Deconfinement in a 2D Optical Lattice of Coupled 1D Boson Systems

We show that a two-dimensional (2D) array of 1D interacting boson tubes has a deconfinement transition between a 1D Mott insulator and a 3D superfluid for commensurate fillings and a dimensional crossover for the incommensurate case. We determine the phase diagram and excitations of this system and discuss the consequences for Bose condensates loaded in 2D optical lattices.

Figure 1

Zero-temperature phase diagram of a 2D lattice of coupled 1D boson systems. The values on the vertical axis are defined up to a factor of order unity. $K$ is the TLL parameter. The corresponding values of $\gamma =Mg/{\hslash }^2{\rho }_0$ are also given. A periodic potential of amplitude $u_0$, commensurate with the density ${\rho }_0$, is applied longitudinally ($u_0\approx 0.03\mu$ for $K=1$ and $u_0\approx 0.02\mu$ for $K=2.5$). For infinite 1D systems only two phases exist: a 1D Mott insulator (1D MI) and a 3D (but anisotropic) superfluid (SF). For finite tubes, a 2D Mott insulator (2D MI) can exist for $J/\mu$ below the horizontal dashed curve (we have taken $N_0=100$ atoms per 1D tube). The vertical dashed line (schematic) indicates that the transition to the 1D MI should take place for $K\simeq 2$. The inset is the phase diagram of a 2D optical lattice of finite 1D systems for $u_0=0$ and $N_0=100$, as a function of chemical potential $\mu$ and the hopping $J$, and for $K=1$ (continuous curve), $K=2$ (dotted curve), $K=4$ ($\gamma =0.71$, dash-dotted curve).