Metastability of Repulsive Bose–Einstein Condensate in a Finite Trap and Instability of Ground State Energies

The stability of trapped bosons with repulsive interaction is studied using an approximate many-body calculation. Instead of using the traditional harmonic trapping potential we consider an anharmonic potential of the form \(V_{anhar}(r)=\frac{1}{2}m\omega ^{2}r^{2}+\lambda r^{4}\) $V_{\mathit{anhar}}(r)=\frac{1}{2}m{\omega }^2{r}^2+\lambda r^4$ . In our method, a correlated two-body basis function is used which considers all two-body correlations. It is explained that negative value of anharmonic parameter ( \(\lambda \) $\lambda$ ) are capable to change a stable condensate into a metastable one. Within this metastable condensate, we slowly increase the number of atom (A) and find a collapsing nature of repulsive condensate. The process of collapse of repulsive Bose–Einstein condensation (BEC) is completely different from the collapsing process of attractive BEC and it is explained in details. A dramatic behaviour of interaction energy, kinetic energy, trapping potential energy along with the total ground state energy of this metastable repulsive BEC is observed. We also study the instability of these zero point energies by varying \(\lambda \) $\lambda$ when fixed number of bosons are trapped by the anharmonic well and find critical values of \(\lambda \) $\lambda$ at which the system collapses. When the number of trapped particle is sufficiently high, a close interplay between number of particle and anharmonic strength is observed to remodel the shape of the effective metastable region.