We define and study holelike excitations (the Lieb II mode) in a weakly interacting Bose liquid subject to external confinement. These excitations are obtained by semiclassical quantization of gray solitons propagating on top of a Thomas-Fermi background. Radiation of phonons by an accelerated gray soliton leads to a finite lifetime of these excitations. It is shown that, for a large number of trapped atoms, most of the Lieb II levels can be experimentally resolved.

• Received 28 September 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.085301