Dynamics of condensate shells: Collective modes and expansion

We explore the physics of three-dimensional shell-shaped condensates, relevant to cold atoms in “bubble traps.” We study the ground state of the condensate wave function, spherically symmetric collective modes, and expansion properties of such a shell using a combination of analytical and numerical techniques. We find two breathing-type modes with frequencies that are distinct from that of the filled spherical condensate. Upon trap release and subsequent expansion, we find that the system displays self-interference fringes. We estimate characteristic time scales, degree of mass accumulation, three-body loss, and kinetic energy release during expansion for a typical system of ${}^{87}\mathrm{Rb}$.

Figure 1

(Color online) Expansion of a thin spherical shell. (a) Evolution of the density as a function of radial position and time. (b) Snapshots of the density profile at times $t=0,3,6,9,12$ (from the lowest curve, subsequent curves are shifted up by 100 for clarity).