  We theoretically analyze the ground state of weakly interacting bosons in the
flux ladder -- the system that has been recently realized by means of ultacold
atoms in the specially designed optical lattice [M. Atala, et al., Nat. Phys.
10, 588 (2014)]. It is argued that, for the system parameters corresponding to
the so-called `vortex phase', the ground state is a fragmented condensate. We
study the Bogoliubov depletion of this condensate and discuss the role of
boundary conditions.
