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      Convergence Properties of the Effective Theory for Trapped Bosons

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          Abstract

          We investigate few-boson systems with resonant interactions in a narrow harmonic trap within an effective theory framework. The size of the model space is identified with the effective theory cutoff. In the universal regime, the interactions of the bosons can be approximated by contact interactions. We investigate the convergence properties of genuine and smeared contact interactions as the size of the model space is increased and present a detailed error analysis. The spectra for few-boson systems with up to 6 identical particles are calculated by combining extrapolations in the cutoff and in the smearing parameter.

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          Feshbach Resonances in Ultracold Gases

          Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules.
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            The unitary three-body problem in a trap

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            We consider either 3 spinless bosons or 3 equal mass spin-1/2 fermions, interacting via a short range potential of infinite scattering length and trapped in an isotropic harmonic potential. For a zero-range model, we obtain analytically the exact spectrum and eigenfunctions: for fermions all the states are universal; for bosons there is a coexistence of decoupled universal and efimovian states. All the universal states, even the bosonic ones, have a tiny 3-body loss rate. For a finite range model, we numerically find for bosons a coupling between zero angular momentum universal and efimovian states; the coupling is so weak that, for realistic values of the interaction range, these bosonic universal states remain long-lived and observable.
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              The Four-Boson System with Short-Range Interactions

              We consider the non-relativistic four-boson system with short-range forces and large scattering length in an effective quantum mechanics approach. We construct the effective interaction potential at leading order in the large scattering length and compute the four-body binding energies using the Yakubovsky equations. Cutoff independence of the four-body binding energies does not require the introduction of a four-body force. This suggests that two- and three-body interactions are sufficient to renormalize the four-body system. We apply the equations to 4He atoms and calculate the binding energy of the 4He tetramer. We observe a correlation between the trimer and tetramer binding energies similar to the Tjon line in nuclear physics. Over the range of binding energies relevant to 4He atoms, the correlation is approximately linear.
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                Author and article information

                Journal
                31 October 2012
                Article
                10.1088/0954-3899/40/5/055004
                1210.8373
                70db232e-3986-45e1-8995-2574cd3cee01

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                J.Phys. G40 (2013) 055004
                26 pages, 14 figures
                cond-mat.quant-gas nucl-th

                Quantum gases & Cold atoms,Nuclear physics
                Quantum gases & Cold atoms, Nuclear physics

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