Measurement of an Efimov Trimer Binding Energy in a Three-Component Mixture of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi>Li</mml:mi><mml:mprescripts /><mml:none /><mml:mn>6</mml:mn></mml:mmultiscripts></mml:math>

Nakajima, Shuta; Horikoshi, Munekazu; Mukaiyama, Takashi; Naidon, Pascal; Ueda, Masahito

doi:10.1103/physrevlett.106.143201

Cited by 114 publications

(169 citation statements)

References 31 publications

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“…In contrast to Ref. [18], other models [24,[33][34][35][36][37][38] have found better agreement with experiments. Our analysis of these treatments, however, indicates that the two-body models used have many of the characteristics of our v hs vdW , therefore satisfying the prerequisite for a universal threebody parameter.…”

Section: Fig 1: (A)contrasting

confidence: 80%

Origin of the Three-Body Parameter Universality in Efimov Physics

et al. 2012

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In recent years extensive theoretical and experimental studies of universal few-body physics have led to advances in our understanding of universal Efimov physics. Whereas theory had been the driving force behind our understanding of Efimov physics for decades, recent experiments have contributed an unexpected discovery. Specifically, measurements have found that the so-called threebody parameter determining several properties of the system is universal, even though fundamental assumptions in the theory of the Efimov effect suggest that it should be a variable property that depends on the precise details of the short-range two-and three-body interactions. The present Letter resolves this apparent contradiction by elucidating previously unanticipated implications of the two-body interactions. Our study shows that the three-body parameter universality emerges because a universal effective barrier in the three-body potentials prevents the three particles from simultaneously getting close together. Our results also show limitations on this universality, as it is more likely to occur for neutral atoms and less likely to extend to light nuclei. PACS numbers: 31.15.ac,31.15.xj, In the early 70's, Vitaly Efimov predicted a strikingly counterintuitive quantum phenomenon [1], today known as Efimov effect: in three-body systems for which the two-body s-wave scattering length a is much larger than the characteristic range r 0 of the two-body interaction, an infinite number of three-body bound states can be formed even when the short-range two-body interactions are too weak to bind a two-body state (a < 0). The Efimov effect, once considered a mysterious and esoteric effect, is today a reality that many experiments in ultracold quantum gases have successfully observed and continued to explore [2][3][4][5][6][7][8][9][10][11][12][13][14]. One of the most fundamental assumptions underlying our theoretical understanding of this peculiar effect is that the weakly bound three-body energy spectrum, and other low-energy three-body scattering observables, should depend on a three-body parameter that encapsulates all details of the interactions at short distances [15]. For this reason, the three-body parameter has been viewed as nonuniversal since its value for any specific system would depend on the precise details of the underlying two-and three-body interactions [16][17][18].In nuclear physics, this picture seems be consistent, i.e., three-body weakly bound state properties seem to be sensitive to the nature of the two-and three-body short-range interactions [17]. More recently, however, Berninger et al. [3] have directly explored this issue for alkali atoms whose scattering lengths are magnetically tuned near different . Even though the short-range physics can be expected to vary from one resonance to another, Efimov resonances were found for values of the magnetic field at which a=a − 3b =−9.1(2)r vdW , where r vdW is the van der Waals length [20, 21]. Therefore, in each of these cases, the three-body parameter was approximatel...

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Section: Fig 1: (A)contrasting

confidence: 80%

Origin of the Three-Body Parameter Universality in Efimov Physics

et al. 2012

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“…Signatures of the Efimov effect are then obtained by monitoring the atom loss from the trap due to the formation of Efimov trimers at scattering lengths for which the trimer energy coincides with that of three free atoms (these scattering lengths are marked by stars in Figure 1A). The most direct probe of Efimov trimers to date comes from radio frequency spectroscopy on an ultracold three-component lithium gas, which yielded the binding energies of an Efimov trimer for different two-body interaction strengths (8,9). An experimental exploration of the size and shape of Efimov states requires a setup where the trimer is sufficiently long lived and can be imaged selectively.…”

Section: One Sentence Summarymentioning

confidence: 99%

Observation of the Efimov state of the helium trimer

Kunitski

Zeller

Voigtsberger

et al. 2015

Science

226

219

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Quantum theory dictates that upon weakening the two-body interaction in a three-body system, an infinite number of three-body bound states of a huge spatial extent emerge just before these three-body states become unbound. Three helium atoms have been predicted to form a molecular system that manifests this peculiarity under natural conditions without artificial tuning of the attraction between particles by an external field. Here we report experimental observation of this long predicted but experimentally elusive Efimov state of 4 He3 by means of Coulomb explosion imaging. We show spatial images of an Efimov state, confirming the predicted size and a typical structure where two atoms are close to each other while the third is far away. One Sentence Summary:We report experimental discovery of a gigantic molecule that consists of three helium atoms and is bound solely by a universal feature of quantum mechanics called "Efimov effect".Ever since the early days of celestial mechanics, the three-body problem posed a major challenge to physicists. In the early 20th century the failure of finding a stable solution for the classical helium atom (2 electrons and a nucleus) heralded the demise of Niels Bohr's program of semiclassical atomic physics (1). Quantum mechanics then added yet another surprising twist to the three-body problem when in 1970 Vitaly Efimov predicted the appearance of an infinite series of stable three-body states of enormous spatial extents (2). These Efimov states are predicted to exist for short-range interactions like the van der Waals force between atoms or the strong force between nucleons. When the potential becomes so shallow that the last two-body bound state is at the verge of becoming unbound or is unbound, then three particles stick together to form Efimov states. Intriguingly, this three-body behavior does not depend on the details of the underlying two-body interactions. This makes the Efimov effect a universal phenomenon, with important applications in particle, nuclear (3, 4), atomic (4), condensed matter (5) and biological physics (6).Figure 1 summarizes two facets of Efimov's prediction, namely the energy spectrum and the structure of an Efimov state. Figure 1A shows how the two-and three-body binding energies (the binding energy of an atomic cluster is defined as the energy needed to separate all constituents of the cluster to infinite distances) change as the depth of the two-body potential is increased. As 2 indicated by the arrow above Figure 1A, the depth of the two-body potential increases along the horizontal axis. As the depth increases, the s-wave scattering length a changes from negative values to infinitely large values to positive values. Negative a values correspond to the domain where shallow two-body bound states do not exist. For positive a, a shallow two-body bound state, the dimer (see the blue solid line), exists. Bound three-body states (called trimers) exist in the green-shaded area. The extremely weakly-bound three-body states close to threshold (see...

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“…This corresponds to what is known as first-order coherence (Naraschewski & Glauber 2001). Second-order coherence (related to the two-body density matrix) is connected to the famous Hanbury-Brown and Twiss effect (Hanbury-Brown & Twiss 1956, Baym 1969, Baym 1998.…”

Section: Structure Of Bose Condensatesmentioning

confidence: 99%

“…(2) denoted by ρ 1 . One can show under rather general conditions that ρ 1 vanishes for homogeneous 3-dimensional Bose systems (Leggett 2006) and also in the case of trapped condensates (Naraschewski & Glauber 2001). Thus this alternative definition of BEC is equivalent to that of one large eigenvalue in the expansion in Eq.…”

Section: Structure Of Bose Condensatesmentioning

confidence: 99%

“…In the limits of high and low field strengths there are good asymptotic quantum numbers (Pethick & Smith 2008). Systems with two components corresponding to population of the lowest two hyperfine states (of two different given projections m F ) have been extensively studied (Ketterle & Zwierlein 2008), and recently also three-component systems (three different m F values) have been realized in experiments (Ottenstein et al 2008, Nakajima et al 2010). The hyperfine energy splitting for different m F due to the magnetic field is of order 10 −6 eV for the alkali atoms typically used in experiment (Pethick & Smith 2008).…”

Section: Two-component Atomic Fermi Gasesmentioning

confidence: 99%

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Comparing and contrasting nuclei and cold atomic gases

Zinner¹,

Jensen²

2013

J. Phys. G: Nucl. Part. Phys.

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Abstract. The experimental revolution in ultracold atomic gas physics over the past decades have brought tremendous amounts of new insight to the world of degenerate quantum systems. Here we compare and constrast the developments of cold atomic gases with the physics of nuclei since many concepts, techniques, and nomenclatures are common to both fields. However, nuclei are finite systems with interactions that are typically much more complicated than those of ultracold atomic gases. The simularities and differences must therefore be carefully addressed for a meaningful comparison and to facilitate fruitful crossdisciplinary activity. We first consider condensates of bosonic and paired systems of fermionic particles with the mean-field description but take great care to point out potential problems in the limit of small particle numbers. Along the way we review some of the basic results of BEC and BCS theory, as well as the BCS-BEC crossover and the Fermi gas in the unitarity limit, all within the context of ultracold atoms. Subsequently, we consider the specific example of an atomic Fermi gas from a nuclear physics perspective, comparing degrees of freedom, interactions, and relevant length and energy scales of cold atoms and nuclei. Next we address some attempts in nuclear physics to transfer the concepts of condensates in nuclei that can in principle be built from bosonic alpha-particle constituents. We also consider Efimov physics, a prime example of nuclear physics transfered to cold atoms, and consider which systems are more likely to show interesting bound state spectra. Finally, we address some recent studies of the BCS-BEC crossover in light nuclei and compare them to the concepts used in ultracold atomic gases. While many-body concepts such as BEC or BCS states are applicable in both subfields, we find that the interactions and finite particle numbers in nuclei can obscure the clear meaning they have in cold atoms. On the other hand, universal results from atomic physics should have impact in certain limits of the nuclear domain. In particular, with advances in the trapping of few-body atomic systems we expect a more direct exchange of ideas and results.

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Measurement of an Efimov Trimer Binding Energy in a Three-Component Mixture ofLi6

Cited by 114 publications

References 31 publications

Origin of the Three-Body Parameter Universality in Efimov Physics

Origin of the Three-Body Parameter Universality in Efimov Physics

Observation of the Efimov state of the helium trimer

Comparing and contrasting nuclei and cold atomic gases

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