  We consider a two-leg boson ladder in an artificial U(1) gauge field and show
that, in the presence of interleg attractive interaction, the flux induced
Vortex state can be melted by dislocations. For increasing flux, instead of the
Meissner to Vortex transition in the commensurate-incommensurate universality
class, first an Ising transition from the Meissner state to a charge density
wave takes place, then, at higher flux, the melted Vortex phase is established
via a disorder point where incommensuration develops in the rung current
correlation function and in momentum distribution.Finally, the quasi-long range
ordered Vortex phase is recovered for sufficiently small interaction. Our
predictions for the observables, such as the spin current and the static
structure factor, could be tested in current experiments with cold atoms in
bosonic ladders.
