Energy levels of three resonantly interacting particles

Efimov, V.N.

doi:10.1016/0375-9474(73)90510-1

Cited by 490 publications

(567 citation statements)

References 5 publications

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“…We have checked that Eq. (C20) reproduces the numerically determined momentum distributions n red,sp (K) for the (2, 1) and (3,2) systems with small a s , a s > 0, well for K r −1 0 .…”

Section: Appendix C: Analytical Expressions For the Non-interacting Amentioning

confidence: 63%

“…Figure 10 shows the occupation numbers n qlm [(qlm) = (000), (100) and (010)] for the ground state with L Π = 0 + symmetry of the (2, 2) system. The behavior is similar for the (2, 1), (3,2) and (3, 3) systems (not shown). As a s approaches 0 − , the numerically obtained occupation numbers agree with the analytical results presented in Appendix C, i.e., n 000 = 1/2, n 01m = 1/6 (m = 0, ±1), and n qlm = 0 for all other qlm.…”

Section: Non-local Propertiesmentioning

confidence: 77%

“…(18)]. The calculations for the (2, 1), (2, 2), (3,2) and (3, 3) systems are performed using r0 = 0.01a ho , r0 = 0.005a ho , r0 = 0.05a ho and r0 = 0.05a ho , respectively. Note the log-log scale.…”

Section: Non-local Propertiesmentioning

confidence: 99%

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Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Blume¹,

Daily²

2011

Comptes Rendus. Physique

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We investigate small equal-mass two-component Fermi gases under external spherically symmetric confinement in which atoms with opposite spins interact through a short-range two-body model potential. We employ a non-perturbative microscopic framework, the stochastic variational approach, and determine the system properties as functions of the interspecies s-wave scattering length as, the orbital angular momentum L of the system, and the numbers N1 and N2 of spin-up and spin-down atoms (with N1 − N2 = 0 or 1 and N ≤ 6, where N = N1 + N2). At unitarity, we determine the energies of the five-and six-particle systems for various ranges r0 of the underlying two-body model potential and extrapolate to the zero-range limit. These energies serve as benchmark results that can be used to validate and assess other numerical approaches. We also present structural properties such as the pair distribution function and the radial density. Furthermore, we analyze the one-body and two-body density matrices. A measure for the molecular condensate fraction is proposed and applied. Our calculations show explicitly that the natural orbitals and the momentum distributions of atomic Fermi gases approach those characteristic for a molecular Bose gas if the s-wave scattering length as, as > 0, is sufficiently small.

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“…We have checked that Eq. (C20) reproduces the numerically determined momentum distributions n red,sp (K) for the (2, 1) and (3,2) systems with small a s , a s > 0, well for K r −1 0 .…”

Section: Appendix C: Analytical Expressions For the Non-interacting Amentioning

confidence: 63%

Section: Non-local Propertiesmentioning

confidence: 77%

See 1 more Smart Citation

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Blume¹,

Daily²

2011

Comptes Rendus. Physique

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“…Since its discovery by Efimov in 1970 [12] many works have been devoted to this subject. See, for example [2,7,9,13,29,33,34,35,37].…”

Section: Introductionmentioning

confidence: 99%

On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum Asymptotics

2007

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ABSTRACT.A model operator H associated with the energy operator of a system describing three particles in interaction, without conservation of the number of particles, is considered. The precise location and structure of the essential spectrum of H is described. The existence of infinitely many eigenvalues below the bottom of the essential spectrum of H is proved for the case where an associated generalized Friedrichs model has a resonance at the bottom of its essential spectrum. An asymptotics for the number N (z) of eigenvalues below the bottom of the essential spectrum is also established. The finiteness of eigenvalues of H below the bottom of the essential spectrum is proved if the associated generalized Friedrichs model has an eigenvalue with energy at the bottom of its essential spectrum.

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“…Efimov trimers open a window into a largely uncharted world of quantum physics based on many-particle bound states. They were discovered in nuclear physics [2][3][4] , but have also been discussed in quantum magnets 5 , biophysics of DNA 6 and, most importantly, in ultra-cold atomic gases. In these systems, it has become possible to fine-tune both the sign and the value of the pair interactions through the Feshbach mechanism 7 , from a scattering length a close to zero up to the unitary point |a| ¼ N. In current experiments, Efimov trimers have not been seen directly, but their presence has been traced through the variations of the rate at which the gas loses particles as the interactions are scanned through the unitary region [8][9][10][11] .…”

mentioning

confidence: 99%

Efimov-driven phase transitions of the unitary Bose gas

Piatecki

Krauth

2014

Nat Commun

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Initially predicted in nuclear physics, Efimov trimers are bound configurations of three quantum particles that fall apart when any one of them is removed. They open a window into a rich quantum world that has become the focus of intense experimental and theoretical research, as the region of 'unitary' interactions, where Efimov trimers form, is now accessible in cold-atom experiments. Here we use a path-integral Monte Carlo algorithm backed up by theoretical arguments to show that unitary bosons undergo a first-order phase transition from a normal gas to a superfluid Efimov liquid, bound by the same effects as Efimov trimers. A triple point separates these two phases and another superfluid phase, the conventional Bose-Einstein condensate, whose coexistence line with the Efimov liquid ends in a critical point. We discuss the prospects of observing the proposed phase transitions in cold-atom systems.

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Energy levels of three resonantly interacting particles

Cited by 490 publications

References 5 publications

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction

On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum Asymptotics

Efimov-driven phase transitions of the unitary Bose gas

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