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AIP conference proceedings

Spatial Correlations in Bose Gases

Mathias Kirk Thøgersen, D. V. Fedorov, A. S. Jensen, Jacob Schach Møller, Dmitri Fedorov

Published Jan 1, 2008• 1 citation
Publisher

Abstract

We calculate energies, condensate fractions and two‐body correlation functions for a system of N identical bosons in a trap. Both attractive and repulsive finite‐range interactions with a large range of positive scattering lengths are used. At small scattering lengths the system is model independent. When the scattering length is comparable to the trap length the properties of the system depend on the details of the interaction.

DOI
10.1063/1.2915644

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We calculate energies, condensate fractions and two‐body correlation functions for a system of N identical bosons in a trap. Both attractive and repulsive finite‐range interactions with a large range of positive scattering lengths are used. At small scattering lengths the system is model independent. When the scattering length is comparable to the trap length the properties of the system depend on the details of the interaction.
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We calculate the energy and the condensate fraction of a system of trapped bosons interacting via a short-range two-body potential with positive scattering length. The potential is attractive and has a two-body bound state. When the scattering length is small compared to the trap length the system is model independent: all potential models —attractive, repulsive and zero-range— provide similar results. When the scattering length is large the attractive model differs qualitatively from the repulsive and zero-range models. In this regime the system with attractive potential becomes independent of the scattering length, with both the energy and the condensate fraction converging towards finite constants.
We investigate systems of identical bosons with the focus on two-body correlations and attractive finite-range potentials. We use a hyperspherical adiabatic method and apply a Faddeev type of decomposition of the wave function. We discuss the structure of a condensate as a function of particle number and scattering length. We establish universal scaling relations for the critical effective radial potentials for distances where the average distance between particle pairs is larger than the interaction range. The correlations in the wave function restore the large-distance mean-field behavior with the correct two-body interaction. We discuss various processes limiting the stability of condensates. With correlations we confirm that macroscopic tunneling dominates when the trap length is about half of the particle number times the scattering length.
We calculate the ground-state energy and the collective excitation frequency of trapped bosons at large scattering length interacting via the realistic two-body van der Waals potential. Our many-body method keeps two-body correlations produced by all interacting pairs. When the scattering length is small compared to the trap size and the number of bosons in the trap is of the order of a few thousands, the mean-field results are in good agreement with the many-body results. However for large particle numbers, even when the condensate is sufficiently dilute, the interatomic correlation comes into the picture. When the scattering length is quite large near the Feshbach resonance, the Bose gas becomes highly correlated. The many-body results are close to the Gross-Pitaevskii results for a small number of bosons, however, large deviations are noted in the large particle limit. We also calculate the lowest collective excitation and the interaction energy for large scattering lengths. The monopole excitation frequency exhibits a pronounced dependence on the scattering length. We also observe a universal behavior for the interaction energy at the limit of large scattering length.