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arXiv:0706.1230

Three bodies bind even when two do not: Efimov states and Fano resonances in atoms and nuclei

A. R. P. Rau

Published Jun 8, 2007• 1 citation
arXivHTMLPDF

Abstract

Efimov's prediction more than three decades ago that three-body bound states can exist when the pairwise attractions do not bind or only support weakly bound states of a pair, has remained unconfirmed till just the past year. This lecture provides the pedagogical background for recent work on Efimov states in neutron-rich nuclei done with I. Mazumdar (TIFR) and V. S. Bhasin (Delhi University), and published in Phys. Rev. Lett. 97, 062503 (2006). Both these nuclear systems and recent observations of cold cesium atoms provide the first clear evidence for the existence of Efimov states.

DOI
10.48550/arxiv.0706.1230

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Efimov's prediction more than three decades ago that three-body bound states can exist when the pairwise attractions do not bind or only support weakly bound states of a pair, has remained unconfirmed till just the past year. This lecture provides the pedagogical background for recent work on Efimov states in neutron-rich nuclei done with I. Mazumdar (TIFR) and V. S. Bhasin (Delhi University), and published in Phys. Rev. Lett. 97, 062503 (2006). Both these nuclear systems and recent observations of cold cesium atoms provide the first clear evidence for the existence of Efimov states.
In the year 2005, we obtained first evidence for the existence of weakly bound quantum states of three resonantly interacting particles, as predicted 35 years earlier by Vitaly Efimov. In our laboratory, the striking signature of an Efimov state was a giant three-body loss resonance observed in a gas of cesium atoms that was evaporatively cooled to temperatures of about 10 nanokelvin. Here, I will give a short personal account on what prepared the ground for this observation, on how things finally happened in our laboratory, and on how our experiments then developed further.
Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the particular type of the two-body interaction potential. Efimov's scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. This resonance develops into a continuum resonance at non-zero collision energies, and we observe a shift of the resonance position as a function of temperature. We also report on a minimum 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 from which to explore the universal properties of resonantly interacting few-body systems.
Armed with a new solution to the four-body problem, we reanalyze the recent Innsbruck observation of an Efimov resonance in three-body collisions of cesium atoms, and show that it provides evidence of new, universal four-body physics as well. Our theoretical treatment of four bosonic atoms in the limit of strong two-body attraction suggests a ubiquitous result: namely, that resonantly-bound states of all four atoms should occur whenever the two-body scattering length is a specific fraction (0.43) of the value where a three-body Efimov resonance occurs. A hitherto unanalyzed feature in the 2006 Innsbruck experiment supports this universal prediction, and it provides the first known evidence to date that a direct four-body recombination process plays a role. While we confirm the conclusion reached previously by some studies that no true Efimov effect exists for four particles, we demonstrate the existence of a universal class of four-body states that are intimately connected with three-body Efimov states.
We are developing theoretical and computational methods to study two related three-body processes in ultracold quantum gases: three-body resonances and three-body recombination. Three-body recombination causes the ultracold gas to heat up and atoms to leave the trap where they are confined. Therefore, it is an undesirable effect in the process of forming ultracold quantum gases. Metastable three-body states (resonances) are formed in the ultracold gas. When decaying they also give additional kinetic energy to the gas, that leads to the heating too. In addition, a reliable method to obtain three-body resonances would be useful in a number of problems in other fields of physics, for example, in models of metastable nuclei or to study dissociative recombination of H3 +. Our project consists of employing computer modeling to develop a method to obtain three-body resonances. The method uses a novel two-step diagonalization approach to solve the three-body Schrödinger equation. The approach employs the SVD method of Tolstikhin et al. coupled with a complex absorbing potential. We tested this method on a model system of three identical bosons with nucleon mass and compared it to the results of a previous study. This model can be employed to understand the 3He nucleus . We found one three-body bound state and four resonances. We are also studying Efimov resonances using a 4He-based model. In a system of identical spinless bosons, Efimov states are a series of loosely bound three-body states which begin to appear as the energy of the two-body bound state approaches zero . Although they were predicted 35 years ago, recent evidence of Efimov states found by Kraemer et al. in a gas of ultracold Cs atoms has sparked great interest by theorists and experimentalists. Efimov resonances are a kind of pre-dissociated Efimov trimer. To search for Efimov resonances we tune the diatom interaction potential, V(r): V(r) → λV(r) as Esry et al. did . We calculated the first two values of λ for which there is a "condensation" (infinite number) of Efimov states. They are λEfimov1 = 0.9765 and λEfimov2 = 6.834. We performed calculations for λ = 2.4, but found no evidence of Efimov resonances. For future work we plan to work with λ ≈ 4 and λ ≈ λEfimov2 where we might see d-wave and higher l-wave Efimov resonances. There is also a many-body project that forms part of this thesis and consists of a direct diagonalization of the Bogolyubov Hamiltonian, which describes elementary excitations of a gas of bosons interacting through a pairwise interaction. We would like to reproduce the corresponding energy spectrum. So far we have performed several convergence tests, but have not observed the desired energy spectrum. We show preliminary results.
In a recent work [Phys. Rev. Lett.94, 143201 (2005)], we reported an accumulation of three-body resonant states attached to n=2n=2n=2 and higher two-body thresholds. A more careful investigation revealed that there are resonances of the same kind above the n=1n=1n=1 threshold as well. This suggests that the resonances attached to the thresholds are Efimov resonances.
Two particles that are just shy of binding may develop an infinite number of shallow bound states when a third particle is added. This counterintuitive effect was first predicted by Efimov for identical bosons interacting with a short-range pairwise potential. The Efimov effect persists for nonidentical particles if at least two of the three bonds are almost bound. The Efimov effect has recently been verified experimentally using ultracold atoms. We explain the origin of this effect using elementary quantum mechanics and summarize the experimental evidence for it.