CorrelatedN-boson systems for arbitrary scattering length

Abstract

We investigate systems of identical bosons with the focus on two-body correlations and attractive finiterange 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.

Hyperspherical lowest-order constrained-variational approximation to resonant Bose-Einstein condensates

“…The solid line represents the results from the H-LOCV approximation. Also shown are the results from the mean-field Gross-Pitaevskii (GP, dashed line) [44] and hyperspherical-Faddeev (Faddeev, dotted line) models [19][20][21][22]. If we zoom in to the a/a ho ≪ 1 domain (inset), we find that all models agree well in the weakly interacting regime.…”

“…Roughly, these methods employ a single macroscopic coordinate -the hyperradius -to denote the collective motion of the condensate as a whole. When suitably complemented by two-body interparticle coordinates, the method has been extended to include realistic two-body potentials between the atoms [15][16][17][18], or else boundary conditions employing realistic (i.e., not renormalized) scattering lengths [19][20][21][22].…”

Hyperspherical approach to dipolar Bose-Einstein condensates beyond the mean-field limit

“…the first line rephrases the angles in terms of interparticle coordinates according to eqs. (16,17). In the last line we went to the large N limit, using that…”

“…Hyperspherical approaches to BEC have proven fruitful in the past, describing, for example, the stability of BECs with attractive contact potentials [10][11][12]; condensate fraction [13]; multicomponent BECs [14]; the influence of realistic two body contact interactions, including effective range corrections [15][16][17] and even formally infinite scattering lengths [18][19][20][21]; realistic two-body interactions [22][23][24]; and condensate dynamics [25][26][27]. These treatments are all necessarily approximate, yet an exciting recent development shows that their accuracy can be enhanced by combining hyperspherical coordinates with solutions to the Gross-Pitaevskii equation (GPE) [28].…”

Stability and correlations in dilute two-dimensional boson systems

“…Instead a finite short-range potential with the correct scattering length should be used. If the correlations are appropriately accounted for, the large-distance behavior must come out correctly with the realistic interaction [12,13]. The consequences for lower dimensions are not yet investigated.…”