  It is shown that the ground state of weakly interacting Bose particles in a
quasi one-dimensional box trap can be converted into an excited stationary
state by an adiabatic cyclic operation that involves a quench of interaction
strength: A sharp impurity potential is applied and its strength is varied
during the cycle, which induces a nonequilibrium stationary state exhibiting
the inversion of population. This process is robust in the sense that the
resultant stationary state is almost independent of the details of the cycle,
such as the position of the impurity as long as the cycle is far enough from
critical regions. The case of the failure of the population inversion due to
the strong interparticle interactions is also examined.
