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Physics

Forty years of Efimov physics: How a bizarre prediction turned into a hot topic

Francesca Ferlaino, Rudolf Grimm

Published Jan 25, 2010• 135 citations
Publisher

Abstract

A prediction that resonantly interacting particles can form weakly bound trimer states remained a mere theoretical oddity for more than three decades until tunable ultracold gases caused the field to explode, with enormous progress in just the last year.
DOI
10.1103/physics.3.9

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More Is Different, Few Is Exotic

As powerful as theoretical physics can be, when it comes to describing the dynamics of several interacting particles, it stumbles at three. This few-body physics is interesting in many contexts, particularly interactions within the nucleus and between atoms and molecules. Although predicted 40 years ago for the special case of resonant interaction, which occurs at the edge of where two-particle bound states start to form, Efimov trimers were only recently observed in ultracold Bose gases. More work followed, revealing evidence of multiple trimer, and even tetramer, states. Now, Pollack et al. (p. [1683][1], published online 19 November; see the Perspective by [Modugno][2] ) observe as many as 11 features near a lithium resonance that can be directly related to different few-body processes. The positions of the features with respect to each other are in excellent agreement with the theoretical prediction, although some deviations, attributed to short-range interactions, present a challenge for a future, more detailed theory. [1]: /lookup/doi/10.1126/science.1182840 [2]: /lookup/doi/10.1126/science.1184235

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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.

Journal of International Crisis and Risk Communication Research•Jan 1, 2006•0 citations
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.
As powerful as theoretical physics can be, when it comes to describing the dynamics of several interacting particles, it stumbles at three. This few-body physics is interesting in many contexts, particularly interactions within the nucleus and between atoms and molecules. Although predicted 40 years ago for the special case of resonant interaction, which occurs at the edge of where two-particle bound states start to form, Efimov trimers were only recently observed in ultracold Bose gases. More work followed, revealing evidence of multiple trimer, and even tetramer, states. Now, Pollack et al. (p. [1683][1], published online 19 November; see the Perspective by [Modugno][2] ) observe as many as 11 features near a lithium resonance that can be directly related to different few-body processes. The positions of the features with respect to each other are in excellent agreement with the theoretical prediction, although some deviations, attributed to short-range interactions, present a challenge for a future, more detailed theory. [1]: /lookup/doi/10.1126/science.1182840 [2]: /lookup/doi/10.1126/science.1184235
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.