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Universality and Beyond: Effective Field Theory for Three-Body Physics in Cold Atoms and Halo Nuclei

Chen Ji

Published Jan 1, 2012• 1 citation

Abstract

Systems, such as cold atoms and light halo nuclei, share universal features at low energies, for which details of inter-particle interactions are not essential.We study threebody physics in such systems in an effective-field-theory (EFT) framework.We will discuss universal behavior in three-body systems and higher-order effectiverange corrections beyond universality.We study effective-range effects perturbatively up to the next-to-next-to-leading order (N 2 LO) for the case of three identical bosons.We apply this analysis to recombination features in cold atomic gases and properties of Helium trimers.Effective range corrections also play an important role in the EFT study of fewnucleon systems and halo nuclei.The ground-state of Helium-6 can be treated as a two-neutron halo with an alpha core.This bound state is generated by the resonant neutron-neutron and neutron-alpha interactions.The latter is dominated by a shallow p-wave resonance.We present a calculation of Helium-6 in an EFT approach appropriate for halo systems.

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Systems, such as cold atoms and light halo nuclei, share universal features at low energies, for which details of inter-particle interactions are not essential.We study threebody physics in such systems in an effective-field-theory (EFT) framework.We will discuss universal behavior in three-body systems and higher-order effectiverange corrections beyond universality.We study effective-range effects perturbatively up to the next-to-next-to-leading order (N 2 LO) for the case of three identical bosons.We apply this analysis to recombination features in cold atomic gases and properties of Helium trimers.Effective range corrections also play an important role in the EFT study of fewnucleon systems and halo nuclei.The ground-state of Helium-6 can be treated as a two-neutron halo with an alpha core.This bound state is generated by the resonant neutron-neutron and neutron-alpha interactions.The latter is dominated by a shallow p-wave resonance.We present a calculation of Helium-6 in an EFT approach appropriate for halo systems.

Effective Field Theory (EFT) provides a powerful framework to exploit a separation of scales in order to perform systematically improvable, model-independent calculations. We apply this method to strongly interacting quantum systems with short-range interactions and large scattering length. Such systems display remarkable universal properties which include a geometric spectrum of shallow three-body states called "Efimov states" and log-periodic dependence of scattering observables on the scattering length. We review the EFT for large scattering length and some of its applications in the physics of cold atoms and nuclear physics. In particular, we discuss the possibility of an infrared limit cycle in QCD and the extension of the EFT to halo nuclei.

Effective Field Theory (EFT) provides a powerful framework to exploit a separation of scales in order to perform systematically improvable, model-independent calculations. We apply this method to strongly interacting quantum systems with short-range interactions and large scattering length. Such systems display remarkable universal properties which include a geometric spectrum of shallow three-body called Efimov states and log-periodic dependence of scattering observables on the scattering length. We review the EFT for large scattering length and some of its applications in the physics of cold atoms and nuclear physics. In particular, we discuss the possibility of an infrared limit cycle in QCD and the extension of the EFT to halo nuclei.

Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms and nuclear physics. In particular, we will discuss the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT approach to the four-body system and N-boson droplets in two spatial dimensions will also be addressed.

Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model‐independent calculations. Particularly interesting are few‐body systems with short‐range interactions and large two‐body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three‐body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms. Recent extensions of this approach to the four‐body system and N‐boson droplets in two spatial dimensions will also be discussed.

The role of an intrinsic four-body scale in universal few-boson systems is the subject of active debate. We study these systems within the framework of effective field theory. For systems of up to six bosons we establish that no four-body scale appears at leading order (LO). However, we find that at next-to-leading order (NLO) a four-body force is needed to obtain renormalized results for binding energies. With the associated parameter fixed to the binding energy of the four-boson system, this force is shown to renormalize the five- and six-body systems as well. We present an original ansatz for the short-distance limit of the bosonic A-body wave function from which we conjecture that new A-body scales appear at N^{A-3} LO. As a specific example, calculations are presented for clusters of helium atoms. Our results apply more generally to other few-body systems governed by a large scattering length, such as light nuclei and halo states, the low-energy properties of which are independent of the detailed internal structure of the constituents.