe its signature as a giant three-body recombination loss9,10 when the strength of the two-body interaction is varied. We also detect a minimum9,11,12 in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point with which to explore the universal properties of resonantly interacting few-body systems7. While Feshbach resonances13,14 have provided the key to control quantum-mechanical interactions on the two-body level, Efimov resonances connect ultracold matter15 to the world of few-body quantum phenomena.
884 citations
References
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Book•
01 Jan 1985TL;DR: Modern Quantum Mechanics as mentioned in this paper is a classic graduate level textbook, covering the main quantum mechanics concepts in a clear, organized and engaging manner, and introduces topics that extend the text's usefulness into the twenty-first century, such as advanced mathematical techniques associated with quantum mechanical calculations.
Abstract: Modern Quantum Mechanics is a classic graduate level textbook, covering the main quantum mechanics concepts in a clear, organized and engaging manner. The author, Jun John Sakurai, was a renowned theorist in particle theory. The second edition, revised by Jim Napolitano, introduces topics that extend the text's usefulness into the twenty-first century, such as advanced mathematical techniques associated with quantum mechanical calculations, while at the same time retaining classic developments such as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell's inequality. A solution manual for instructors using this textbook can be downloaded from www.cambridge.org/9781108422413.
4,221 citations
Book•
01 Jan 1966
TL;DR: In this paper, the authors present a survey of various approaches to the solution of three-particle problems, as well as a discussion of the Efimov effect, and the general approach to multiparticle reaction theory.
Abstract: Much progress has been made in scattering theory since the publication of the first edition of this book fifteen years ago, and it is time to update it. Needless to say, it was impossible to incorporate all areas of new develop- ment. Since among the newer books on scattering theory there are three excellent volumes that treat the subject from a much more abstract mathe- matical point of view (Lax and Phillips on electromagnetic scattering, Amrein, Jauch and Sinha, and Reed and Simon on quantum scattering), I have refrained from adding material concerning the abundant new mathe- matical results on time-dependent formulations of scattering theory. The only exception is Dollard's beautiful "scattering into cones" method that connects the physically intuitive and mathematically clean wave-packet description to experimentally accessible scattering rates in a much more satisfactory manner than the older procedure. Areas that have been substantially augmented are the analysis of the three-dimensional Schrodinger equation for non central potentials (in Chapter 10), the general approach to multiparticle reaction theory (in Chapter 16), the specific treatment of three-particle scattering (in Chapter 17), and inverse scattering (in Chapter 20). The additions to Chapter 16 include an introduction to the two-Hilbert space approach, as well as a derivation of general scattering-rate formulas. Chapter 17 now contains a survey of various approaches to the solution of three-particle problems, as well as a discussion of the Efimov effect.
4,044 citations
"Universality in few-body systems wi..." refers background in this paper
...In order to introduce some basic concepts associated with universality in systems with a large scattering length, we begin with a brief review of scattering theory [7,8]....
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...To obtain the 3-body elastic scattering rate, the effects of 2-body elastic collisions, with the third particle infinitely far away, must be subtracted [7]....
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TL;DR: In this paper, it was shown that a wide class of non-Abelian gauge theories have, up to calculable logarithmic corrections, free-field-theory asymptotic behavior.
Abstract: It is shown that a wide class of non-Abelian gauge theories have, up to calculable logarithmic corrections, free-field-theory asymptotic behavior. It is suggested that Bjorken scaling may be obtained from strong-interaction dynamics based on non-Abelian gauge symmetry.
3,334 citations
"Universality in few-body systems wi..." refers background in this paper
...QCD has a single coupling constant s( ) with an asymptotically free ultraviolet fixed point: s( ) → 0 as → ∞ [50,51]....
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...It is a familiar feature of quantum chromodynamics, the quantum field theory that describes the strong interactions [50,51]....
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TL;DR: The Bose-Einstein condensation (BEC) phenomenon was first introduced by Bose as discussed by the authors, who derived the Planck law for black-body radiation by treating the photons as a gas of identical particles.
Abstract: In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein generalized Bose's theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted that at sufficiently low temperatures the particles would become locked together in the lowest quantum state of the system. We now know that this phenomenon, called Bose-Einstein condensation (BEC), only happens for "bosons" – particles with a total spin that is an integer multiple of h, the Planck constant divided by 2π.
3,298 citations