Condition for collapse as a function of the initial width <em>v</em>(0) and <em>P</em> values for <em>G</em> = 0 (the bigger strip shaded area) and <em>G</em> = −0.03 (grey shaded area)

2013-08-19T00:00:00Z (GMT) by Wei Qi Zhaoxin Liang Zhidong Zhang
<p><strong>Figure 5.</strong> Condition for collapse as a function of the initial width <em>v</em>(0) and <em>P</em> values for <em>G</em> = 0 (the bigger strip shaded area) and <em>G</em> = −0.03 (grey shaded area). The dotted and dashed lines correspond to the equilibrium point for each <em>P</em> in the cases of <em>G</em> = 0 and <em>G</em> = −0.03 respectively.</p> <p><strong>Abstract</strong></p> <p>We take into account the higher-order corrections in two-body scattering interactions within a mean-field description, and investigate the stability conditions and collective excitations of a harmonically trapped Bose–Einstein condensate (BEC). Our results show that the presence of higher-order corrections causes drastic changes to the stability condition of a BEC. In particular, we predict that with the help of the higher-order interaction, a BEC can now collapse even for positive scattering lengths; whereas, a usually unstable BEC with a negative scattering length can be stabilized by positive higher-order effects. The low-lying collective excitations are significantly modified as well, compared to those without the higher-order corrections. The conditions for a possible experimental scenario are also proposed.</p>