Comment on “Ground-state fragmentation phase transition for attractive bosons in anisotropic traps”

In a recent article [Phys. Rev. A 88, 063641 (2013)], Cizek and Kasevich claimed that quantum fragmentation occurs in the metastable state of a Bose-Einstein condensate with an attractive interaction confined in an elongated harmonic potential. This result was obtained using the two-state Gaussian variational method. However, modified methods show that no fragmentation occurs for the parameters used by Cizek and Kasevich.

Figure 1

Eigenvalues ${\varepsilon }_0$ and ${\varepsilon }_1$ of the single-particle density matrix (circles) and the energy per particle ${\mu }_{t,0}=E_0/N$ (squares) as a function of ${\omega }_r/{\omega }_z$ with ${\omega }_r=2\pi \times 3.5\mathrm{kHz}$. The open and filled data are obtained using the method in Ref. [1] and by the present method, respectively.

Figure 2

Profiles of the functions ${\psi }_0(r=0,z),{\varphi }_2(r=0,z)$, and ${\psi }_2(r=0,z)$ along the $z$ axis. The values of the variational parameters are taken to minimize $E_0$ for ${\omega }_r/{\omega }_z=8$.