Stability of Superfluid and Supersolid Phases of Dipolar Bosons in Optical Lattices

We perform a stability analysis of superfluid (SF) and supersolid (SS) phases of polarized dipolar bosons in two-dimensional optical lattices at high filling factors and zero temperature, and obtain the phase boundaries between SF, checkerboard SS (CSS), striped SS (SSS), and collapse. We show that the phase diagram can be explored through the application of an external field and the tuning of its direction with respect to the optical lattice plane. In particular, we find a transition between the CSS and SSS phases.

Figure 1

(a) Schematic picture of a 2D lattice system, where a square represents a site. (b) The dipole vector is shown in the spherical polar coordinates.

Figure 2

Left: Phase diagrams in the ($V_x/U$, $V_y/U$) plane for $J/(\nu U)=0.1$. While only the NN interactions are considered in (a), the full dipolar interactions are included in (b). The solid (dotted) lines represent phase boundaries for continuous (discontinuous) transitions. The dashed-dotted green lines and the dashed red lines separate the stable and unstable regions of the CSS state and those of the SSS. Right: Schematic pictures of SF (I), CSS (II), SSS1 (III), SSS2 (IV), SSa1 (V), SSb1 (VI), and SSc1 (VII).

Figure 3

Excitation spectra ${\epsilon }_{\mathrm{CSS}}^{-}(q_x,q_y=0)$ and ${\epsilon }_{\mathrm{SSS}1}^{-}(q_x=0,q_y)$ for $J/(\nu U)=0.1$, and $V_x=U$. (a) The real part and (b) the imaginary parts of ${\epsilon }_{\mathrm{CSS}}^{-}(q_x,q_y=0)$. (c) The real part and (d) the imaginary parts of ${\epsilon }_{\mathrm{SSS}1}^{-}(q_x=0,q_y)$.