Deconfinement and phase diagram of bosons in a linear optical lattice   with a particle reservoir
  We investigate the zero-temperature phases of bosons in a one-dimensional optical lattice with an explicit tunnel coupling to a Bose condensed particle reservoir. Renormalization group analysis of this system is shown to reveal three phases: one in which the linear system is fully phase-locked to the reservoir; one in which Josephson vortices between the one-dimensional system and the particle reservoir deconfine due to quantum fluctuations, leading to a decoupled state in which the one-dimensional system is metallic; and one in which the one-dimensional system is in a Mott insulating state. 
Kingshuk Majumdar and H. A. Fertig