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Science

More Is Different, Few Is Exotic

Published Dec 17, 2009• 0 citations
Publisher

Abstract

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

DOI
10.1126/science.326.5960.1588-f

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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, published online 19 November; see the Perspective by Modugno ) 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.
Few-Body Problem Seemingly simple, quantum mechanical few-body systems are notoriously difficult to describe. Efimov trimers, three-body bound states with interactions tuned to be in close vicinity of the formation of two-body bound states, are the most tractable of these systems, with relevance, for example, in nuclear physics. Observed recently in ultracold atomic gases through their signatures in the rate of inelastic three-body collisions, Efimov trimers are predicted to appear at interaction strengths whose ratios are universally specified. By measuring binding energy as a function of interaction strength, Lompe et al. (p. 940 ) directly observed the association of three distinguishable atoms into a bound state. This technique may enable more precise studies of the trimer state, potentially revealing the nature of nonuniversal corrections suggested by prior experiments.
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.
Under certain circumstances, three or more interacting particles may form bound states. Although the general few-body problem is not analytically solvable, the so-called Efimov trimers appear for a system of three particles with resonant two-body interactions. The binding energies of these trimers are predicted to be universally connected to each other, independent of the microscopic details of the interaction. By exploiting a Feshbach resonance to widely tune the interactions between trapped ultracold lithium atoms, we find evidence for two universally connected Efimov trimers and their associated four-body bound states. A total of 11 precisely determined three- and four-body features are found in the inelastic-loss spectrum. Their relative locations on either side of the resonance agree well with universal theory, whereas a systematic deviation from universality is found when comparing features across the resonance.
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.