The stability of Bose--Einstein condensates in a two-dimensional shallow trap

The stability of Bose--Einstein condensates (BECs) loaded into atwo-dimensional shallow harmonic potential well is studied. By usingthe variational method, the ground state properties for interactingBECs in the shallow trap are discussed. It is shown that the possiblestable bound state can exist. The depth of the shallow well plays animportant role in stabilizing the BECs. The stability of BECs in theshallow trap with the periodic modulating of atom interaction byusing the Feshbach resonance is also discussed. The results show thatthe collapse and diffusion of BECs in a shallow trap can becontrolled by the temporal modulation of the scattering length.