Wall tension of a Bose-Einstein condensate: Effects of quantum fluctuations and finite-range interactions

We investigate the effects of quantum fluctuations (QFs) and finite-range interatomic interactions on the ground state and wall tension of a Bose-Einstein condensate (BEC) at zero temperature by means of modified Gross-Pitaevskii equations. The QFs are shown to stiffen the condensate near the hard wall, narrowing the density profile and raising the wall tension above its mean-field value by an amount proportional to square-root of the gas parameter. Finite-range corrections always reduces the wall tension relative to the QFs correction value regardless of the effective range. We find the ordering $\gamma_0 < \gamma_{\rm II} < \gamma_{\rm I}$ in the dilute regime and identify a crossover condition under which the two beyond-mean-field contributions mutually cancel. These results provide an experimentally accessible way for probing beyond-LHY physics through precision measurements of the wall tension in ultracold Bose gases.