Dimensionality effects on the strongly interacting Bose-Einstein condensate with three-body interactions

Abstract

Using the density-functional theory, the Ginzburg Pitaevskii Gross (GPG) equation for Bose-Einstein (BE) condensate, confined in a magnetic trap, is modified to include contribution from three-body collisions in the strongly interacting regime a>><i>l</i>, 'a' is the scattering length and '<i>l</i>' being the characteristic low energy length scale. This generalized GPG equation has been solved numerically using the analytically derived Thomas-Fermi order parameter, which also includes three-body interactions. The order parameter, chemical potential, extent of correlation and other ground state properties are computed when the aspect ratio, &#955;, is varied from1.0 to 0.05 (&#955; represents the anisotropy of the magnetic trap). As &#955; is varied from 1.0 to 0.05, the condensate shape changes from isotropic three-dimensional (3-D) to highly anisotropic quasi one-dimensional (1-D). The stability of the BE condensate increases with decrease in &#955;, which is also borne out by the behavior of chemical potential and the total energy per particle, as there is a decrease of about four times for a=5000 a₀ as well as for a=7000 a₀, 'a₀' being the Bohr radius. The extent of correlations, however, increases by more than five folds, showing that quasi 1-D BE condensate is highly correlated. Both two- and three-body interaction energies show a decrease with decrease in &#955;: three-body interaction energy staying below two-body interaction energy for a=5000 a₀ while for a=7000 a₀, a cross-over occurs between the two at &#955; ~ 0.35. As one goes from 3-D to quasi 1-D, the percentage difference for various physical quantities, computed between only two-body interactions and when both two- and three-body interactions are considered, shows a decrease, suggesting that the effect of three-body collisions become increasingly less significant in agreement with the recent study.