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arXiv:cond-mat/0203400 · Physical Review Letters

Correlated Trapped Bosons and the Many-Body Efimov Effect

Ole Gade Sørensen, D. V. Fedorov, A. S. Jensen

Published Oct 4, 2002• 33 citations
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Abstract

We study two-body correlations in systems of identical bosons. We use a Faddeev type of decomposition of the wave function where all pairs of particles are treated equally. At large scattering length appears a series of Efimov-like states, i.e., spatially extended, model-independent many-body bound states inside the trap. They may play a role in the decay of Bose-Einstein condensates.

DOI
10.1103/physrevlett.89.173002

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We study two-body correlations in systems of identical bosons. We use a Faddeev type of decomposition of the wave function where all pairs of particles are treated equally. At large scattering length appears a series of Efimov-like states, i.e., spatially extended, model-independent many-body bound states inside the trap. They may play a role in the decay of Bose-Einstein condensates.
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We formulate a method to study two-body correlations in a system of N identical bosons interacting via central two-body potentials. We use the adiabatic hyperspherical approach and assume a Faddeev-like decomposition of the wave function. For a fixed hyperradius we derive variationally an optimal integro-differential equation for the hyperangular eigenvalue and wave function. This equation reduces substantially by assuming the interaction range much smaller than the size of the N-body system. At most, one-dimensional integrals then remain. We view a Bose-Einstein condensate pictorially as a structure in the landscape of the potential given as a function of the one-dimensional hyperradial coordinate. The quantum states of the condensate can be located in one of the two potential minima. We derive and discuss properties of the solutions and illustrate with numerical results. The correlations lower the interaction energy substantially. The new multibody Efimov states are solutions independent of details of the two-body potential. We compare with mean-field results and available experimental data.
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We formulate a method to study two-body correlations in a condensate of N identical bosons. We use the adiabatic hyperspheric approach and assume a Faddeev-like decomposition of the wave function. We derive for a fixed hyper-radius an integro-differential equation for the angular eigenvalue and wave function. We discuss properties of the solutions and illustrate with numerical results. The correlations lower the interaction energy for N=20N=20N=20 by about a factor of 5.